Image Processing Toolbox™ User’s Guide R2013b How to Contact MathWorks Web Newsgroup www.mathworks.com/contact_TS.html Technical Support www.mathworks.com comp.soft-sys.matlab [email protected] [email protected] [email protected] [email protected] [email protected] Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 (Phone) 508-647-7001 (Fax) The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. Image Processing Toolbox™ User’s Guide © COPYRIGHT 1993–2013 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from The MathWorks, Inc. FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by, for, or through the federal government of the United States. By accepting delivery of the Program or Documentation, the government hereby agrees that this software or documentation qualifies as commercial computer software or commercial computer software documentation as such terms are used or defined in FAR 12.212, DFARS Part 227.72, and DFARS 252.227-7014. Accordingly, the terms and conditions of this Agreement and only those rights specified in this Agreement, shall pertain to and govern the use, modification, reproduction, release, performance, display, and disclosure of the Program and Documentation by the federal government (or other entity acquiring for or through the federal government) and shall supersede any conflicting contractual terms or conditions. If this License fails to meet the government’s needs or is inconsistent in any respect with federal procurement law, the government agrees to return the Program and Documentation, unused, to The MathWorks, Inc. Trademarks MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See www.mathworks.com/trademarks for a list of additional trademarks. Other product or brand names may be trademarks or registered trademarks of their respective holders. Patents MathWorks products are protected by one or more U.S. patents. Please see www.mathworks.com/patents for more information. Revision History August 1993 May 1997 April 2001 June 2001 July 2002 May 2003 September 2003 June 2004 August 2004 October 2004 March 2005 September 2005 March 2006 September 2006 March 2007 September 2007 March 2008 October 2008 March 2009 September 2009 March 2010 September 2010 April 2011 September 2011 March 2012 September 2012 March 2013 September 2013 First printing Second printing Third printing Online only Online only Fourth printing Online only Online only Online only Fifth printing Online only Online only Online only Online only Online only Online only Online only Online only Online only Online only Online only Online only Online only Online only Online only Online only Online only Online only Version 1 Version 2 Revised for Version 3.0 Revised for Version 3.1 (Release 12.1) Revised for Version 3.2 (Release 13) Revised for Version 4.0 (Release 13.0.1) Revised for Version 4.1 (Release 13.SP1) Revised for Version 4.2 (Release 14) Revised for Version 5.0 (Release 14+) Revised for Version 5.0.1 (Release 14SP1) Revised for Version 5.0.2 (Release 14SP2) Revised for Version 5.1 (Release 14SP3) Revised for Version 5.2 (Release 2006a) Revised for Version 5.3 (Release 2006b) Revised for Version 5.4 (Release 2007a) Revised for Version 6.0 (Release 2007b) Revised for Version 6.1 (Release 2008a) Revised for Version 6.2 (Release 2008b) Revised for Version 6.3 (Release 2009a) Revised for Version 6.4 (Release 2009b) Revised for Version 7.0 (Release 2010a) Revised for Version 7.1 (Release 2010b) Revised for Version 7.2 (Release 2011a) Revised for Version 7.3 (Release 2011b) Revised for Version 8.0 (Release 2012a) Revised for Version 8.1 (Release 2012b) Revised for Version 8.2 (Release 2013a) Revised for Version 8.3 (Release 2013b) Contents Getting Started 1 Image Processing Toolbox Product Description . . . . . . Key Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 1-2 Configuration Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3 Related Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4 ..................................... 1-5 Image Import and Export . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Step 1: Read and Display an Image . . . . . . . . . . . . . . . . . . . Step 2: Check How the Image Appears in the Workspace . . Step 3: Improve Image Contrast . . . . . . . . . . . . . . . . . . . . . Step 4: Write the Image to a Disk File . . . . . . . . . . . . . . . . Step 5: Check the Contents of the Newly Written File . . . . 1-6 1-6 1-6 1-7 1-8 1-10 1-10 Image Enhancement and Analysis . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Step 1: Read Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Step 2: Use Morphological Opening to Estimate the Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Step 3: View the Background Approximation as a Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Step 4: Subtract the Background Image from the Original Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Step 5: Increase the Image Contrast . . . . . . . . . . . . . . . . . . Step 6: Threshold the Image . . . . . . . . . . . . . . . . . . . . . . . . Step 7: Identify Objects in the Image . . . . . . . . . . . . . . . . . Step 8: Examine One Object . . . . . . . . . . . . . . . . . . . . . . . . . Step 9: View All Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . Step 10: Compute Area of Each Object . . . . . . . . . . . . . . . . Step 11: Compute Area-based Statistics . . . . . . . . . . . . . . . 1-12 1-13 1-13 Compilability 1-13 1-14 1-15 1-16 1-17 1-17 1-18 1-19 1-20 1-21 v Step 12: Create Histogram of the Area . . . . . . . . . . . . . . . . 1-22 Getting Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Product Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . Image Processing Examples . . . . . . . . . . . . . . . . . . . . . . . . . MATLAB Newsgroup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-23 1-23 1-23 1-24 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-25 Introduction 2 vi Contents Images in MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 Expressing Image Locations . . . . . . . . . . . . . . . . . . . . . . . . Pixel Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spatial Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 2-3 2-4 Image Types in the Toolbox . . . . . . . . . . . . . . . . . . . . . . . . Overview of Image Types . . . . . . . . . . . . . . . . . . . . . . . . . . . Binary Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indexed Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grayscale Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Truecolor Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10 2-10 2-11 2-12 2-14 2-15 Converting Between Image Types . . . . . . . . . . . . . . . . . . . 2-19 Converting Between Image Classes . . . . . . . . . . . . . . . . . Overview of Image Class Conversions . . . . . . . . . . . . . . . . . Losing Information in Conversions . . . . . . . . . . . . . . . . . . . Converting Indexed Images . . . . . . . . . . . . . . . . . . . . . . . . . 2-21 2-21 2-21 2-21 Working with Image Sequences . . . . . . . . . . . . . . . . . . . . . Overview of Toolbox Functions That Work with Image Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Image Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Multi-Frame Image Arrays . . . . . . . . . . . . . . . . . . . 2-23 2-23 2-26 2-27 Image Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview of Image Arithmetic Functions . . . . . . . . . . . . . . Image Arithmetic Saturation Rules . . . . . . . . . . . . . . . . . . . Nesting Calls to Image Arithmetic Functions . . . . . . . . . . . 2-29 2-29 2-30 2-30 Reading and Writing Image Data 3 .......... 3-2 Reading Image Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3 Writing Image Data to a File . . . . . . . . . . . . . . . . . . . . . . . . Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specifying Format-Specific Parameters . . . . . . . . . . . . . . . . Reading and Writing Binary Images in 1-Bit Format . . . . Determining the Storage Class of the Output File . . . . . . . 3-5 3-5 3-6 3-6 3-7 Converting Between Graphics File Formats . . . . . . . . . . 3-8 Working with DICOM Files . . . . . . . . . . . . . . . . . . . . . . . . . Overview of DICOM Support . . . . . . . . . . . . . . . . . . . . . . . . Reading Metadata from a DICOM File . . . . . . . . . . . . . . . . Reading Image Data from a DICOM File . . . . . . . . . . . . . . Writing Image Data or Metadata to a DICOM File . . . . . . 3-9 3-9 3-10 3-12 3-13 Working with Mayo Analyze 7.5 Files . . . . . . . . . . . . . . . . 3-19 Working with Interfile Files . . . . . . . . . . . . . . . . . . . . . . . . 3-20 Working with High Dynamic Range Images . . . . . . . . . . Understanding Dynamic Range . . . . . . . . . . . . . . . . . . . . . . Reading a High Dynamic Range Image . . . . . . . . . . . . . . . . Creating a High Dynamic Range Image . . . . . . . . . . . . . . . Viewing a High Dynamic Range Image . . . . . . . . . . . . . . . . Writing a High Dynamic Range Image to a File . . . . . . . . . 3-21 3-21 3-21 3-22 3-22 3-23 Getting Information About a Graphics File vii Displaying and Exploring Images 4 viii Contents Image Display and Exploration Overview . . . . . . . . . . . . 4-2 Displaying Images Using the imshow Function . . . . . . . Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specifying the Initial Image Magnification . . . . . . . . . . . . . Controlling the Appearance of the Figure . . . . . . . . . . . . . . Displaying Each Image in a Separate Figure . . . . . . . . . . . Displaying Multiple Images in the Same Figure . . . . . . . . 4-4 4-4 4-6 4-6 4-7 4-8 Using the Image Viewer App to Explore Images . . . . . . Image Viewer App Overview . . . . . . . . . . . . . . . . . . . . . . . . Opening the Image Viewer . . . . . . . . . . . . . . . . . . . . . . . . . . Specifying the Initial Image Magnification . . . . . . . . . . . . . Specifying the Colormap . . . . . . . . . . . . . . . . . . . . . . . . . . . . Importing Image Data from the Workspace . . . . . . . . . . . . Exporting Image Data to the Workspace . . . . . . . . . . . . . . . Saving the Image Data Displayed in the Image Viewer . . . Closing the Image Viewer . . . . . . . . . . . . . . . . . . . . . . . . . . . Printing the Image in the Image Viewer . . . . . . . . . . . . . . . 4-11 4-11 4-13 4-14 4-15 4-17 4-18 4-18 4-20 4-20 Exploring Very Large Images . . . . . . . . . . . . . . . . . . . . . . . Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Creating an R-Set File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Opening an R-Set File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21 4-21 4-21 4-22 Using Image Viewer App Navigation Aids . . . . . . . . . . . . Navigating an Image Using the Overview Tool . . . . . . . . . Panning the Image Displayed in the Image Viewer . . . . . . Zooming In and Out on an Image in the Image Viewer App . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specifying the Magnification of the Image . . . . . . . . . . . . . 4-23 4-23 4-26 Getting Information about the Pixels in an Image . . . . Determining the Value of Individual Pixels . . . . . . . . . . . . Determining the Values of a Group of Pixels . . . . . . . . . . . Determining the Display Range of an Image . . . . . . . . . . . 4-30 4-30 4-32 4-35 4-27 4-27 Measuring the Distance Between Two Pixels . . . . . . . . . Using the Distance Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exporting Endpoint and Distance Data . . . . . . . . . . . . . . . . Customizing the Appearance of the Distance Tool . . . . . . . 4-37 4-37 4-38 4-39 Getting Information About an Image Using the Image Information Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-40 Adjusting Image Contrast Using the Adjust Contrast Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Understanding Contrast Adjustment . . . . . . . . . . . . . . . . . Starting the Adjust Contrast Tool . . . . . . . . . . . . . . . . . . . . Using the Histogram Window to Adjust Image Contrast . . Using the Window/Level Tool to Adjust Image Contrast . . Modifying Image Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-42 4-42 4-43 4-46 4-47 4-50 Crop an Image Using the Image Viewer App . . . . . . . . . 4-52 Viewing Image Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . Image Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . View Image Sequences in the Video Viewer App . . . . . . . . Viewing Image Sequences as a Montage . . . . . . . . . . . . . . . Converting a Multiframe Image to a Movie . . . . . . . . . . . . 4-55 4-55 4-55 4-64 4-66 Displaying Different Image Types . . . . . . . . . . . . . . . . . . . Displaying Indexed Images . . . . . . . . . . . . . . . . . . . . . . . . . Displaying Grayscale Images . . . . . . . . . . . . . . . . . . . . . . . . Displaying Binary Images . . . . . . . . . . . . . . . . . . . . . . . . . . Displaying Truecolor Images . . . . . . . . . . . . . . . . . . . . . . . . 4-67 4-67 4-68 4-69 4-71 Adding a Colorbar to a Displayed Image . . . . . . . . . . . . . 4-73 Printing Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Printing and Handle Graphics Object Properties . . . . . . . . 4-75 4-75 Setting Toolbox Preferences . . . . . . . . . . . . . . . . . . . . . . . . Viewing and Changing Preferences Using the Preferences Dialog Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Retrieving the Values of Toolbox Preferences Programmatically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-77 4-77 4-77 ix Setting the Values of Toolbox Preferences Programmatically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-78 Building GUIs with Modular Tools 5 Modular Interactive Tools . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2 Displaying the Target Image . . . . . . . . . . . . . . . . . . . . . . . . 5-10 Creating the Modular Tools . . . . . . . . . . . . . . . . . . . . . . . . Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Associating Modular Tools with a Particular Image . . . . . . Getting the Handle of the Target Image . . . . . . . . . . . . . . . Specifying the Parent of a Modular Tool . . . . . . . . . . . . . . . Positioning the Modular Tools in a GUI . . . . . . . . . . . . . . . Build a Pixel Information GUI . . . . . . . . . . . . . . . . . . . . . . . Adding Navigation Aids to a GUI . . . . . . . . . . . . . . . . . . . . 5-11 5-11 5-12 5-14 5-15 5-18 5-19 5-22 Customizing Modular Tool Interactivity . . . . . . . . . . . . . Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Build Image Comparison Tool . . . . . . . . . . . . . . . . . . . . . . . 5-28 5-28 5-29 Creating Your Own Modular Tools . . . . . . . . . . . . . . . . . . Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Create Angle Measurement Tool . . . . . . . . . . . . . . . . . . . . . 5-33 5-33 5-35 Geometric Transformations 6 Resize an Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specifying the Interpolation Method . . . . . . . . . . . . . . . . . . Preventing Aliasing by Using Filters . . . . . . . . . . . . . . . . . . x Contents 6-2 6-2 6-3 6-4 Rotate an Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5 Crop an Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-6 2-D Geometric Transformations . . . . . . . . . . . . . . . . . . . . . Defining the Geometric Transformation . . . . . . . . . . . . . . . Performing the Geometric Transformation . . . . . . . . . . . . . Understanding Geometric Transformation . . . . . . . . . . . . . Specifying Fill Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-8 6-9 6-11 6-12 6-13 Perform a 2-D Translation . . . . . . . . . . . . . . . . . . . . . . . . . . 6-15 N-Dimensional Spatial Transformations . . . . . . . . . . . . . 6-20 Register an Image Using Spatial Referencing Objects to Enhance the Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-22 Image Registration 7 Image Registration Techniques . . . . . . . . . . . . . . . . . . . . . 7-2 Control Point Registration . . . . . . . . . . . . . . . . . . . . . . . . . 7-4 Using cpselect in a Script . . . . . . . . . . . . . . . . . . . . . . . . . . 7-5 Register an Aerial Photograph to a Digital Orthophoto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-6 Geometric Transformation Types . . . . . . . . . . . . . . . . . . . 7-12 Control Point Selection Procedure . . . . . . . . . . . . . . . . . . 7-13 Start the Control Point Selection Tool . . . . . . . . . . . . . . . 7-15 xi Find Visual Elements Common to Both Images . . . . . . . Using Scroll Bars to View Other Parts of an Image . . . . . . Using the Detail Rectangle to Change the View . . . . . . . . . Panning the Image Displayed in the Detail Window . . . . . Zooming In and Out on an Image . . . . . . . . . . . . . . . . . . . . . Specifying the Magnification of the Images . . . . . . . . . . . . . Locking the Relative Magnification of the Moving and Fixed Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-18 7-18 7-18 7-20 7-20 7-21 Select Matching Control Point Pairs . . . . . . . . . . . . . . . . Picking Control Point Pairs Manually . . . . . . . . . . . . . . . . . Using Control Point Prediction . . . . . . . . . . . . . . . . . . . . . . Moving Control Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deleting Control Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-24 7-24 7-26 7-29 7-29 Export Control Points to the Workspace . . . . . . . . . . . . . Saving Your Control Point Selection Session . . . . . . . . . . . 7-30 7-30 Use Cross-Correlation to Improve Control Point Placement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-32 Intensity-Based Automatic Image Registration . . . . . . . 7-33 Registering Multimodal MRI Images . . . . . . . . . . . . . . . . 7-35 7-22 Designing and Implementing 2-D Linear Filters for Image Data 8 Designing and Implementing Linear Filters in the Spatial Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performing Linear Filtering of Images Using imfilter . . . . Filtering an Image with Predefined Filter Types . . . . . . . . xii Contents 8-2 8-2 8-2 8-4 8-5 8-13 Designing Linear Filters in the Frequency Domain . . . FIR Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Frequency Transformation Method . . . . . . . . . . . . . . . . . . . Frequency Sampling Method . . . . . . . . . . . . . . . . . . . . . . . . Windowing Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Creating the Desired Frequency Response Matrix . . . . . . . Computing the Frequency Response of a Filter . . . . . . . . . 8-15 8-16 8-16 8-18 8-19 8-21 8-22 Transforms 9 Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition of Fourier Transform . . . . . . . . . . . . . . . . . . . . . . Discrete Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . Applications of the Fourier Transform . . . . . . . . . . . . . . . . 9-2 9-2 9-7 9-10 Discrete Cosine Transform . . . . . . . . . . . . . . . . . . . . . . . . . DCT Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The DCT Transform Matrix . . . . . . . . . . . . . . . . . . . . . . . . . DCT and Image Compression . . . . . . . . . . . . . . . . . . . . . . . . 9-15 9-15 9-17 9-17 Radon Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radon Transformation Definition . . . . . . . . . . . . . . . . . . . . Plotting the Radon Transform . . . . . . . . . . . . . . . . . . . . . . . Viewing the Radon Transform as an Image . . . . . . . . . . . . Detecting Lines Using the Radon Transform . . . . . . . . . . . 9-19 9-19 9-22 9-24 9-25 The Inverse Radon Transformation . . . . . . . . . . . . . . . . . Inverse Radon Transform Definition . . . . . . . . . . . . . . . . . . Reconstructing an Image from Parallel Projection Data . . 9-29 9-29 9-32 Fan-Beam Projection Data . . . . . . . . . . . . . . . . . . . . . . . . . Fan-Beam Projection Data Definition . . . . . . . . . . . . . . . . . Computing Fan-Beam Projection Data . . . . . . . . . . . . . . . . Reconstructing an Image from Fan-Beam Projection Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reconstructing a Head Phantom Image . . . . . . . . . . . . . . . 9-36 9-36 9-37 9-39 9-40 xiii Morphological Operations 10 Morphology Fundamentals: Dilation and Erosion . . . . 10-2 Understanding Dilation and Erosion . . . . . . . . . . . . . . . . . . 10-2 Understanding Structuring Elements . . . . . . . . . . . . . . . . . 10-5 Dilating an Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-9 Eroding an Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-10 Combining Dilation and Erosion . . . . . . . . . . . . . . . . . . . . . 10-12 Dilation- and Erosion-Based Functions . . . . . . . . . . . . . . . . 10-14 Morphological Reconstruction . . . . . . . . . . . . . . . . . . . . . . Understanding Morphological Reconstruction . . . . . . . . . . Understanding the Marker and Mask . . . . . . . . . . . . . . . . . Pixel Connectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flood-Fill Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finding Peaks and Valleys . . . . . . . . . . . . . . . . . . . . . . . . . . 10-17 10-17 10-19 10-20 10-23 10-26 Distance Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-36 Labeling and Measuring Objects in a Binary Image . . . Understanding Connected-Component Labeling . . . . . . . . Selecting Objects in a Binary Image . . . . . . . . . . . . . . . . . . Finding the Area of the Foreground of a Binary Image . . . Finding the Euler Number of a Binary Image . . . . . . . . . . 10-39 10-39 10-41 10-42 10-43 Lookup Table Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 10-44 Creating a Lookup Table . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-44 Using a Lookup Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-44 Analyzing and Enhancing Images 11 Getting Information about Image Pixel Values and Image Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Getting Image Pixel Values Using impixel . . . . . . . . . . . . Creating an Intensity Profile of an Image Using improfile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv Contents 11-2 11-2 11-3 Displaying a Contour Plot of Image Data . . . . . . . . . . . . . . 11-7 Creating an Image Histogram Using imhist . . . . . . . . . . . . 11-9 Getting Summary Statistics About an Image . . . . . . . . . . . 11-10 Computing Properties for Image Regions . . . . . . . . . . . . . . 11-10 Analyzing Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detecting Edges Using the edge Function . . . . . . . . . . . . . . Detecting Corners Using the corner Function . . . . . . . . . . . Tracing Object Boundaries in an Image . . . . . . . . . . . . . . . Detecting Lines Using the Hough Transform . . . . . . . . . . . Analyzing Image Homogeneity Using Quadtree Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-11 11-11 11-13 11-15 11-20 Analyzing the Texture of an Image . . . . . . . . . . . . . . . . . . Understanding Texture Analysis . . . . . . . . . . . . . . . . . . . . . Using Texture Filter Functions . . . . . . . . . . . . . . . . . . . . . . Gray-Level Co-Occurrence Matrix (GLCM) . . . . . . . . . . . . . 11-27 11-27 11-27 11-31 Adjusting Pixel Intensity Values . . . . . . . . . . . . . . . . . . . . Understanding Intensity Adjustment . . . . . . . . . . . . . . . . . Adjusting Intensity Values to a Specified Range . . . . . . . . Adjusting Intensity Values Using Histogram Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adjusting Intensity Values Using Contrast-Limited Adaptive Histogram Equalization . . . . . . . . . . . . . . . . . . Enhancing Color Separation Using Decorrelation Stretching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-37 11-37 11-38 Removing Noise from Images . . . . . . . . . . . . . . . . . . . . . . . Understanding Sources of Noise in Digital Images . . . . . . Removing Noise By Linear Filtering . . . . . . . . . . . . . . . . . . Removing Noise By Median Filtering . . . . . . . . . . . . . . . . . Removing Noise By Adaptive Filtering . . . . . . . . . . . . . . . . 11-50 11-50 11-50 11-51 11-54 11-24 11-42 11-44 11-45 ROI-Based Processing 12 Specifying a Region of Interest (ROI) . . . . . . . . . . . . . . . . Overview of ROI Processing . . . . . . . . . . . . . . . . . . . . . . . . . 12-2 12-2 xv Creating a Binary Mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . Creating an ROI Without an Associated Image . . . . . . . . . Creating an ROI Based on Color Values . . . . . . . . . . . . . . . 12-2 12-3 12-4 Filtering an ROI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview of ROI Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . Filtering a Region in an Image . . . . . . . . . . . . . . . . . . . . . . . Specifying the Filtering Operation . . . . . . . . . . . . . . . . . . . . 12-5 12-5 12-5 12-6 Filling an ROI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-8 Image Deblurring 13 Understanding Deblurring . . . . . . . . . . . . . . . . . . . . . . . . . Causes of Blurring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deblurring Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deblurring Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-2 13-2 13-2 13-4 Deblurring with the Wiener Filter . . . . . . . . . . . . . . . . . . Refining the Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-6 13-6 Deblurring with a Regularized Filter . . . . . . . . . . . . . . . . Refining the Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-7 13-8 Deblurring with the Lucy-Richardson Algorithm . . . . . Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reducing the Effect of Noise Amplification . . . . . . . . . . . . . Accounting for Nonuniform Image Quality . . . . . . . . . . . . . Handling Camera Read-Out Noise . . . . . . . . . . . . . . . . . . . Handling Undersampled Images . . . . . . . . . . . . . . . . . . . . . Example: Using the deconvlucy Function to Deblur an Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Refining the Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-10 13-10 13-10 13-11 13-11 13-12 13-12 13-15 Deblurring with the Blind Deconvolution Algorithm . . 13-16 Example: Using the deconvblind Function to Deblur an Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-16 xvi Contents Refining the Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-21 Creating Your Own Deblurring Functions . . . . . . . . . . . 13-23 Avoiding Ringing in Deblurred Images . . . . . . . . . . . . . . 13-24 Color 14 Displaying Colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-2 Reducing the Number of Colors in an Image . . . . . . . . . 14-4 Reducing Colors Using Color Approximation . . . . . . . . . . . 14-4 Reducing Colors Using imapprox . . . . . . . . . . . . . . . . . . . . . 14-10 Dithering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-11 Converting Color Data Between Color Spaces . . . . . . . . Understanding Color Spaces and Color Space Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Converting Between Device-Independent Color Spaces . . . Performing Profile-Based Color Space Conversions . . . . . . Converting Between Device-Dependent Color Spaces . . . . 14-13 14-13 14-13 14-17 14-21 Neighborhood and Block Operations 15 Neighborhood or Block Processing: An Overview . . . . . 15-2 Performing Sliding Neighborhood Operations . . . . . . . Understanding Sliding Neighborhood Processing . . . . . . . . Implementing Linear and Nonlinear Filtering as Sliding Neighborhood Operations . . . . . . . . . . . . . . . . . . . . . . . . . 15-3 15-3 Performing Distinct Block Operations . . . . . . . . . . . . . . . 15-8 15-5 xvii Understanding Distinct Block Processing . . . . . . . . . . . . . . Implementing Block Processing Using the blockproc Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applying Padding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Block Size and Performance . . . . . . . . . . . . . . . . . . . . . . . . . Using Parallel Block Processing on large Image Files . . . . Working with Data in Unsupported Formats . . . . . . . . . . . Using Columnwise Processing to Speed Up Sliding Neighborhood or Distinct Block Operations . . . . . . . Understanding Columnwise Processing . . . . . . . . . . . . . . . Using Column Processing with Sliding Neighborhood Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using Column Processing with Distinct Block Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-8 15-9 15-11 15-13 15-15 15-17 15-26 15-26 15-26 15-28 Code Generation for Image Processing Toolbox Functions 16 Supported Functions .............................. 16-2 GPU Computing with Image Processing Toolbox Functions 17 ........................ 17-2 List of Supported Functions with Limitations and Other Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-3 Perform Thresholding and Morphological Operations on a GPU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-5 Image Processing on a GPU xviii Contents Index xix xx Contents 1 Getting Started This chapter contains two examples to get you started doing image processing using MATLAB® and the Image Processing Toolbox™ software. The examples contain cross-references to other sections in the documentation manual that have in-depth discussions on the concepts presented in the examples. • “Image Processing Toolbox Product Description” on page 1-2 • “Configuration Notes” on page 1-3 • “Related Products” on page 1-4 • “Compilability” on page 1-5 • “Image Import and Export” on page 1-6 • “Image Enhancement and Analysis” on page 1-12 • “Getting Help” on page 1-23 • “Acknowledgments” on page 1-25 1 Getting Started Image Processing Toolbox Product Description Perform image processing, analysis, and algorithm development Image Processing Toolbox provides a comprehensive set of reference-standard algorithms, functions, and apps for image processing, analysis, visualization, and algorithm development. You can perform image enhancement, image deblurring, feature detection, noise reduction, image segmentation, geometric transformations, and image registration. Many toolbox functions are multithreaded to take advantage of multicore and multiprocessor computers. Image Processing Toolbox supports a diverse set of image types, including high dynamic range, gigapixel resolution, embedded ICC profile, and tomographic. Visualization functions let you explore an image, examine a region of pixels, adjust the contrast, create contours or histograms, and manipulate regions of interest (ROIs). With toolbox algorithms you can restore degraded images, detect and measure features, analyze shapes and textures, and adjust color balance. Key Features • Image enhancement, filtering, and deblurring • Image analysis, including segmentation, morphology, feature extraction, and measurement • Geometric transformations and intensity-based image registration methods • Image transforms, including FFT, DCT, Radon, and fan-beam projection • Workflows for processing, displaying, and navigating arbitrarily large images • Image Viewer and Video Viewer apps • DICOM file import and export 1-2 Configuration Notes Configuration Notes To determine if the Image Processing Toolbox software is installed on your system, type this command at the MATLAB prompt. ver When you enter this command, MATLAB displays information about the version of MATLAB you are running, including a list of all toolboxes installed on your system and their version numbers. For a list of the new features in this version of the toolbox, see the Release Notes documentation. Many of the toolbox functions are MATLAB files with a series of MATLAB statements that implement specialized image processing algorithms. You can view the MATLAB code for these functions using the statement type function_name You can extend the capabilities of the toolbox by writing your own files, or by using the toolbox in combination with other toolboxes, such as the Signal Processing Toolbox™ software and the Wavelet Toolbox™ software. For information about installing the toolbox, see the installation guide. For the most up-to-date information about system requirements, see the system requirements page, available in the products area at the MathWorks Web site (www.mathworks.com). 1-3 1 Getting Started Related Products MathWorks provides several products that are relevant to the kinds of tasks you can perform with the Image Processing Toolbox software and that extend the capabilities of MATLAB. For information about these related products, see www.mathworks.com/products/image/related.html. 1-4 Compilability Compilability The Image Processing Toolbox software is compilable with the MATLAB Compiler™ except for the following functions that launch GUIs: • cpselect • implay • imtool 1-5 1 Getting Started Image Import and Export In this section... “Introduction” on page 1-6 “Step 1: Read and Display an Image” on page 1-6 “Step 2: Check How the Image Appears in the Workspace” on page 1-7 “Step 3: Improve Image Contrast” on page 1-8 “Step 4: Write the Image to a Disk File” on page 1-10 “Step 5: Check the Contents of the Newly Written File” on page 1-10 Introduction This example shows how to read an image into the MATLAB workspace, adjust the contrast in the image, and then write the adjusted image to a file. Step 1: Read and Display an Image First, clear the MATLAB workspace of any variables and close open figure windows. clear, close all To read an image, use the imread command. The example reads one of the sample images included with the toolbox, pout.tif, and stores it in an array named I. I = imread('pout.tif'); imread infers from the file that the graphics file format is Tagged Image File Format (TIFF). For the list of supported graphics file formats, see the imread function reference documentation. Now display the image. The toolbox includes two image display functions: imshow and imtool. imshow is the toolbox’s fundamental image display function. imtool starts the Image Tool which presents an integrated environment for displaying images and performing some common image processing tasks. The Image Tool provides all the image display capabilities 1-6 Image Import and Export of imshow but also provides access to several other tools for navigating and exploring images, such as scroll bars, the Pixel Region tool, Image Information tool, and the Contrast Adjustment tool. For more information, see“Image Display and Exploration Overview” on page 4-2. You can use either function to display an image. This example uses imshow. imshow(I) Grayscale Image pout.tif Step 2: Check How the Image Appears in the Workspace To see how the imread function stores the image data in the workspace, check the Workspace browser in the MATLAB desktop. The Workspace browser displays information about all the variables you create during a MATLAB session. The imread function returned the image data in the variable I, which is a 291-by-240 element array of uint8 data. MATLAB can store images as uint8, uint16, or double arrays. You can also get information about variables in the workspace by calling the whos command. whos MATLAB responds with Name Size Bytes Class Attributes 1-7 1 Getting Started I 291x240 69840 uint8 For more information about image storage classes, see “Converting Between Image Classes” on page 2-21. Step 3: Improve Image Contrast pout.tif is a somewhat low contrast image. To see the distribution of intensities in pout.tif, you can create a histogram by calling the imhist function. (Precede the call to imhist with the figure command so that the histogram does not overwrite the display of the image I in the current figure window.) figure, imhist(I) Notice how the intensity range is rather narrow. It does not cover the potential range of [0, 255], and is missing the high and low values that would result in good contrast. The toolbox provides several ways to improve the contrast in an image. One way is to call the histeq function to spread the intensity values over the full range of the image, a process called histogram equalization. I2 = histeq(I); 1-8 Image Import and Export Display the new equalized image, I2, in a new figure window. figure, imshow(I2) Equalized Version of pout.tif Call imhist again to create a histogram of the equalized image I2. If you compare the two histograms, the histogram of I2 is more spread out than the histogram of I1. figure, imhist(I2) 1-9 1 Getting Started The toolbox includes several other functions that perform contrast adjustment, including the imadjust and adapthisteq functions. See “Adjusting Pixel Intensity Values” on page 11-37 for more information. In addition, the toolbox includes an interactive tool, called the Adjust Contrast tool, that you can use to adjust the contrast and brightness of an image displayed in the Image Tool. To use this tool, call the imcontrast function or access the tool from the Image Tool. For more information, see “Adjusting Image Contrast Using the Adjust Contrast Tool” on page 4-42. Step 4: Write the Image to a Disk File To write the newly adjusted image I2 to a disk file, use the imwrite function. If you include the filename extension '.png', the imwrite function writes the image to a file in Portable Network Graphics (PNG) format, but you can specify other formats. imwrite (I2, 'pout2.png'); See the imwrite function reference page for a list of file formats it supports. See also “Writing Image Data to a File” on page 3-5 for more information about writing image data to files. Step 5: Check the Contents of the Newly Written File To see what imwrite wrote to the disk file, use the imfinfo function. imfinfo('pout2.png') The imfinfo function returns information about the image in the file, such as its format, size, width, and height. See “Getting Information About a Graphics File” on page 3-2 for more information about using imfinfo. ans = Filename: FileModDate: FileSize: Format: FormatVersion: Width: 1-10 'pout2.png' '29-Dec-2005 09:34:39' 36938 'png' [] 240 Image Import and Export Height: BitDepth: ColorType: FormatSignature: Colormap: Histogram: InterlaceType: Transparency: SimpleTransparencyData: BackgroundColor: RenderingIntent: Chromaticities: Gamma: XResolution: YResolution: ResolutionUnit: XOffset: YOffset: OffsetUnit: SignificantBits: ImageModTime: Title: Author: Description: Copyright: CreationTime: Software: Disclaimer: Warning: Source: Comment: OtherText: 291 8 'grayscale' [137 80 78 71 13 10 26 10] [] [] 'none' 'none' [] [] [] [] [] [] [] [] [] [] [] [] '29 Dec 2005 14:34:39 +0000' [] [] [] [] [] [] [] [] [] [] [] 1-11 1 Getting Started Image Enhancement and Analysis In this section... “Introduction” on page 1-13 “Step 1: Read Image” on page 1-13 “Step 2: Use Morphological Opening to Estimate the Background” on page 1-13 “Step 3: View the Background Approximation as a Surface” on page 1-14 “Step 4: Subtract the Background Image from the Original Image” on page 1-15 “Step 5: Increase the Image Contrast” on page 1-16 “Step 6: Threshold the Image” on page 1-17 “Step 7: Identify Objects in the Image” on page 1-17 “Step 8: Examine One Object” on page 1-18 “Step 9: View All Objects” on page 1-19 “Step 10: Compute Area of Each Object” on page 1-20 “Step 11: Compute Area-based Statistics” on page 1-21 “Step 12: Create Histogram of the Area” on page 1-22 1-12 Image Enhancement and Analysis Introduction Using an image of rice grains, this example illustrates how you can enhance an image to correct for nonuniform illumination, and then use the enhanced image to identify individual grains. This enables you to learn about the characteristics of the grains and easily compute statistics for all the grains in the image. Step 1: Read Image Read and display the grayscale image rice.png. I = imread('rice.png'); imshow(I) Grayscale Image rice.png Step 2: Use Morphological Opening to Estimate the Background In the sample image, the background illumination is brighter in the center of the image than at the bottom. In this step, the example uses a morphological opening operation to estimate the background illumination. Morphological opening is an erosion followed by a dilation, using the same structuring element for both operations. The opening operation has the effect of removing objects that cannot completely contain the structuring element. For more information about morphological image processing, see “Morphological Filtering”. 1-13 1 Getting Started background = imopen(I,strel('disk',15)); The example calls the imopen function to perform the morphological opening operation. Note how the example calls the strel function to create a disk-shaped structuring element with a radius of 15. To remove the rice grains from the image, the structuring element must be sized so that it cannot fit entirely inside a single grain of rice. Step 3: View the Background Approximation as a Surface Use the surf command to create a surface display of the background (the background approximation created in Step 2). The surf command creates colored parametric surfaces that enable you to view mathematical functions over a rectangular region. However, the surf function requires data of class double, so you first need to convert background using the double command: figure, surf(double(background(1:8:end,1:8:end))),zlim([0 255]); set(gca,'ydir','reverse'); The example uses MATLAB indexing syntax to view only 1 out of 8 pixels in each direction; otherwise, the surface plot would be too dense. The example also sets the scale of the plot to better match the range of the uint8 data and reverses the y-axis of the display to provide a better view of the data. (The pixels at the bottom of the image appear at the front of the surface plot.) In the surface display, [0, 0] represents the origin, or upper-left corner of the image. The highest part of the curve indicates that the highest pixel values of background (and consequently rice.png) occur near the middle rows of the image. The lowest pixel values occur at the bottom of the image and are represented in the surface plot by the lowest part of the curve. The surface plot is a Handle Graphics® object. You can use object properties to fine-tune its appearance. For more information, see the surface reference page. 1-14 Image Enhancement and Analysis Surface Plot Step 4: Subtract the Background Image from the Original Image To create a more uniform background, subtract the background image, background, from the original image, I, and then view the image: I2 = I - background; figure, imshow(I2) Image with Uniform Background 1-15 1 Getting Started Step 5: Increase the Image Contrast After subtraction, the image has a uniform background but is now a bit too dark. Use imadjust to adjust the contrast of the image. imadjust increases the contrast of the image by saturating 1% of the data at both low and high intensities of I2 and by stretching the intensity values to fill the uint8 dynamic range. See the imadjust reference page for more information. The following example adjusts the contrast in the image created in the previous step and displays it: I3 = imadjust(I2); figure, imshow(I3); Image After Intensity Adjustment 1-16 Image Enhancement and Analysis Step 6: Threshold the Image Create a binary version of the image so you can use toolbox functions to count the number of rice grains. Use the im2bw function to convert the grayscale image into a binary image by using thresholding. The function graythresh automatically computes an appropriate threshold to use to convert the grayscale image to binary. Remove background noise with bwareaopen: level = graythresh(I3); bw = im2bw(I3,level); bw = bwareaopen(bw, 50); figure, imshow(bw) Binary Version of the Image Step 7: Identify Objects in the Image The function bwconncomp finds all the connected components (objects) in the binary image. The accuracy of your results depends on the size of the objects, the connectivity parameter (4, 8, or arbitrary), and whether or not any objects are touching (in which case they could be labeled as one object). Some of the rice grains in bw are touching. Enter the following at the command line: cc = bwconncomp(bw, 4) cc.NumObjects You will receive the output shown below: 1-17 1 Getting Started cc = Connectivity: ImageSize: NumObjects: PixelIdxList: 4 [256 256] 95 {1x95 cell} ans = 95 Step 8: Examine One Object Each distinct object is labeled with the same integer value. Show the grain that is the 50th connected component: grain = false(size(bw)); grain(cc.PixelIdxList{50}) = true; figure, imshow(grain); The 50th Connected Component 1-18 Image Enhancement and Analysis Step 9: View All Objects One way to visualize connected components is to create a label matrix, and then display it as a pseudo-color indexed image. Use labelmatrix to create a label matrix from the output of bwconncomp. Note that labelmatrix stores the label matrix in the smallest numeric class necessary for the number of objects. Since bw contains only 95 objects, the label matrix can be stored as uint8: labeled = labelmatrix(cc); whos labeled Name Size labeled 256x256 Bytes 65536 Class Attributes uint8 In the pseudo-color image, the label identifying each object in the label matrix maps to a different color in the associated colormap matrix. Use label2rgb to choose the colormap, the background color, and how objects in the label matrix map to colors in the colormap: RGB_label = label2rgb(labeled, @spring, 'c', 'shuffle'); figure, imshow(RGB_label) Label Matrix Displayed as Pseudocolor Image 1-19 1 Getting Started Step 10: Compute Area of Each Object Each rice grain is one connected component in the cc structure. Use regionprops on cc to compute the area. graindata = regionprops(cc, 'basic') MATLAB responds with graindata = 95x1 struct array with fields: Area Centroid BoundingBox To find the area of the 50th component, use dot notation to access the Area field in the 50th element of graindata structure array: graindata(50).Area ans = 194 1-20 Image Enhancement and Analysis Step 11: Compute Area-based Statistics Create a vector grain_areas to hold the area measurement for each grain: grain_areas = [graindata.Area]; Find the grain with the smallest area: [min_area, idx] = min(grain_areas) grain = false(size(bw)); grain(cc.PixelIdxList{idx}) = true; figure, imshow(grain); min_area = 61 idx = 16 Smallest Grain 1-21 1 Getting Started Step 12: Create Histogram of the Area Use hist to create a histogram of the rice grain area: nbins = 20; figure, hist(grain_areas, nbins) title('Histogram of Rice Grain Area'); 1-22 Getting Help Getting Help In this section... “Product Documentation” on page 1-23 “Image Processing Examples” on page 1-23 “MATLAB Newsgroup” on page 1-24 Product Documentation The Image Processing Toolbox documentation is available online in both HTML and PDF formats. To access the HTML help, select Help from the menu bar of the MATLAB desktop. In the Help Navigator pane, click the Contents tab and expand the Image Processing Toolbox topic in the list. To access the PDF help, click Image Processing Toolbox in the Contents tab of the Help browser and go to the link under Printable (PDF) Documentation on the Web. (Note that to view the PDF help, you must have Adobe® Acrobat® Reader installed.) For reference information about any of the Image Processing Toolbox functions, type in the MATLAB command window help functionname For example, help imtool Image Processing Examples The Image Processing Toolbox software is supported by a full complement of example applications. These are very useful as templates for your own end-user applications, or for seeing how to use and combine your toolbox functions for powerful image analysis and enhancement. To view all the examples, call the iptdemos function. This displays an HTML page in the MATLAB Help browser that lists all the examples. The toolbox examples are located under the subdirectory 1-23 1 Getting Started matlabroot\toolbox\images\imdemos where matlabroot represents your MATLAB installation directory. MATLAB Newsgroup If you read newsgroups on the Internet, you might be interested in the MATLAB newsgroup (comp.soft-sys.matlab). This newsgroup gives you access to an active MATLAB user community. It is an excellent way to seek advice and to share algorithms, sample code, and MATLAB files with other MATLAB users. 1-24 Acknowledgments Acknowledgments This table lists the copyright owners of the images used in the Image Processing Toolbox documentation. Image Source cameraman Copyright Massachusetts Institute of Technology. Used with permission. cell Cancer cell from a rat’s prostate, courtesy of Alan W. Partin, M.D., Ph.D., Johns Hopkins University School of Medicine. circuit Micrograph of 16-bit A/D converter circuit, courtesy of Steve Decker and Shujaat Nadeem, MIT, 1993. concordaerial and westconcordaerial Visible color aerial photographs courtesy of mPower3/Emerge. concordorthophoto and westconcordorthophoto Orthoregistered photographs courtesy of Massachusetts Executive Office of Environmental Affairs, MassGIS. forest Photograph of Carmanah Ancient Forest, British Columbia, Canada, courtesy of Susan Cohen. LAN files Permission to use Landsat data sets provided by Space Imaging, LLC, Denver, Colorado. liftingbody Picture of M2-F1 lifting body in tow, courtesy of NASA (Image number E-10962). m83 M83 spiral galaxy astronomical image courtesy of Anglo-Australian Observatory, photography by David Malin. moon Copyright Michael Myers. Used with permission. saturn Voyager 2 image, 1981-08-24, NASA catalog #PIA01364. solarspectra Courtesy of Ann Walker. Used with permission. 1-25 1 1-26 Getting Started Image Source tissue Courtesy of Alan W. Partin, M.D., PhD., Johns Hopkins University School of Medicine. trees Trees with a View, watercolor and ink on paper, copyright Susan Cohen. Used with permission. 2 Introduction This chapter introduces you to the fundamentals of image processing using MATLAB and the Image Processing Toolbox software. • “Images in MATLAB” on page 2-2 • “Expressing Image Locations” on page 2-3 • “Image Types in the Toolbox” on page 2-10 • “Converting Between Image Types” on page 2-19 • “Converting Between Image Classes” on page 2-21 • “Working with Image Sequences” on page 2-23 • “Image Arithmetic” on page 2-29 2 Introduction Images in MATLAB The basic data structure in MATLAB is the array, an ordered set of real or complex elements. This object is naturally suited to the representation of images, real-valued ordered sets of color or intensity data. MATLAB stores most images as two-dimensional arrays (i.e., matrices), in which each element of the matrix corresponds to a single pixel in the displayed image. (Pixel is derived from picture element and usually denotes a single dot on a computer display.) For example, an image composed of 200 rows and 300 columns of different colored dots would be stored in MATLAB as a 200-by-300 matrix. Some images, such as truecolor images, require a three-dimensional array, where the first plane in the third dimension represents the red pixel intensities, the second plane represents the green pixel intensities, and the third plane represents the blue pixel intensities. This convention makes working with images in MATLAB similar to working with any other type of matrix data, and makes the full power of MATLAB available for image processing applications. 2-2 Expressing Image Locations Expressing Image Locations In this section... “Pixel Indices” on page 2-3 “Spatial Coordinates” on page 2-4 Pixel Indices Often, the most convenient method for expressing locations in an image is to use pixel indices. The image is treated as a grid of discrete elements, ordered from top to bottom and left to right, as illustrated by the following figure. Pixel Indices For pixel indices, the row increases downward, while the column increases to the right. Pixel indices are integer values, and range from 1 to the length of the row or column. There is a one-to-one correspondence between pixel indices and subscripts for the first two matrix dimensions in MATLAB. For example, the data for the pixel in the fifth row, second column is stored in the matrix element (5,2). You use normal MATLAB matrix subscripting to access values of individual pixels. For example, the MATLAB code I(2,15) returns the value of the pixel at row 2, column 15 of the image I. Similarly, the MATLAB code 2-3 2 Introduction RGB(2,15,:) returns the R, G, B values of the pixel at row 2, column 15 of the image RGB. The correspondence between pixel indices and subscripts for the first two matrix dimensions in MATLAB makes the relationship between an image’s data matrix and the way the image is displayed easy to understand. Spatial Coordinates Another method for expressing locations in an image is to use a system of continuously varying coordinates rather than discrete indices. This lets you consider an image as covering a square patch, for example. In a spatial coordinate system like this, locations in an image are positions on a plane, and they are described in terms of x and y (not row and column as in the pixel indexing system). From this Cartesian perspective, an (x,y) location such as (3.2,5.3) is meaningful, and is distinct from pixel (5,3). Intrinsic Coordinates By default, the toolbox uses a spatial coordinate system for an image that corresponds to the image’s pixel indices. It’s called the intrinsic coordinate system and is illustrated in the following figure. Notice that y increases downward, because this orientation is consistent with the way in which digital images are typically viewed. 2-4 Expressing Image Locations Intrinsic Coordinate System The intrinsic coordinates (x,y) of the center point of any pixel are identical to the column and row indices for that pixel. For example, the center point of the pixel in row 5, column 3 has spatial coordinates x = 3.0, y = 5.0. This correspondence simplifies many toolbox functions considerably. Be aware, however, that the order of coordinate specification (3.0,5.0) is reversed in intrinsic coordinates relative to pixel indices (5,3). Several functions primarily work with spatial coordinates rather than pixel indices, but as long as you are using the default spatial coordinate system (intrinsic coordinates), you can specify locations in terms of their columns (x) and rows (y). When looking at the intrinsic coordinate system, note that the upper left corner of the image is located at (0.5,0.5), not at (0,0), and the lower right corner of the image is located at (numCols + 0.5, numRows + 0.5), where numCols and numRows are the number of rows and columns in the image. In contrast, the upper left pixel is pixel (1,1) and the lower right pixel is pixel (numRows, numCols). The center of the upper left pixel is (1.0, 1.0) and the center of the lower right pixel is (numCols, numRows). In fact, the center coordinates of every pixel are integer valued. The center of the pixel with indices (r, c) — where r and c are integers by definition — falls at the point x = c, y = r in the intrinsic coordinate system. 2-5 2 Introduction World Coordinates In some situations, you might want to use a world coordinate system (also called a nondefault spatial coordinate system). For example, you could shift the origin by specifying that the upper left corner of an image is the point (19.0,7.5), rather than (0.5,0.5). Or, you might want to specify a coordinate system in which every pixel covers a 5-by-5 meter patch on the ground. One way to define a world coordinate system for an image is to specify the XData and YData image properties for the image. The XData and YData image properties are two-element vectors that control the range of coordinates spanned by the image. When you do this, the MATLAB axes coordinates become identical to the world (nondefault) coordinates. If you do not specify XData and YData, the axes coordinates are identical to the intrinsic coordinates of the image. By default, for an image A, XData is [1 size(A,2)], and YData is [1 size(A,1)]. With this default, the world coordinate system and intrinsic coordinate system coincide perfectly. For example, if A is a 100 row by 200 column image, the default XData is [1 200], and the default YData is [1 100]. The values in these vectors are actually the coordinates for the center points of the first and last pixels (not the pixel edges), so the actual coordinate range spanned is slightly larger. For instance, if XData is [1 200], the interval in X spanned by the image is [0.5 200.5]. It’s also possible to set XData or YData such that the x-axis or y-axis is reversed. You’d do this by placing the larger value first. (For example, set the YData to [1000 1].) This is a common technique to use with geospatial data. These commands display an image using nondefault XData and YData. A = magic(5); x = [19.5 23.5]; y = [8.0 12.0]; image(A,'XData',x,'YData',y), axis image, colormap(jet(25)) 2-6 Expressing Image Locations Specifying Coordinate Information To specify a world (nondefault spatial) coordinate system for an image, use the spatial referencing objects imref2d and imref3d. Spatial referencing objects let you define the location of the image in a world coordinate system and specify the image resolution, including nonsquare pixel shapes. These objects also support methods for converting between the world, intrinsic, and subscript coordinate systems. Several toolbox functions accept or return spatial referencing objects: imwarp, imshow, imshowpair, imfuse, imregtform, and imregister. This example creates a spatial referencing object associated with a 2-by-2 image where the world extent is 4 units/pixel in the x direction and 2 units/pixel in the y direction. The example creates the object, specifying the pixels dimensions as arguments but does not specify world limits in the x and y directions. You could specify other information when creating an object, see imref2d for more information. 2-7 2 Introduction I = [1 2; 3 4] R = imref2d(size(I),4,2) R = imref2d with properties: XWorldLimits: YWorldLimits: ImageSize: PixelExtentInWorldX: PixelExtentInWorldY: ImageExtentInWorldX: ImageExtentInWorldY: XIntrinsicLimits: YIntrinsicLimits: [2 10] [1 5] [2 2] 4 2 8 4 [0.5000 2.5000] [0.5000 2.5000] The imref2d object contains information about the image, some of it provided by you and some of it derived by the object. The following table provides descriptions of spatial referencing object fields. 2-8 Field Description XWorldLimits Upper and lower bounds along the X dimension in world coordinates (nondefault spatial coordinates) YWorldLimits Upper and lower bounds along the Y dimension in world coordinates (nondefault spatial coordinates) ImageSize Size of the image, returned by the size function. PixelExtentInWorldX Size of pixel along the X dimension PixelExtentInWorldY Size of pixel along the Y dimension ImageExtentInWorldX Size of image along the X dimension ImageExtentInWorldY Size of image along the Y dimension Expressing Image Locations Field Description XIntrinsicLimits Upper and lower bounds along X dimension in intrinsic coordinates (default spatial coordinates) YIntrinsicLimits Upper and lower bounds along Y dimension in intrinsic coordinates (default spatial coordinates). The following figure illustrates how these properties map to elements of an image. ImageExtentInWorldX: 8 xWorldLimits: [2 10] yWorldLimits: [1 5] ImageExtentInWorldY: 4 1 2 3 1 2 PixelExtentInWorldY: 2 0,0 3 4 5 6 7 9 8 10 PixelExtentInWorldX: 4 4 I(1,1) I(1,2) I(2,1) I(2,2) 5 ImageSize: [ 2 2] You can also use the XData and YData properties to define a world (nondefault spatial) coordinate system. Several toolbox functions accept this data as arguments and returns coordinates in the world coordinate system. These functions are: bwselect, imcrop, impixel, roifill, roipoly, and imtransform) 2-9 2 Introduction Image Types in the Toolbox In this section... “Overview of Image Types” on page 2-10 “Binary Images” on page 2-11 “Indexed Images” on page 2-12 “Grayscale Images” on page 2-14 “Truecolor Images” on page 2-15 Overview of Image Types The Image Processing Toolbox software defines four basic types of images, summarized in the following table. These image types determine the way MATLAB interprets data matrix elements as pixel intensity values. For information about converting between image types, see “Converting Between Image Types” on page 2-19. Image Type Interpretation Binary (Also known as a bilevel image) Logical array containing only 0s and 1s, interpreted as black and white, respectively. See “Binary Images” on page 2-11 for more information. Indexed (Also known as a pseudocolor image) Array of class logical, uint8, uint16, single, or double whose pixel values are direct indices into a colormap. The colormap is an m-by-3 array of class double. For single or double arrays, integer values range from [1, p]. For logical, uint8, or uint16 arrays, values range from [0, p-1]. See “Indexed Images” on page 2-12 for more information. 2-10 Image Types in the Toolbox Image Type Interpretation Grayscale (Also known as an intensity, gray scale, or gray level image) Array of class uint8, uint16, int16, single, or double whose pixel values specify intensity values. Truecolor (Also known as an RGB image ) For single or double arrays, values range from [0, 1]. For uint8, values range from [0,255]. For uint16, values range from [0, 65535]. For int16, values range from [-32768, 32767]. See “Grayscale Images” on page 2-14 for more information. m-by-n-by-3 array of class uint8, uint16, single, or double whose pixel values specify intensity values. For single or double arrays, values range from [0, 1]. For uint8, values range from [0, 255]. For uint16, values range from [0, 65535]. See “Truecolor Images” on page 2-15 for more information. Binary Images In a binary image, each pixel assumes one of only two discrete values: 1 or 0. A binary image is stored as a logical array. By convention, this documentation uses the variable name BW to refer to binary images. The following figure shows a binary image with a close-up view of some of the pixel values. Pixel Values in a Binary Image 2-11 2 Introduction Indexed Images An indexed image consists of an array and a colormap matrix. The pixel values in the array are direct indices into a colormap. By convention, this documentation uses the variable name X to refer to the array and map to refer to the colormap. The colormap matrix is an m-by-3 array of class double containing floating-point values in the range [0,1]. Each row of map specifies the red, green, and blue components of a single color. An indexed image uses direct mapping of pixel values to colormap values. The color of each image pixel is determined by using the corresponding value of X as an index into map. 2-12 Image Types in the Toolbox A colormap is often stored with an indexed image and is automatically loaded with the image when you use the imread function. After you read the image and the colormap into the MATLAB workspace as separate variables, you must keep track of the association between the image and colormap. However, you are not limited to using the default colormap--you can use any colormap that you choose. The relationship between the values in the image matrix and the colormap depends on the class of the image matrix. If the image matrix is of class single or double, it normally contains integer values 1 through p, where p is the length of the colormap. the value 1 points to the first row in the colormap, the value 2 points to the second row, and so on. If the image matrix is of class logical, uint8 or uint16, the value 0 points to the first row in the colormap, the value 1 points to the second row, and so on. The following figure illustrates the structure of an indexed image. In the figure, the image matrix is of class double, so the value 5 points to the fifth row of the colormap. Pixel Values Index to Colormap Entries in Indexed Images 2-13 2 Introduction Grayscale Images A grayscale image (also called gray-scale, gray scale, or gray-level) is a data matrix whose values represent intensities within some range. MATLAB stores a grayscale image as an individual matrix, with each element of the matrix corresponding to one image pixel. By convention, this documentation uses the variable name I to refer to grayscale images. The matrix can be of class uint8, uint16, int16, single, or double. While grayscale images are rarely saved with a colormap, MATLAB uses a colormap to display them. For a matrix of class single or double, using the default grayscale colormap, the intensity 0 represents black and the intensity 1 represents white. For a matrix of type uint8, uint16, or int16, the intensity intmin(class(I)) represents black and the intensity intmax(class(I)) represents white. The figure below depicts a grayscale image of class double. Pixel Values in a Grayscale Image Define Gray Levels 2-14 Image Types in the Toolbox Truecolor Images A truecolor image is an image in which each pixel is specified by three values — one each for the red, blue, and green components of the pixel’s color. MATLAB store truecolor images as an m-by-n-by-3 data array that defines red, green, and blue color components for each individual pixel. Truecolor images do not use a colormap. The color of each pixel is determined by the combination of the red, green, and blue intensities stored in each color plane at the pixel’s location. Graphics file formats store truecolor images as 24-bit images, where the red, green, and blue components are 8 bits each. This yields a potential of 16 million colors. The precision with which a real-life image can be replicated has led to the commonly used term truecolor image. A truecolor array can be of class uint8, uint16, single, or double. In a truecolor array of class single or double, each color component is a value between 0 and 1. A pixel whose color components are (0,0,0) is displayed as black, and a pixel whose color components are (1,1,1) is displayed as white. The three color components for each pixel are stored along the third dimension of the data array. For example, the red, green, and blue color components of the pixel (10,5) are stored in RGB(10,5,1), RGB(10,5,2), and RGB(10,5,3), respectively. 2-15 2 Introduction The following figure depicts a truecolor image of class double. The Color Planes of a Truecolor Image To determine the color of the pixel at (2,3), you would look at the RGB triplet stored in (2,3,1:3). Suppose (2,3,1) contains the value 0.5176, (2,3,2) contains 0.1608, and (2,3,3) contains 0.0627. The color for the pixel at (2,3) is 0.5176 0.1608 0.0627 2-16 Image Types in the Toolbox To further illustrate the concept of the three separate color planes used in a truecolor image, the code sample below creates a simple image containing uninterrupted areas of red, green, and blue, and then creates one image for each of its separate color planes (red, green, and blue). The example displays each color plane image separately, and also displays the original image. RGB=reshape(ones(64,1)*reshape(jet(64),1,192),[64,64,3]); R=RGB(:,:,1); G=RGB(:,:,2); B=RGB(:,:,3); imshow(R) figure, imshow(G) figure, imshow(B) figure, imshow(RGB) The Separated Color Planes of an RGB Image 2-17 2 Introduction Notice that each separated color plane in the figure contains an area of white. The white corresponds to the highest values (purest shades) of each separate color. For example, in the Red Plane image, the white represents the highest concentration of pure red values. As red becomes mixed with green or blue, gray pixels appear. The black region in the image shows pixel values that contain no red values, i.e., R == 0. 2-18 Converting Between Image Types Converting Between Image Types The toolbox includes many functions that you can use to convert an image from one type to another, listed in the following table. For example, if you want to filter a color image that is stored as an indexed image, you must first convert it to truecolor format. When you apply the filter to the truecolor image, MATLAB filters the intensity values in the image, as is appropriate. If you attempt to filter the indexed image, MATLAB simply applies the filter to the indices in the indexed image matrix, and the results might not be meaningful. You can perform certain conversions just using MATLAB syntax. For example, you can convert a grayscale image to truecolor format by concatenating three copies of the original matrix along the third dimension. RGB = cat(3,I,I,I); The resulting truecolor image has identical matrices for the red, green, and blue planes, so the image displays as shades of gray. In addition to these image type conversion functions, there are other functions that return a different image type as part of the operation they perform. For example, the region of interest functions return a binary image that you can use to mask an image for filtering or for other operations. Note When you convert an image from one format to another, the resulting image might look different from the original. For example, if you convert a color indexed image to a grayscale image, the resulting image displays as shades of grays, not color. Function Description demosaic Convert Bayer pattern encoded image to truecolor (RGB) image. dither Use dithering to convert a grayscale image to a binary image or to convert a truecolor image to an indexed image. gray2ind Convert a grayscale image to an indexed image. 2-19 2 Introduction Function Description grayslice Convert a grayscale image to an indexed image by using multilevel thresholding. im2bw Convert a grayscale image, indexed image, or truecolor image, to a binary image, based on a luminance threshold. ind2gray Convert an indexed image to a grayscale image. ind2rgb Convert an indexed image to a truecolor image. mat2gray Convert a data matrix to a grayscale image, by scaling the data. rgb2gray Convert a truecolor image to a grayscale image. Note: To work with images that use other color spaces, such as HSV, first convert the image to RGB, process the image, and then convert it back to the original color space. For more information about color space conversion routines, see“Color”. rgb2ind 2-20 Convert a truecolor image to an indexed image. Converting Between Image Classes Converting Between Image Classes In this section... “Overview of Image Class Conversions” on page 2-21 “Losing Information in Conversions” on page 2-21 “Converting Indexed Images” on page 2-21 Overview of Image Class Conversions You can convert uint8 and uint16 image data to double using the MATLAB double function. However, converting between classes changes the way MATLAB and the toolbox interpret the image data. If you want the resulting array to be interpreted properly as image data, you need to rescale or offset the data when you convert it. For easier conversion of classes, use one of these functions: im2uint8, im2uint16, im2int16, im2single, or im2double. These functions automatically handle the rescaling and offsetting of the original data of any image class. For example, this command converts a double-precision RGB image with data in the range [0,1] to a uint8 RGB image with data in the range [0,255]. RGB2 = im2uint8(RGB1); Losing Information in Conversions When you convert to a class that uses fewer bits to represent numbers, you generally lose some of the information in your image. For example, a uint16 grayscale image is capable of storing up to 65,536 distinct shades of gray, but a uint8 grayscale image can store only 256 distinct shades of gray. When you convert a uint16 grayscale image to a uint8 grayscale image, im2uint8 quantizes the gray shades in the original image. In other words, all values from 0 to 127 in the original image become 0 in the uint8 image, values from 128 to 385 all become 1, and so on. Converting Indexed Images It is not always possible to convert an indexed image from one storage class to another. In an indexed image, the image matrix contains only indices into 2-21 2 Introduction a colormap, rather than the color data itself, so no quantization of the color data is possible during the conversion. For example, a uint16 or double indexed image with 300 colors cannot be converted to uint8, because uint8 arrays have only 256 distinct values. If you want to perform this conversion, you must first reduce the number of the colors in the image using the imapprox function. This function performs the quantization on the colors in the colormap, to reduce the number of distinct colors in the image. See “Reducing Colors Using imapprox” on page 14-10 for more information. 2-22 Working with Image Sequences Working with Image Sequences In this section... “Overview of Toolbox Functions That Work with Image Sequences” on page 2-23 “Process Image Sequences” on page 2-26 “Process Multi-Frame Image Arrays” on page 2-27 Overview of Toolbox Functions That Work with Image Sequences Some applications work with collections of images related by time, such as frames in a movie, or by spatial location, such as magnetic resonance imaging (MRI) slices. These collections of images are referred to by a variety of names, such as image sequences or image stacks. The ability to create N-dimensional arrays can provide a convenient way to store image sequences. For example, an m-by-n-by-p array can store an array of p two-dimensional images, such as grayscale or binary images, as shown in the following figure. An m-by-n-by-3-by-p array can store truecolor images where each image is made up of three planes. Multidimensional Array Containing an Image Sequence Many toolbox functions can operate on multi-dimensional arrays and, consequently, can operate on image sequences. For example, if you pass a multi-dimensional array to the imtransform function, it applies the same 2-D transformation to all 2-D planes along the higher dimension. 2-23 2 Introduction Some toolbox functions that accept multi-dimensional arrays, however, do not by default interpret an m-by-n-by-p or an m-by-n-by-3-by-p array as an image sequence. To use these functions with image sequences, you must use particular syntax and be aware of other limitations. The following table lists these toolbox functions and provides guidelines about how to use them to process image sequences. For information about displaying image sequences, see “Viewing Image Sequences” on page 4-55. Function Image Sequence Dimensions Guideline When Used with an Image Sequence bwlabeln m-by-n-by-p only Must use the bwlabeln(BW,conn) syntax with a 2-D connectivity. deconvblind m-by-n-by-p or m-by-n-by-3-by-p PSF argument can be either 1-D m-by-n-by-p or m-by-n-by-3-by-p PSF argument can be either 1-D m-by-n-by-p or m-by-n-by-3-by-p PSF argument can be either 1-D entropyfilt m-by-n-by-p only nhood argument must be 2-D. imabsdiff m-by-n-by-p or m-by-n-by-3-by-p Image sequences must be the same size. imadd m-by-n-by-p or m-by-n-by-3-by-p Image sequences must be the same size. Cannot add scalar to image sequence. imbothat m-by-n-by-p only SE argument must be 2-D. imclose m-by-n-by-p only SE argument must be 2-D. imdilate m-by-n-by-p only SE argument must be 2-D. imdivide m-by-n-by-p or m-by-n-by-3-by-p Image sequences must be the same size. imerode m-by-n-by-p only SE argument must be 2-D. imextendedmax m-by-n-by-p only deconvlucy edgetaper or 2-D. or 2-D. or 2-D. Must use the imextendedmax(I,h,conn) syntax with a 2-D connectivity. 2-24 Working with Image Sequences Function Image Sequence Dimensions imextendedmin m-by-n-by-p only Guideline When Used with an Image Sequence Must use the imextendedmin(I,h,conn) syntax with a 2-D connectivity. imfilter m-by-n-by-p or m-by-n-by-3-by-p With grayscale images, h can be 2-D. With truecolor images (RGB), h can be 2-D or 3-D. imhmax m-by-n-by-p only Must use the imhmax(I,h,conn) syntax with a 2-D connectivity. imhmin m-by-n-by-p only Must use the imhmin(I,h,conn) syntax with a 2-D connectivity. imlincomb m-by-n-by-p or m-by-n-by-3-by-p Image sequences must be the same size. immultiply m-by-n-by-p or m-by-n-by-3-by-p Image sequences must be the same size. imopen m-by-n-by-p only SE argument must be 2-D. imregionalmax m-by-n-by-p only Must use the imextendedmax(I,conn) syntax with a 2-D connectivity. imregionalmin m-by-n-by-p only Must use the imextendedmin(I,conn) syntax with a 2-D connectivity. imsubtract m-by-n-by-p or m-by-n-by-3-by-p Image sequences must be the same size. imtophat m-by-n-by-p only SE argument must be 2-D. imwarp m-by-n-by-p or m-by-n-by-3-by-p TFORM argument must be 2-D. padarray m-by-n-by-p or m-by-n-by-3-by-p PADSIZE argument must be a rangefilt m-by-n-by-p only NHOOD argument must be 2-D. stdfilt m-by-n-by-p only NHOOD argument must be 2-D. two-element vector. 2-25 2 Introduction Function tformarray Image Sequence Dimensions Guideline When Used with an Image Sequence m-by-n-by-p or m-by-n-by-3-by-p • T must be 2-D to 2-D (compatible with imtransform). • R must be 2-D. • TDIMS_A and TDIMS_B must be 2-D, i.e., [2 1] or [1 2]. • TSIZE_B must be a two-element array [D1 D2], where D1 and D2 are the first and second transform dimensions of the output space. • TMAP_B must be [TSIZE_B 2]. • F can be a scalar or a p-by-1 array, for m-by-n-by-p arrays. Or F can be a scalar, 1-by-p array; 3-by-1 array; or 3-by-p array, for m-by-n-by-3-by-p arrays. watershed m-by-n-by-p only Must use watershed(I,conn) syntax with a 2-D connectivity. Process Image Sequences This example starts by reading a series of images from a directory into the MATLAB workspace, storing the images in an m-by-n-by-p array. The example then passes the entire array to the stdfilt function and performs standard deviation filtering on each image in the sequence. Note that, to use stdfilt with an image sequence, you must use the nhood argument, specifying a 2-D neighborhood. % Create an array of filenames that make up the image sequence fileFolder = fullfile(matlabroot,'toolbox','images','imdemos'); dirOutput = dir(fullfile(fileFolder,'AT3_1m4_*.tif')); fileNames = {dirOutput.name}'; numFrames = numel(fileNames); 2-26 Working with Image Sequences I = imread(fileNames{1}); % Preallocate the array sequence = zeros([size(I) numFrames],class(I)); sequence(:,:,1) = I; % Create image sequence array for p = 2:numFrames sequence(:,:,p) = imread(fileNames{p}); end % Process sequence sequenceNew = stdfilt(sequence,ones(3)); % View results figure; for k = 1:numFrames imshow(sequence(:,:,k)); title(sprintf('Original Image # %d',k)); pause(1); imshow(sequenceNew(:,:,k),[]); title(sprintf('Processed Image # %d',k)); pause(1); end Process Multi-Frame Image Arrays The toolbox includes two functions, immovie and montage, that work with a specific type of multi-dimensional array called a multi-frame array. In this array, images, called frames in this context, are concatenated along the fourth dimension. Multi-frame arrays are either m-by-n-by-1-by-p, for grayscale, binary, or indexed images, or m-by-n-by-3-by-p, for truecolor images, where p is the number of frames. For example, a multi-frame array containing five, 480-by-640 grayscale or indexed images would be 480-by-640-by-1-by-5. An array with five 480-by-640 truecolor images would be 480-by-640-by-3-by-5. 2-27 2 Introduction Note To process a multi-frame array of grayscale images as an image sequence, as described in “Working with Image Sequences” on page 2-23, you can use the squeeze function to remove the singleton dimension. You can use the cat command to create a multi-frame array. For example, the following stores a group of images (A1, A2, A3, A4, and A5) in a single array. A = cat(4,A1,A2,A3,A4,A5) You can also extract frames from a multiframe image. For example, if you have a multiframe image MULTI, this command extracts the third frame. FRM3 = MULTI(:,:,:,3) Note that, in a multiframe image array, each image must be the same size and have the same number of planes. In a multiframe indexed image, each image must also use the same colormap. 2-28 Image Arithmetic Image Arithmetic In this section... “Overview of Image Arithmetic Functions” on page 2-29 “Image Arithmetic Saturation Rules” on page 2-30 “Nesting Calls to Image Arithmetic Functions” on page 2-30 Overview of Image Arithmetic Functions Image arithmetic is the implementation of standard arithmetic operations, such as addition, subtraction, multiplication, and division, on images. Image arithmetic has many uses in image processing both as a preliminary step in more complex operations and by itself. For example, image subtraction can be used to detect differences between two or more images of the same scene or object. You can do image arithmetic using the MATLAB arithmetic operators. The Image Processing Toolbox software also includes a set of functions that implement arithmetic operations for all numeric, nonsparse data types. The toolbox arithmetic functions accept any numeric data type, including uint8, uint16, and double, and return the result image in the same format. The functions perform the operations in double precision, on an element-by-element basis, but do not convert images to double-precision values in the MATLAB workspace. Overflow is handled automatically. The functions saturate return values to fit the data type. For more information, see these additional topics: Note On Intel® architecture processors, the image arithmetic functions can take advantage of the Intel Integrated Performance Primitives (Intel IPP) library, thus accelerating their execution time. The Intel IPP library is only activated, however, when the data passed to these functions is of specific classes. See the reference pages for the individual arithmetic functions for more information. 2-29 2 Introduction Image Arithmetic Saturation Rules The results of integer arithmetic can easily overflow the data type allotted for storage. For example, the maximum value you can store in uint8 data is 255. Arithmetic operations can also result in fractional values, which cannot be represented using integer arrays. MATLAB arithmetic operators and the Image Processing Toolbox arithmetic functions use these rules for integer arithmetic: • Values that exceed the range of the integer type are saturated to that range. • Fractional values are rounded. For example, if the data type is uint8, results greater than 255 (including Inf) are set to 255. The following table lists some additional examples. Result Class Truncated Value 300 uint8 255 -45 uint8 0 10.5 uint8 11 Nesting Calls to Image Arithmetic Functions You can use the image arithmetic functions in combination to perform a series of operations. For example, to calculate the average of two images, C= A+B 2 You could enter I = imread('rice.png'); I2 = imread('cameraman.tif'); K = imdivide(imadd(I,I2), 2); % not recommended When used with uint8 or uint16 data, each arithmetic function rounds and saturates its result before passing it on to the next operation. This can significantly reduce the precision of the calculation. A better way to perform 2-30 Image Arithmetic this calculation is to use the imlincomb function. imlincomb performs all the arithmetic operations in the linear combination in double precision and only rounds and saturates the final result. K = imlincomb(.5,I,.5,I2); % recommended 2-31 2 2-32 Introduction 3 Reading and Writing Image Data This chapter describes how to get information about the contents of a graphics file, read image data from a file, and write image data to a file, using standard graphics and medical file formats. • “Getting Information About a Graphics File” on page 3-2 • “Reading Image Data” on page 3-3 • “Writing Image Data to a File” on page 3-5 • “Converting Between Graphics File Formats” on page 3-8 • “Working with DICOM Files” on page 3-9 • “Working with Mayo Analyze 7.5 Files” on page 3-19 • “Working with Interfile Files” on page 3-20 • “Working with High Dynamic Range Images” on page 3-21 3 Reading and Writing Image Data Getting Information About a Graphics File To obtain information about a graphics file and its contents, use the imfinfo function. You can use imfinfo with any of the formats supported by MATLAB. Use the imformats function to determine which formats are supported. Note You can also get information about an image displayed in the Image Tool — see “Getting Information About an Image Using the Image Information Tool” on page 4-40. The information returned by imfinfo depends on the file format, but it always includes at least the following: • Name of the file • File format • Version number of the file format • File modification date • File size in bytes • Image width in pixels • Image height in pixels • Number of bits per pixel • Image type: truecolor (RGB), grayscale (intensity), or indexed 3-2 Reading Image Data Reading Image Data To import an image from any supported graphics image file format, in any of the supported bit depths, use the imread function. This example reads a truecolor image into the MATLAB workspace as the variable RGB. RGB = imread('football.jpg'); If the image file format uses 8-bit pixels, imread stores the data in the workspace as a uint8 array. For file formats that support 16-bit data, such as PNG and TIFF, imread creates a uint16 array. imread uses two variables to store an indexed image in the workspace: one for the image and another for its associated colormap. imread always reads the colormap into a matrix of class double, even though the image array itself may be of class uint8 or uint16. [X,map] = imread('trees.tif'); In these examples, imread infers the file format to use from the contents of the file. You can also specify the file format as an argument to imread. imread supports many common graphics file formats, such as Microsoft® Windows® Bitmap (BMP), Graphics Interchange Format (GIF), Joint Photographic Experts Group (JPEG), Portable Network Graphics (PNG), and Tagged Image File Format (TIFF) formats. For the latest information concerning the bit depths and/or image formats supported, see imread and imformats. If the graphics file contains multiple images, imread imports only the first image from the file. To import additional images, you must use imread with format-specific arguments to specify the image you want to import. In this example, imread imports a series of 27 images from a TIFF file and stores the images in a four-dimensional array. You can use imfinfo to determine how many images are stored in the file. mri = zeros([128 128 1 27],'uint8'); % preallocate 4-D array for frame=1:27 [mri(:,:,:,frame),map] = imread('mri.tif',frame); end 3-3 3 Reading and Writing Image Data When a file contains multiple images that are related in some way, you can call image processing algorithms directly. For more information, see “Working with Image Sequences” on page 2-23. If you are working with a large file, you may want to try block processing to reduce memory usage. For more information, see “Neighborhood or Block Processing: An Overview” on page 15-2. 3-4 Writing Image Data to a File Writing Image Data to a File In this section... “Overview” on page 3-5 “Specifying Format-Specific Parameters” on page 3-6 “Reading and Writing Binary Images in 1-Bit Format” on page 3-6 “Determining the Storage Class of the Output File” on page 3-7 Overview To export image data from the MATLAB workspace to a graphics file in one of the supported graphics file formats, use the imwrite function. When using imwrite, you specify the MATLAB variable name and the name of the file. If you include an extension in the filename, imwrite attempts to infer the desired file format from it. For example, the file extension .jpg infers the Joint Photographic Experts Group (JPEG) format. You can also specify the format explicitly as an argument to imwrite. This example loads the indexed image X from a MAT-file, clown.mat, along with the associated colormap map, and then exports the image as a bitmap (BMP) file. load clown whos Your output appears as shown: Name X caption map Size 200x320 2x1 81x3 Bytes 512000 4 1944 Class Attributes double char double Export the image as a bitmap file: imwrite(X,map,'clown.bmp') 3-5 3 Reading and Writing Image Data Specifying Format-Specific Parameters When using imwrite with some graphics formats, you can specify additional format-specific parameters. For example, with PNG files, you can specify the bit depth. This example writes a grayscale image I to a 4-bit PNG file. imwrite(I,'clown.png','BitDepth',4); This example writes an image A to a JPEG file, using an additional parameter to specify the compression quality parameter. imwrite(A, 'myfile.jpg', 'Quality', 100); For more information about these additional format-specific syntaxes, see the imwrite reference page. Reading and Writing Binary Images in 1-Bit Format In certain file formats, such as TIFF, a binary image can be stored in a 1-bit format. When you read in a binary image in 1-bit format, imread stores the data in the workspace as a logical array. If the file format supports it, imwrite writes binary images as 1-bit images by default. This example reads in a binary image and writes it as a TIFF file. BW = imread('text.png'); imwrite(BW,'test.tif'); To verify the bit depth of test.tif, call imfinfo and check the BitDepth field. info = imfinfo('test.tif'); info.BitDepth ans = 1 Note When writing binary files, MATLAB sets the ColorType field to 'grayscale'. 3-6 Writing Image Data to a File Determining the Storage Class of the Output File imwrite uses the following rules to determine the storage class used in the output image. Storage Class of Image logical Storage Class of Output Image File If the output image file format supports 1-bit images, imwrite creates a 1-bit image file. If the output image file format specified does not support 1-bit images, imwrite exports the image data as a uint8 grayscale image. uint8 If the output image file format supports unsigned 8-bit images, imwrite creates an unsigned 8-bit image file. uint16 If the output image file format supports unsigned 16-bit images (PNG or TIFF), imwrite creates an unsigned 16-bit image file. If the output image file format does not support 16-bit images, imwrite scales the image data to class uint8 and creates an 8-bit image file. int16 Partially supported; depends on file format. single Partially supported; depends on file format. double MATLAB scales the image data to uint8 and creates an 8-bit image file, because most image file formats use 8 bits. 3-7 3 Reading and Writing Image Data Converting Between Graphics File Formats To change the graphics format of an image, use imread to import the image into the MATLAB workspace and then use the imwrite function to export the image, specifying the appropriate file format. To illustrate, this example uses the imread function to read an image in TIFF format into the workspace and write the image data as JPEG format. moon_tiff = imread('moon.tif'); imwrite(moon_tiff,'moon.jpg'); For the specifics of which bit depths are supported for the different graphics formats, and for how to specify the format type when writing an image to file, see the reference pages for imread and imwrite. 3-8 Working with DICOM Files Working with DICOM Files In this section... “Overview of DICOM Support” on page 3-9 “Reading Metadata from a DICOM File” on page 3-10 “Reading Image Data from a DICOM File” on page 3-12 “Writing Image Data or Metadata to a DICOM File” on page 3-13 Overview of DICOM Support The Digital Imaging and Communications in Medicine (DICOM) Standard is a joint project of the American College of Radiology (ACR) and the National Electrical Manufacturers Association (NEMA). The standard facilitates interoperability of medical imaging equipment by specifying a set of media storage services, a file format, and a medical directory structure to facilitate access to the images and related information stored on interchange media. For detailed information about the standard, see the official DICOM web site. MATLAB provides the following support for working with files in the DICOM format: • Reading any file that complies with the DICOM standard • Writing three different types of DICOM files, or DICOM information objects (IOD), with validation: - Secondary capture (default) Magnetic resonance Computed tomography • Writing many more types of DICOM files without validation, by setting the createmode flag to 'copy' when writing data to a file. Note MATLAB supports working with DICOM files. There is no support for working with DICOM network capabilities. 3-9 3 Reading and Writing Image Data Reading Metadata from a DICOM File DICOM files contain metadata that provide information about the image data, such as the size, dimensions, bit depth, modality used to create the data, and equipment settings used to capture the image. To read metadata from a DICOM file, use the dicominfo function. dicominfo returns the information in a MATLAB structure where every field contains a specific piece of DICOM metadata. You can use the metadata structure returned by dicominfo to specify the DICOM file you want to read using dicomread — see “Reading Image Data from a DICOM File” on page 3-12. The following example reads the metadata from a sample DICOM file that is included with the toolbox. info = dicominfo('CT-MONO2-16-ankle.dcm') info = Filename: FileModDate: FileSize: Format: FormatVersion: Width: Height: BitDepth: ColorType: FileMetaInformationGroupLength: FileMetaInformationVersion: MediaStorageSOPClassUID: MediaStorageSOPInstanceUID: TransferSyntaxUID: ImplementationClassUID: . . . [1x89 char] '18-Dec-2000 11:06:43' 525436 'DICOM' 3 512 512 16 'grayscale' 192 [2x1 uint8] '1.2.840.10008.5.1.4.1.1.7' [1x50 char] '1.2.840.10008.1.2' '1.2.840.113619.6.5' Handling Private Metadata The DICOM specification defines many of these metadata fields, but files can contain additional fields, called private metadata. This private metadata is 3-10 Working with DICOM Files typically defined by equipment vendors to provide additional information about the data they provide. When dicominfo encounters a private metadata field in a DICOM file, it returns the metadata creating a generic name for the field based on the group and element tags of the metadata. For example, if the file contained private metadata at group 0009 and element 0006, dicominfo creates the name:Private_0009_0006. dicominfo attempts to interpret the private metadata, if it can. For example, if the metadata is a text string, dicominfo processes the data. If it can’t interpret the data, dicominfo returns a sequence of bytes. If you need to process a DICOM file created by a manufacturer that uses private metadata, and you prefer to view the correct name of the field as well as the data, you can create your own copy of the DICOM data dictionary and update it to include definitions of the private metadata. You will need information about the private metadata that vendors typically provide in DICOM compliance statements. For more information about updating DICOM dictionary, see “Creating Your Own Copy of the DICOM Dictionary” on page 3-11. Creating Your Own Copy of the DICOM Dictionary MathWorks uses a DICOM dictionary that contains definitions of thousands of standard DICOM metadata fields. If your DICOM file contains metadata that is not defined this dictionary, you can update the dictionary, creating your own copy that it includes these private metadata fields. To create your own dictionary, perform this procedure: 1 Make a copy of the text version of the DICOM dictionary that is included with MATLAB. This file, called dicom-dict.txt is located in matlabroot/toolbox/images/medformats or matlabroot/toolbox/images/iptformats depending on which version of the Image Processing Toolbox software you are working with. Do not attempt to edit the MAT-file version of the dictionary, dicom-dict.mat. 2 Edit your copy of the DICOM dictionary, adding entries for the metadata. Insert the new metadata field using the group and element tag, type, and other information. Follow the format of the other entries in the file. The 3-11 3 Reading and Writing Image Data creator of the metadata (e.g., an equipment vendor) must provide you with the information. 3 Save your copy of the dictionary. 4 Set MATLAB to use your copy of the DICOM dictionary, dicomdict function. Reading Image Data from a DICOM File To read image data from a DICOM file, use the dicomread function. The dicomread function reads files that comply with the DICOM specification but can also read certain common noncomplying files. When using dicomread, you can specify the filename as an argument, as in the following example. The example reads the sample DICOM file that is included with the toolbox. I = dicomread('CT-MONO2-16-ankle.dcm'); You can also use the metadata structure returned by dicominfo to specify the file you want to read, as in the following example. info = dicominfo('CT-MONO2-16-ankle.dcm'); I = dicomread(info); Viewing Images from DICOM Files To view the image data imported from a DICOM file, use one of the toolbox image display functions imshow or imtool. Note, however, that because the image data in this DICOM file is signed 16-bit data, you must use the autoscaling syntax with either display function to make the image viewable. imshow(I,'DisplayRange',[]) 3-12 Working with DICOM Files Writing Image Data or Metadata to a DICOM File To write image data or metadata to a file in DICOM format, use the dicomwrite function. This example writes the image I to the DICOM file ankle.dcm. dicomwrite(I,'ankle.dcm') Writing Metadata with the Image Data When writing image data to a DICOM file, dicomwrite automatically includes the minimum set of metadata fields required by the type of DICOM information object (IOD) you are creating. dicomwrite supports the following DICOM IODs with full validation. • Secondary capture (default) • Magnetic resonance • Computed tomography dicomwrite can write many other types of DICOM data (e.g., X-ray, radiotherapy, nuclear medicine) to a file; however, dicomwrite does not perform any validation of this data. See dicomwrite for more information. 3-13 3 Reading and Writing Image Data You can also specify the metadata you want to write to the file by passing to dicomwrite an existing DICOM metadata structure that you retrieved using dicominfo. In the following example, the dicomwrite function writes the relevant information in the metadata structure info to the new DICOM file. info = dicominfo('CT-MONO2-16-ankle.dcm'); I = dicomread(info); dicomwrite(I,'ankle.dcm',info) Note that the metadata written to the file is not identical to the metadata in the info structure. When writing metadata to a file, there are certain fields that dicomwrite must update. To illustrate, look at the instance ID in the original metadata and compare it with the ID in the new file. info.SOPInstanceUID ans = 1.2.840.113619.2.1.2411.1031152382.365.1.736169244 Now, read the metadata from the newly created DICOM file, using dicominfo, and check the SOPInstanceUID field. info2 = dicominfo('ankle.dcm'); info2.SOPInstanceUID ans = 1.2.841.113411.2.1.2411.10311244477.365.1.63874544 Note that the instance ID in the newly created file differs from the ID in the original file. Understanding Explicit Versus Implicit VR Attributes DICOM attributes provide the length and then the data. When writing data to a file, you can include a two-letter value representation (VR) with the attribute or you can let DICOM infer the value representation from the data dictionary. When you specify the VR option with the value 'explicit', the dicomwrite function includes the VR in the attribute. The following figure shows the attributes with and without the VR. 3-14 Working with DICOM Files Removing Confidential Information from a DICOM File When using a DICOM file as part of a training set, blinded study, or a presentation, you might want to remove confidential patient information, a process called anonymizing the file. To do this, use the dicomanon function. The dicomanon function creates a new series with new study values, changes some of the metadata, and then writes the file. For example, you could replace steps 4, 5, and 6 in the example in “Example: Creating a New DICOM Series” on page 3-15 with a call to the dicomanon function. Example: Creating a New DICOM Series When writing a modified image to a DICOM file, you might want to make the modified image the start of a new series. In the DICOM standard, images can be organized into series. When you write an image with metadata to a DICOM file, dicomwrite puts the image in the same series by default. To create a new series, you must assign a new DICOM unique identifier to the SeriesInstanceUID metadata field. The following example illustrates this process. 1 Read an image from a DICOM file into the MATLAB workspace. I = dicomread('CT-MONO2-16-ankle.dcm'); To view the image, use either of the toolbox display functions imshow or imtool. Because the DICOM image data is signed 16-bit data, you must use the autoscaling syntax. imtool(I,'DisplayRange',[]) 3-15 3 Reading and Writing Image Data 2 Read the metadata from the same DICOM file. info = dicominfo('CT-MONO2-16-ankle.dcm'); To identify the series an image belongs to, view the value of the SeriesInstanceUID field. info.SeriesInstanceUID ans = 1.2.840.113619.2.1.2411.1031152382.365.736169244 3 You typically only start a new DICOM series when you modify the image in some way. This example removes all the text from the image. The example finds the maximum and minimum values of all pixels in the image. The pixels that form the white text characters are set to the maximum pixel value. max(I(:)) ans = 4080 3-16 Working with DICOM Files min(I(:)) ans = 32 To remove these text characters, the example sets all pixels with the maximum value to the minimum value. Imodified = I; Imodified(Imodified == 4080) = 32; View the processed image. imshow(Imodified,[]) 4 Generate a new DICOM unique identifier (UID) using the dicomuid function. You need a new UID to write the modified image as a new series. uid = dicomuid uid = 1.3.6.1.4.1.9590.100.1.1.56461980611264497732341403390561061497 dicomuid is guaranteed to generate a unique UID. 3-17 3 Reading and Writing Image Data 5 Set the value of the SeriesInstanceUID field in the metadata associated with the original DICOM file to the generated value. info.SeriesInstanceUID = uid; 6 Write the modified image to a new DICOM file, specifying the modified metadata structure, info, as an argument. Because you set the SeriesInstanceUID value, the image you write is part of a new series. dicomwrite(Imodified,'ankle_newseries.dcm',info); To verify this operation, view the image and the SeriesInstanceUID metadata field in the new file. For information about the syntax variations that specify nondefault spatial coordinates, see the reference page for imshow. 3-18 Working with Mayo Analyze 7.5 Files Working with Mayo Analyze 7.5 Files Analyze 7.5 is a file format, developed by the Mayo Clinic, for storing MRI data. An Analyze 7.5 data set consists of two files: • Header file (filename.hdr) — Provides information about dimensions, identification, and processing history. You use the analyze75info function to read the header information. • Image file (filename.img) — Image data, whose data type and ordering are described by the header file. You use analyze75read to read the image data into the MATLAB workspace. Note The Analyze 7.5 format uses the same dual-file data set organization and the same filename extensions as the Interfile format; however, the file formats are not interchangeable. To learn how to read data from an Interfile data set, see “Working with Interfile Files” on page 3-20. The following example calls the analyze75info function to read the metadata from the Analyze 7.5 header file. The example then passes the info structure returned by analyze75info to the analyze75read function to read the image data from the image file. info = analyze75info('brainMRI.hdr'); X = analyze75read(info); 3-19 3 Reading and Writing Image Data Working with Interfile Files Interfile is a file format that was developed for the exchange of nuclear medicine image data. An Interfile data set consists of two files: • Header file (filename.hdr) — Provides information about dimensions, identification and processing history. You use the interfileinfo function to read the header information. • Image file (filename.img) — Image data, whose data type and ordering are described by the header file. You use interfileread to read the image data into the MATLAB workspace. Note The Interfile format uses the same dual-file data set organization and the same filename extensions as the Analyze 7.5 format; however, the file formats are not interchangeable. To learn how to read data from an Analyze 7.5 data set, see “Working with Mayo Analyze 7.5 Files” on page 3-19. The following example calls the interfileinfo function to read the metadata from an Interfile header file. The example then reads the image data from the corresponding image file in the Interfile data set. The file used in the example can be downloaded from the Interfile Archive maintained by the Department of Medical Physics and Bioengineering, University College, London, UK. info = interfileinfo('dyna'); X = interfileread('dyna'); 3-20 Working with High Dynamic Range Images Working with High Dynamic Range Images In this section... “Understanding Dynamic Range” on page 3-21 “Reading a High Dynamic Range Image” on page 3-21 “Creating a High Dynamic Range Image” on page 3-22 “Viewing a High Dynamic Range Image” on page 3-22 “Writing a High Dynamic Range Image to a File” on page 3-23 Understanding Dynamic Range Dynamic range refers to the range of brightness levels, from dark to light. The dynamic range of real-world scenes can be quite high. High Dynamic Range (HDR) images attempt to capture the whole tonal range of real-world scenes (called scene-referred), using 32-bit floating-point values to store each color channel. HDR images contain a high level of detail, close to the range of human vision. The toolbox includes functions for reading, creating, and writing HDR images, and a tone-map operator for displaying HDR images on a computer monitor. Reading a High Dynamic Range Image To read a high dynamic range image into the MATLAB workspace, use the hdrread function. hdr_image = hdrread('office.hdr'); The output image hdr_image is an m-by-n-by-3 image of type single. whos Name hdr_image Size Bytes Class 665x1000x3 7980000 single Attributes Note, however, that before you can display a high dynamic range image, you must convert it to a dynamic range appropriate to a computer display, a process called tone mapping. Tone mapping algorithms scale the dynamic range down while attempting to preserve the appearance of the original 3-21 3 Reading and Writing Image Data image. For more information, see “Viewing a High Dynamic Range Image” on page 3-22. Creating a High Dynamic Range Image To create a high dynamic range image from a group of low dynamic range images, use the makehdr function. Note that the low dynamic range images must be spatially registered and the image files must contain EXIF metadata. Specify the low-dynamic range images in a cell array. hdr_image = makehdr(files); Viewing a High Dynamic Range Image If you try to view a HDR image using imshow, the image does not display correctly. To view an HDR image, you must first convert the data to a dynamic range that can be displayed correctly on a computer. Use the tonemap function to 3-22 Working with High Dynamic Range Images perform this conversion. tonemap converts the high dynamic range image into an RGB image of class uint8. rgb = tonemap(hdr_image); whos Name hdr_image rgb Size 665x1000x3 665x1000x3 Bytes 7980000 1995000 Class Attributes single uint8 After converting the HDR image, try to display the image again. imshow(rgb); Writing a High Dynamic Range Image to a File To write a high dynamic range image from the MATLAB workspace into a file, use the hdrwrite function. 3-23 3 Reading and Writing Image Data hdrwrite(hdr,'filename'); 3-24 4 Displaying and Exploring Images This section describes the image display and exploration tools provided by the Image Processing Toolbox software. • “Image Display and Exploration Overview” on page 4-2 • “Displaying Images Using the imshow Function” on page 4-4 • “Using the Image Viewer App to Explore Images” on page 4-11 • “Exploring Very Large Images” on page 4-21 • “Using Image Viewer App Navigation Aids” on page 4-23 • “Getting Information about the Pixels in an Image” on page 4-30 • “Measuring the Distance Between Two Pixels” on page 4-37 • “Getting Information About an Image Using the Image Information Tool” on page 4-40 • “Adjusting Image Contrast Using the Adjust Contrast Tool” on page 4-42 • “Crop an Image Using the Image Viewer App” on page 4-52 • “Viewing Image Sequences” on page 4-55 • “Displaying Different Image Types” on page 4-67 • “Adding a Colorbar to a Displayed Image” on page 4-73 • “Printing Images” on page 4-75 • “Setting Toolbox Preferences” on page 4-77 4 Displaying and Exploring Images Image Display and Exploration Overview The Image Processing Toolbox software includes two display functions, imshow and imtool. Both functions work within the Handle Graphics architecture: they create an image object and display it in an axes object contained in a figure object. imshow is the toolbox’s fundamental image display function. Use imshow when you want to display any of the different image types supported by the toolbox, such as grayscale (intensity), truecolor (RGB), binary, and indexed. For more information, see “Displaying Images Using the imshow Function” on page 4-4. The imshow function is also a key building block for image applications you can create using the toolbox modular tools. For more information, see .“Build Interactive Tools” The other toolbox display function, imtool, launches the Image Viewer app, which presents an integrated environment for displaying images and performing some common image-processing tasks. The Image Viewer provides all the image display capabilities of imshow but also provides access to several other tools for navigating and exploring images, such as scroll bars, the Pixel Region tool, the Image Information tool, and the Adjust Contrast tool. For more information, see “Using the Image Viewer App to Explore Images” on page 4-11. In general, using the toolbox functions to display images is preferable to using MATLAB image display functions image and imagesc because the toolbox functions set certainHandle Graphics properties automatically to optimize the image display. The following table lists these properties and their settings for each image type. In the table, X represents an indexed image, I represents a grayscale image, BW represents a binary image, and RGB represents a truecolor image. Note Both imshow and imtool can perform automatic scaling of image data. When called with the syntax imshow(I,'DisplayRange',[]), and similarly for imtool, the functions set the axes CLim property to [min(I(:)) max(I(:))]. CDataMapping is always scaled for grayscale images, so that the value min(I(:)) is displayed using the first colormap color, and the value max(I(:)) is displayed using the last colormap color. 4-2 Image Display and Exploration Overview Handle Graphics Property Indexed Images Grayscale Images Binary Images Truecolor Images CData (Image) Set to the data in Set to the data in Set to data in BW Set to data in RGB X I Set to 'direct' Set to 'scaled' Set to 'direct' Ignored when CData is 3-D CLim (Axes) Does not apply double: [0 1] uint8: [0 255] uint16: [0 65535] Set to [0 1] Ignored when CData is 3-D Colormap Set to data in map Set to grayscale colormap Set to a grayscale colormap whose values range from black to white Ignored when CData is 3-D CDataMapping (Image) (Figure) 4-3 4 Displaying and Exploring Images Displaying Images Using the imshow Function In this section... “Overview” on page 4-4 “Specifying the Initial Image Magnification” on page 4-6 “Controlling the Appearance of the Figure” on page 4-6 “Displaying Each Image in a Separate Figure” on page 4-7 “Displaying Multiple Images in the Same Figure” on page 4-8 Overview To display image data, use the imshow function. The following example reads an image into the MATLAB workspace and then displays the image in a MATLAB figure window. moon = imread('moon.tif'); imshow(moon); The imshow function displays the image in a MATLAB figure window, as shown in the following figure. 4-4 Displaying Images Using the imshow Function Image Displayed in a Figure Window by imshow You can also pass imshow the name of a file containing an image. imshow('moon.tif'); This syntax can be useful for scanning through images. Note, however, that when you use this syntax, imread does not store the image data in the MATLAB workspace. If you want to bring the image into the workspace, you must use the getimage function, which retrieves the image data from the current Handle Graphics image object. This example assigns the image data from moon.tif to the variable moon, if the figure window in which it is displayed is currently active. moon = getimage; For more information about using imshow to display the various image types supported by the toolbox, see “Displaying Different Image Types” on page 4-67. 4-5 4 Displaying and Exploring Images Specifying the Initial Image Magnification By default, imshow attempts to display an image in its entirety at 100% magnification (one screen pixel for each image pixel). However, if an image is too large to fit in a figure window on the screen at 100% magnification, imshow scales the image to fit onto the screen and issues a warning message. To override the default initial magnification behavior for a particular call to imshow, specify the InitialMagnification parameter. For example, to view an image at 150% magnification, use this code. pout = imread('pout.tif'); imshow(pout, 'InitialMagnification', 150) imshow attempts to honor the magnification you specify. However, if the image does not fit on the screen at the specified magnification, imshow scales the image to fit and issues a warning message. You can also specify the text string 'fit' as the initial magnification value. In this case, imshow scales the image to fit the current size of the figure window. To change the default initial magnification behavior of imshow, set the ImshowInitialMagnification toolbox preference. To set the preference, open the Image Processing Toolbox Preferences dialog by calling iptprefs or by selecting Preferences from the MATLAB Desktop File menu. When imshow scales an image, it uses interpolation to determine the values for screen pixels that do not directly correspond to elements in the image matrix. For more information, see “Specifying the Interpolation Method” on page 6-3. Controlling the Appearance of the Figure By default, when imshow displays an image in a figure, it surrounds the image with a gray border. You can change this default and suppress the border using the 'border' parameter, as shown in the following example. imshow('moon.tif','Border','tight') 4-6 Displaying Images Using the imshow Function The following figure shows the same image displayed with and without a border. Image Displayed With and Without a Border The 'border' parameters affect only the image being displayed in the call to imshow. If you want all the images that you display using imshow to appear without the gray border, set the Image Processing Toolbox 'ImshowBorder' preference to 'tight'. You can also use preferences to include visible axes in the figure. For more information about preferences, see iptprefs. Displaying Each Image in a Separate Figure The simplest way to display multiple images is to display them in separate figure windows. MATLAB does not place any restrictions on the number of images you can display simultaneously. imshow always displays an image in the current figure. If you display two images in succession, the second image replaces the first image. To view 4-7 4 Displaying and Exploring Images multiple figures with imshow, use the figure command to explicitly create a new empty figure before calling imshow for the next image. For example, to view the first three frames in an array of grayscale images I, imshow(I(:,:,:,1)) figure, imshow(I(:,:,:,2)) figure, imshow(I(:,:,:,3)) Displaying Multiple Images in the Same Figure You can use the imshow function with the MATLAB subplot function or the MATLAB subimage function to display multiple images in a single figure window. For additional options, see “Viewing Image Sequences” on page 4-55. Note The Image Viewer app (imtool) does not support this capability. Dividing a Figure Window into Multiple Display Regions subplot divides a figure into multiple display regions. The syntax of subplot is subplot(m,n,p) This syntax divides the figure into an m-by-n matrix of display regions and makes the pth display region active. Note When you use subplot to display multiple color images in one figure window, the images must share the colormap of the last image displayed. In some cases, as illustrated by the following example, the display results can be unacceptable. As an alternative, you can use the subimage function, described in “Using the subimage Function to Display Multiple Images” on page 4-10, or you can map all images to the same colormap as you load them. 4-8 Displaying Images Using the imshow Function For example, you can use this syntax to display two images side by side. [X1,map1]=imread('forest.tif'); [X2,map2]=imread('trees.tif'); subplot(1,2,1), imshow(X1,map1) subplot(1,2,2), imshow(X2,map2) In the figure, note how the first image displayed, X1, appears dark after the second image is displayed. Two Images in Same Figure Using the Same Colormap 4-9 4 Displaying and Exploring Images Using the subimage Function to Display Multiple Images subimage converts images to truecolor before displaying them and therefore circumvents the colormap sharing problem. This example uses subimage to display the forest and the trees images with better results. [X1,map1]=imread('forest.tif'); [X2,map2]=imread('trees.tif'); subplot(1,2,1), subimage(X1,map1) subplot(1,2,2), subimage(X2,map2) Two Images in Same Figure Using Separate Colormaps 4-10 Using the Image Viewer App to Explore Images Using the Image Viewer App to Explore Images In this section... “Image Viewer App Overview” on page 4-11 “Opening the Image Viewer” on page 4-13 “Specifying the Initial Image Magnification” on page 4-14 “Specifying the Colormap” on page 4-15 “Importing Image Data from the Workspace” on page 4-17 “Exporting Image Data to the Workspace” on page 4-18 “Saving the Image Data Displayed in the Image Viewer” on page 4-18 “Closing the Image Viewer” on page 4-20 “Printing the Image in the Image Viewer” on page 4-20 Image Viewer App Overview The Image Viewer app is an image display and exploration tool that presents an integrated environment for displaying images and performing common image-processing tasks. The Image Viewer provides access to several other tools: • Pixel Information tool — for getting information about the pixel under the pointer • Pixel Region tool — for getting information about a group of pixels • Distance tool — for measuring the distance between two pixels • Image Information tool — for getting information about image and image file metadata • Adjust Contrast tool and associated Window/Level tool — for adjusting the contrast of the image displayed in the Image Viewer and modifying the actual image data. You can save the adjusted data to the workspace or a file. • Crop Image tool — for defining a crop region on the image and cropping the image. You can save the cropped image to the workspace or a file. 4-11 4 Displaying and Exploring Images • Display Range tool — for determining the display range of the image data In addition, the Image Viewer provides several navigation aids that can help explore large images: • Overview tool — for determining what part of the image is currently visible in the Image Viewer and changing this view. • Pan tool — for moving the image to view other parts of the image • Zoom tool — for getting a closer view of any part of the image. • Scroll bars — for navigating over the image. The following figure shows the image displayed in the Image Viewer app with many of the related tools open and active. Image Viewer App and Related Tools 4-12 Using the Image Viewer App to Explore Images Opening the Image Viewer To start the Image Viewer, click Image Viewer on the Apps tab, or use the imtool function. You can also start another Image Viewer from within an existing Image Viewer by using the New option from the File menu. To bring image data into the Image Viewer, you can use either the Open or Import from Workspace options from the File menu — see “Importing Image Data from the Workspace” on page 4-17. You can also specify the name of the MATLAB workspace variable that contains image data when you call imtool, as follows: moon = imread('moon.tif'); imtool(moon) Alternatively, you can specify the name of the graphics file containing the image. This syntax can be useful for scanning through graphics files. imtool('moon.tif'); Note When you specify a file name, the image data is not stored in a MATLAB workspace variable. To bring the image displayed in the Image Viewer into the workspace, you must use the getimage function or the Export to Workspace option from the Image Viewer File menu — see “Exporting Image Data to the Workspace” on page 4-18. 4-13 4 Displaying and Exploring Images Specifying the Initial Image Magnification The Image Viewer attempts to display an image in its entirety at 100% magnification (one screen pixel for each image pixel) and always honors any magnification value you specify. If the image is too big to fit in a figure on the screen, the Image Viewer shows only a portion of the image, adding scroll bars to allow navigation to parts of the image that are not currently visible. If the specified magnification would make the image too large to fit on the screen, the Image Viewer scales the image to fit, without issuing a warning. This is the default behavior, specified by the 'InitialMagnification' parameter value 'adaptive'. To override this default initial magnification behavior for a particular call to imtool, specify the InitialMagnification parameter. For example, to view an image at 150% magnification, use this code. pout = imread('pout.tif'); imtool(pout, 'InitialMagnification', 150) You can also specify the text string 'fit' as the initial magnification value. In this case, imtool scales the image to fit the default size of a figure window. Another way to change the default initial magnification behavior of the Image Viewer is to set the ImtoolInitialMagnification toolbox preference. The magnification value you specify remains in effect until you change it. To set the preference, use iptsetpref or open the Image Processing Preferences panel by calling iptprefs or by selecting File > Preferences in the Image Viewer menu. To learn more about toolbox preferences, see iptprefs. When the Image Viewer scales an image, it uses interpolation to determine the values for screen pixels that do not directly correspond to elements in the image matrix. For more information, see “Specifying the Interpolation Method” on page 6-3. 4-14 Using the Image Viewer App to Explore Images Specifying the Colormap A colormap is a matrix that can have any number of rows, but must have three columns. Each row in the colormap is interpreted as a color, with the first element specifying the intensity of red, the second green, and the third blue. To specify the color map used to display an indexed image or a grayscale image in the Image Viewer, select the Choose Colormap option on the Tools menu. This activates the Choose Colormap tool. Using this tool you can select one of the MATLAB colormaps or select a colormap variable from the MATLAB workspace. When you select a colormap, the Image Viewer executes the colormap function you specify and updates the image displayed. You can edit the colormap command in the Evaluate Colormap text box; for example, you can change the number of entries in the colormap (default is 256). You can enter your own colormap function in this field. Press Enter to execute the command. When you choose a colormap, the image updates to use the new map. If you click OK, the Image Viewer applies the colormap and closes the Choose Colormap tool. If you click Cancel, the image reverts to the previous colormap. 4-15 4 Displaying and Exploring Images Choose from MATLAB colormaps. Specify colormap in the workspace. Evaluate a colormap function. Click OK to select the colormap and close the dialog box. Image Viewer Choose Colormap Tool 4-16 Using the Image Viewer App to Explore Images Importing Image Data from the Workspace To import image data from the MATLAB workspace into the Image Viewer, use the Import from Workspace option on the Image Viewer File menu. In the dialog box, shown below, you select the workspace variable that you want to import into the workspace. The following figure shows the Import from Workspace dialog box. You can use the Filter menu to limit the images included in the list to certain image types, i.e., binary, indexed, intensity (grayscale), or truecolor. Image Viewer Import from Workspace Dialog Box 4-17 4 Displaying and Exploring Images Exporting Image Data to the Workspace To export the image displayed in the Image Viewer to the MATLAB workspace, you can use the Export to Workspace option on the Image Viewer File menu. (Note that when exporting data, changes to the display range will not be preserved.) In the dialog box, shown below, you specify the name you want to assign to the variable in the workspace. By default, the Image Viewer prefills the variable name field with BW, for binary images, RGB, for truecolor images, and I for grayscale or indexed images. If the Image Viewer contains an indexed image, this dialog box also contains a field where you can specify the name of the associated colormap. Image Viewer Export Image to Workspace Dialog Box Using the getimage Function to Export Image Data You can also use the getimage function to bring image data from the Image Viewer into the MATLAB workspace. The getimage function retrieves the image data (CData) from the current Handle Graphics image object. Because, by default, the Image Viewer does not make handles to objects visible, you must use the toolbox function imgca to get a handle to the image axes displayed in the Image Viewer. The following example assigns the image data from moon.tif to the variable moon if the figure window in which it is displayed is currently active. moon = getimage(imgca); Saving the Image Data Displayed in the Image Viewer To save the image data displayed in the Image Viewer, select the Save as option from the Image Viewer File menu. The Image Viewer opens the Save Image dialog box, shown in the following figure. Use this dialog box to navigate your file system to determine where to save the image file and 4-18 Using the Image Viewer App to Explore Images specify the name of the file. Choose the graphics file format you want to use from among many common image file formats listed in the Files of Type menu. If you do not specify a file name extension, the Image Viewer adds an extension to the file associated with the file format selected, such as .jpg for the JPEG format. Select image file format. Image Viewer Save Image Dialog Box Note Changes you make to the display range will not be saved. If you would like to preserve your changes, use imcontrast. 4-19 4 Displaying and Exploring Images Closing the Image Viewer To close the Image Viewer, use the Close button in the window title bar or select the Close option from the Image Viewer File menu. If you used the imtool function to start the Image Viewer you can get a handle to the app. You can use this handle to close the app. When you close the Image Viewer, any related tools that are currently open also close. Because the Image Viewer does not make the handles to its figure objects visible, the Image Viewer does not close when you call the MATLAB close all command. If you want to close multiple Image Viewers, use the syntax imtool close all or select Close all from the Image Viewer File menu. Printing the Image in the Image Viewer To print the image displayed in the Image Viewer, select the Print to Figure option from the File menu. The Image Viewer opens another figure window and displays the image. Use the Print option on the File menu of this figure window to print the image. See “Printing Images” on page 4-75 for more information. 4-20 Exploring Very Large Images Exploring Very Large Images In this section... “Overview” on page 4-21 “Creating an R-Set File” on page 4-21 “Opening an R-Set File” on page 4-22 Overview If you are viewing a very large image, it might not load in Image Viewer, or it could load, but zooming and panning are slow. In either case, creating a reduced resolution data set (R-Set) can improve performance. Use the Image Viewer to navigate an R-Set image the same way you navigate a standard image. Creating an R-Set File To create an R-Set file, use the function rsetwrite. For example, to create an R-Set from a TIFF file called 'LargeImage.tif', enter the following: rsetfile = rsetwrite ('LargeImage.tif') rsetwrite saves an R-Set file named 'LargeImage.rset' in the current directory. Or, if you want to save the R-Set file under a different name, enter the following: rsetfile = rsetwrite('LargeImage.tif', 'New_Name') You can create an R-Set file directly from a TIFF or NITF file, or you can create one from another type of image file by first creating an Image Adapter object. See “Working with Data in Unsupported Formats” on page 15-17 for more information. The time required to create an R-Set varies, depending on the size of the initial file and the capability of your machine. A progress bar shows an estimate of time required. If you cancel the operation, processing stops, no file is written, and the rsetfile variable will be empty. 4-21 4 Displaying and Exploring Images Opening an R-Set File Open an R-Set file from the command line: imtool('LargeImage.rset') 4-22 Using Image Viewer App Navigation Aids Using Image Viewer App Navigation Aids In this section... “Navigating an Image Using the Overview Tool” on page 4-23 “Panning the Image Displayed in the Image Viewer” on page 4-26 “Zooming In and Out on an Image in the Image Viewer App” on page 4-27 “Specifying the Magnification of the Image” on page 4-27 Navigating an Image Using the Overview Tool If an image is large or viewed at a large magnification, the Image Viewer displays only a portion of the entire image and automatically includes scroll bars to allow navigation around the image. To determine which part of the image is currently visible in the Image Viewer, use the Overview tool. The Overview tool displays the entire image, scaled to fit. Superimposed over this view of the image is a rectangle, called the detail rectangle. The detail rectangle shows which part of the image is currently visible in the Image Viewer. You can change the portion of the image visible in the Image Viewer by moving the detail rectangle over the image in the Overview tool. 4-23 4 Displaying and Exploring Images Overview tool button Overview tool Detail rectangle Image Viewer with Overview Tool The following sections provide more information about using the Overview tool. • “Starting the Overview Tool” on page 4-24 • “Moving the Detail Rectangle to Change the Image View” on page 4-25 • “Specifying the Color of the Detail Rectangle” on page 4-25 • “Getting the Position and Size of the Detail Rectangle” on page 4-25 • “Printing the View of the Image in the Overview Tool” on page 4-26 Starting the Overview Tool You can start the Overview tool by clicking the Overview button in the Image Viewer toolbar or by selecting the Overview option from the Image 4-24 Using Image Viewer App Navigation Aids ViewerTools menu. You can also change the preferences, so the Overview tool will open automatically when you open the Image Viewer. For more information on setting preferences, see iptprefs. Moving the Detail Rectangle to Change the Image View 1 Start the Overview tool by clicking the Overview button in the Image Viewer toolbar or by selecting Overview from the Tools menu. The Overview tool opens in a separate window containing a view of the entire image, scaled to fit. If the Overview tool is already active, clicking the Overview button brings the tool to the front of the windows open on your screen. 2 Using the mouse, move the pointer into the detail rectangle. The pointer changes to a fleur, . 3 Press and hold the mouse button to drag the detail rectangle anywhere on the image. The Image Viewer updates the view of the image to make the specified region visible. Specifying the Color of the Detail Rectangle By default, the color of the detail rectangle in the Overview tool is blue. You can change the color of the rectangle to achieve better contrast with the predominant color of the underlying image. To do this, right-click anywhere inside the boundary of the detail rectangle and select a color from the Set Color option on the context menu. Getting the Position and Size of the Detail Rectangle To get the current position and size of the detail rectangle, right-click anywhere inside it and select Copy Position from the context menu. You can also access this option from the Edit menu of the Overview tool. This option copies the position information to the clipboard. The position information is a vector of the form [xmin ymin width height]. You can paste this position vector into the MATLAB workspace or another application. 4-25 4 Displaying and Exploring Images Printing the View of the Image in the Overview Tool You can print the view of the image displayed in the Overview tool. Select the Print to Figure option from the Overview tool File menu. See “Printing Images” on page 4-75 for more information. Panning the Image Displayed in the Image Viewer To change the portion of the image displayed in the Image Viewer, use the Pan tool to move the image displayed in the window. This is called panning the image. 1 Click the Pan tool button in the toolbar or select Pan from the Tools menu. When the Pan tool is active, a checkmark appears next to the Pan selection in the menu. 2 Move the pointer over the image in the Image Viewer, using the mouse. The pointer changes to an open-hand shape . 3 Press and hold the mouse button and drag the image in the Image Viewer. When you drag the image, the pointer changes to the closed-hand shape . 4 To turn off panning, click the Pan tool button again or click the Pan option in the Tools menu. Note As you pan the image in the Image Viewer, the Overview tool updates the position of the detail rectangle — see “Navigating an Image Using the Overview Tool” on page 4-23. 4-26 Using Image Viewer App Navigation Aids Zooming In and Out on an Image in the Image Viewer App To enlarge an image to get a closer look or shrink an image to see the whole image in context, use the Zoom buttons on the toolbar. (You can also zoom in or out on an image by changing the magnification — see “Specifying the Magnification of the Image” on page 4-27 or by using the Ctrl+Plus or Ctrl+Minus keys. Note that these are the Plus(+) and Minus(-) keys on the numeric keypad of your keyboard.) 1 Click the appropriate magnifying glass button in the Image Viewer toolbar or select the Zoom In or Zoom Out option in the Tools menu. When the Zoom tool is active, a checkmark appears next to the appropriate Zoom selection in the menu. 2 Move the pointer over the image you want to zoom in or out on, using the mouse. The pointer changes to the appropriate magnifying glass icon. With each click, the Image Viewer changes the magnification of the image, centering the new view of the image on the spot where you clicked. When you zoom in or out on an image, the magnification value displayed in the magnification edit box changes and the Overview window updates the position of the detail rectangle. 3 To leave zoom mode, click the active zoom button again to deselect it or click the Zoom option in the Tools menu. Specifying the Magnification of the Image To enlarge an image to get a closer look or to shrink an image to see the whole image in context, you can use the magnification edit box, shown in the following figure. (You can also use the Zoom buttons to enlarge or shrink an image. See “Zooming In and Out on an Image in the Image Viewer App” on page 4-27 for more information.) 4-27 4 Displaying and Exploring Images Magnification menu Magnification edit box Image Viewer Magnification Edit Box and Menu To change the magnification of an image, 1 Move the pointer into the magnification edit box. The pointer changes to the text entry cursor. 2 Type a new value in the magnification edit box and press Enter. The Image Viewer changes the magnification of the image and displays the new view in the window. You can also specify a magnification by clicking the menu associated with the magnification edit box and selecting from a list of preset magnifications. If 4-28 Using Image Viewer App Navigation Aids you choose the Fit to Window option, the Image Viewer scales the image so that the entire image is visible. 4-29 4 Displaying and Exploring Images Getting Information about the Pixels in an Image In this section... “Determining the Value of Individual Pixels” on page 4-30 “Determining the Values of a Group of Pixels” on page 4-32 “Determining the Display Range of an Image” on page 4-35 Determining the Value of Individual Pixels The Image Viewer displays information about the location and value of individual pixels in an image in the bottom left corner of the tool. (You can also obtain this information by opening a figure with imshow and then calling impixelinfo from the command line.) The pixel value and location information represent the pixel under the current location of the pointer. The Image Viewer updates this information as you move the pointer over the image. For example, view an image in the Image Viewer. imtool('moon.tif') 4-30 Getting Information about the Pixels in an Image The following figure shows the Image Viewer with pixel location and value displayed in the Pixel Information tool. For more information, see “Saving the Pixel Value and Location Information” on page 4-31. Pixel under the pointer Pixel value and location information Pixel Information in Image Viewer App Saving the Pixel Value and Location Information To save the pixel location and value information displayed, right-click a pixel in the image and choose the Copy pixel info option. The Image Viewer copies the x- and y-coordinates and the pixel value to the clipboard. To paste this pixel information into the MATLAB workspace or another application, right-click and select Paste from the context menu. 4-31 4 Displaying and Exploring Images Determining the Values of a Group of Pixels To view the values of pixels in a specific region of an image displayed in the Image Viewer, use the Pixel Region tool. The Pixel Region tool superimposes a rectangle, called the pixel region rectangle, over the image displayed in the Image Viewer. This rectangle defines the group of pixels that are displayed, in extreme close-up view, in the Pixel Region tool window. The following figure shows the Image Viewer with the Pixel Region tool. Note how the Pixel Region tool includes the value of each pixel in the display. Pixel Region tool button Pixel Region rectangle Pixel Region tool The following sections provide more information about using the Pixel Region tool. • “Selecting a Region” on page 4-33 • “Customizing the View” on page 4-33 4-32 Getting Information about the Pixels in an Image • “Determining the Location of the Pixel Region Rectangle” on page 4-34 • “Printing the View of the Image in the Pixel Region Tool” on page 4-35 Selecting a Region 1 To start the Pixel Region tool, click the Pixel Region button in the Image Viewer toolbar or select the Pixel Region option from the Tools menu. (Another option is to open a figure using imshow and then call impixelregion from the command line.) The Image Viewer displays the pixel region rectangle Pixel Region tool. in the center of the target image and opens the Note Scrolling the image can move the pixel region rectangle off the part of the image that is currently displayed. To bring the pixel region rectangle back to the center of the part of the image that is currently visible, click the Pixel Region button again. For help finding the Pixel Region tool in large images, see “Determining the Location of the Pixel Region Rectangle” on page 4-34. 2 Using the mouse, position the pointer over the pixel region rectangle. The pointer changes to the fleur shape, . 3 Click the left mouse button and drag the pixel region rectangle to any part of the image. As you move the pixel region rectangle over the image, the Pixel Region tool updates the pixel values displayed. You can also move the pixel region rectangle by moving the scroll bars in the Pixel Region tool window. Customizing the View To get a closer view of image pixels, use the zoom buttons on the Pixel Region tool toolbar. As you zoom in, the size of the pixels displayed in the Pixel Region tool increase and fewer pixels are visible. As you zoom out, the size of the pixels in the Pixel Region tool decrease and more pixels are visible. To change the number of pixels displayed in the tool, without changing the magnification, resize the Pixel Region tool using the mouse. 4-33 4 Displaying and Exploring Images As you zoom in or out, note how the size of the pixel region rectangle changes according to the magnification. You can resize the pixel region rectangle using the mouse. Resizing the pixel region rectangle changes the magnification of pixels displayed in the Pixel Region tool. If the magnification allows, the Pixel Region tool overlays each pixel with its numeric value. For RGB images, this information includes three numeric values, one for each band of the image. For indexed images, this information includes the index value and the associated RGB value. If you would rather not see the numeric values in the display, go to the Pixel Region tool Edit menu and clear the Superimpose Pixel Values option. Pixel Region Tool Edit Menu Determining the Location of the Pixel Region Rectangle To determine the current location of the pixel region in the target image, you can use the pixel information given at the bottom of the tool. This information includes the x- and y-coordinates of pixels in the target image coordinate system. When you move the pixel region rectangle over the target image, the pixel information given at the bottom of the tool is not updated until you move the cursor back over the Pixel Region tool. You can also retrieve the current position of the pixel region rectangle by selecting the Copy Position option from the Pixel Region tool Edit menu. 4-34 Getting Information about the Pixels in an Image This option copies the position information to the clipboard. The position information is a vector of the form [xmin ymin width height]. To paste this position vector into the MATLAB workspace or another application, right-click and select Paste from the context menu. The following figure shows these components of the Pixel Region tool. Pixel Region Rectangle Location Information Printing the View of the Image in the Pixel Region Tool You can print the view of the image displayed in the Pixel Region tool. Select the Print to Figure option from the Pixel Region tool File menu. See “Printing Images” on page 4-75 for more information. Determining the Display Range of an Image The Image Viewer provides information about the display range of pixels in a grayscale image. The display range is the value of the axes CLim property, which controls the mapping of image CData to the figure colormap. CLim is 4-35 4 Displaying and Exploring Images a two-element vector [cmin cmax] specifying the CData value to map to the first color in the colormap (cmin) and the CData value to map to the last color in the colormap (cmax). Data values in between are linearly scaled. The Image Viewer displays this information in the Display Range tool at the bottom right corner of the window. The Image Viewer does not show the display range for indexed, truecolor, or binary images. (You can also obtain this information by opening a figure window with imshow and then calling imdisplayrange from the command line.) For example, view an image in the Image Viewer. imtool('moon.tif') The following figure shows the Image Viewer displaying the image with display range information. Display Range tool Display Range Information in Image Viewer App 4-36 Measuring the Distance Between Two Pixels Measuring the Distance Between Two Pixels In this section... “Using the Distance Tool” on page 4-37 “Exporting Endpoint and Distance Data” on page 4-38 “Customizing the Appearance of the Distance Tool” on page 4-39 Using the Distance Tool 1 Display an image in the Image Viewer. imtool('moon.tif') 2 Click the Distance tool button in the Image Viewer toolbar or select Measure Distance from the Tools menu. The Distance tool allows you to measure distance with a click-and-drag approach. When you move the pointer over the image, the pointer changes to cross hairs . Position the cross hairs at the beginning of the region you wish to measure, hold down the mouse button, drag the cross hairs to the end of the region, and release the button. The Distance tool displays the Euclidean distance between the two endpoints of the line in a label superimposed over the line. The tool specifies the distance in data units determined by the XData and YData properties, which is pixels, by default. 4-37 4 Displaying and Exploring Images Distance tool button Distance tool 3 An alternative to using the Distance tool in Image Viewer is to open a figure window using imshow and then call imdistline. The Distance tool appears as a horizontal line displayed over the image. You can reposition the line or grab either of its endpoints to resize the tool. Exporting Endpoint and Distance Data To save the endpoint locations and distance information, right-click the Distance tool and choose the Export to Workspace option from the context menu. The Distance tool opens the Export to Workspace dialog box. You can use this dialog box to specify the names of the variables used to store this information. 4-38 Measuring the Distance Between Two Pixels After you click OK, the Distance tool creates the variables in the workspace, as in the following example. whos Name distance point1 point2 Size 1x1 1x2 1x2 Bytes 8 16 16 Class Attributes double double double Customizing the Appearance of the Distance Tool Using the Distance tool context menu, you can customize many aspects of the Distance tool appearance and behavior. Position the pointer over the line and right-click to access these context menu options. • Toggling the distance tool label on and off using the Show Distance Label option. • Changing the color used to display the Distance tool line using the Set color option. • Constraining movement of the tool to either horizontal or vertical using the Constrain drag option. • Deleting the distance tool object using the Delete option. Right-click the Distance tool to access this context menu. 4-39 4 Displaying and Exploring Images Getting Information About an Image Using the Image Information Tool To get information about the image displayed in the Image Viewer, use the Image Information tool. The Image Information tool can provide two types of information about an image: • Basic information — Includes width, height, class, and image type. For grayscale and indexed images, this information also includes the minimum and maximum intensity values. • Image metadata — Displays all the metadata from the graphics file that contains the image. This is the same information returned by the imfinfo function or the dicominfo function. Note The Image Information tool can display image metadata only when you specify the filename containing the image to Image Viewer, e.g., imtool('moon.tif'). For example, view an image in the Image Viewer. imtool('moon.tif') Start the Image Information tool by clicking the Image Information button in the Image Viewer toolbar or selecting the Image Information option from the Tools menu in the Image Viewer. (Another option is to open a figure window using imshow and then call imageinfo from the command line.) 4-40 Getting Information About an Image Using the Image Information Tool The following figure shows the Image Viewer with the Image Information tool. In the figure, the Image Information tool displays both basic image information and image metadata because a file name was specified with imtool. Image Information tool button Image Information tool Basic image information Image metadata Image Viewer App with Image Information Tool 4-41 4 Displaying and Exploring Images Adjusting Image Contrast Using the Adjust Contrast Tool In this section... “Understanding Contrast Adjustment” on page 4-42 “Starting the Adjust Contrast Tool” on page 4-43 “Using the Histogram Window to Adjust Image Contrast” on page 4-46 “Using the Window/Level Tool to Adjust Image Contrast” on page 4-47 “Modifying Image Data” on page 4-50 Understanding Contrast Adjustment An image lacks contrast when there are no sharp differences between black and white. Brightness refers to the overall lightness or darkness of an image. To change the contrast or brightness of an image, the Adjust Contrast tool performs contrast stretching. In this process, pixel values below a specified value are displayed as black, pixel values above a specified value are displayed as white, and pixel values in between these two values are displayed as shades of gray. The result is a linear mapping of a subset of pixel values to the entire range of grays, from black to white, producing an image of higher contrast. The following figure shows this mapping. Note that the lower limit and upper limit mark the boundaries of the window, displayed graphically as the red-tinted window in the Adjust Contrast tool — see “Starting the Adjust Contrast Tool” on page 4-43 4-42 Adjusting Image Contrast Using the Adjust Contrast Tool Relationship of Pixel Values to Display Range The Adjust Contrast tool accomplishes this contrast stretching by modifying the CLim property of the axes object that contains the image. The CLim property controls the mapping of image pixel values to display intensities. By default, the Image Viewer sets the CLim property to the default display range according to the data type. For example, the display range of an image of class uint8 is from 0 to 255. When you use the Adjust Contrast tool, you change the contrast in the image by changing the display range which affects the mapping between image pixel values and the black-to-white range. You create a window over the range that defines which pixels in the image map to the black in the display range by shrinking the range from the bottom up. Starting the Adjust Contrast Tool This section describes how to use the Adjust Contrast tool in the Image Viewer. 1 View an image in the Image Viewer. imtool('moon.tif') You can also use the Adjust Contrast tool independent of the Image Viewer by calling the imcontrast function. 4-43 4 Displaying and Exploring Images in the Image Viewer toolbar, or select the Adjust Contrast option from the Image Viewer Tools menu. The Adjust Contrast tool opens in a separate window containing a histogram of the image displayed in the Image Viewer. The histogram shows the data range of the image and the display range of the image. The data range is the range of intensity values actually used in the image. The display range is the black-to-white mapping used to display the image, which is determined by the image class. The Adjust Contrast tool works by manipulating the display range; the data range of the image remains constant. 2 Click Adjust Contrast For example, in the following figure, the histogram for the image shows that the data range of the image is 74 to 224 and the display range is the default display range for the uint8 class, 0 to 255. The pixel values for the image are clustered in the middle of the display range. Adjusting the contrast spreads the pixel values across the display range, revealing much more detail in the image. To adjust the contrast of the image, you can manipulate the red-tinted rectangular box, called a window, that the Adjust Contrast tool overlays on the histogram. By changing the size and position of this window using the mouse, you can modify the display range of the image and improve its contrast and brightness — see “Using the Histogram Window to Adjust Image Contrast” on page 4-46. 4-44 Adjusting Image Contrast Using the Adjust Contrast Tool Adjust Contrast tool button Adjust Contrast tool Data range Contrast adjustment window Image histogram Click to change pixel values in image. Adjust Contrast in Image Viewer 4-45 4 Displaying and Exploring Images Note You can also use the Window/Level tool to adjust contrast and brightness using the mouse. (The name comes from medical applications.) Click Window/Level in the Image Viewer toolbar or select the Window/Level option from the Image Viewer Tools menu. For more information about using the Window/Level tool, see “Using the Window/Level Tool to Adjust Image Contrast” on page 4-47. When you close the Adjust Contrast tool, the Window/Level tool remains active. To turn off the Window/Level tool, click the Window/Level button or one of the navigation buttons in the Image Viewer toolbar. Using the Histogram Window to Adjust Image Contrast To adjust image contrast using the Adjust Contrast tool, you manipulate the size of the red-tinted window displayed over the histogram, using any of the following methods. • Grabbing one of the red handles on the right and left edges of the window and dragging it. You can also change the position of the window by grabbing the center line and dragging the window to the right or left. • Specifying the size and position of the window in the Minimum and Maximum fields. You can also define these values by clicking the dropper button associated with these fields. When you do this, the pointer becomes an eye dropper shape. Position the eye dropper pointer over the pixel in the image that you want to be the minimum (or maximum) value and click the mouse button. • Specifying the size and position of the window in the Width and Center fields. • Selecting the Match data range button in the Scale Display Range part of the tool. When you choose this option, the size of the window changes from the default display range to the data range of the image. • Trimming outliers at the top and bottom of the image data range. If you select the Eliminate outliers option, the Adjust Contrast tool removes the top 1% and the bottom 1%, but you can specify other percentages. When you specify a percentage, the Adjust Contrast tool applies half the 4-46 Adjusting Image Contrast Using the Adjust Contrast Tool percentage to the top and half to the bottom. (You can perform this same operation using the stretchlim function.) The following figure shows these methods of adjusting contrast. The Image Viewer updates the display range values displayed in the lower right corner of the Image Viewer as you change the size of the window. Specify minimum and maximum values. Drag either handle to resize window. Specify midpoint and width. Choose autoscaling option. Drag midline to move window. Using the Window/Level Tool to Adjust Image Contrast To start the Window/Level tool, click Window/Level toolbar. in the Image Viewer Using the Window/Level tool, you can change the contrast and brightness of an image by simply dragging the mouse over the image. Moving the mouse horizontally affects contrast; moving the mouse vertically affects brightness. Note that any contrast adjustments you make using the Window/Level tool are 4-47 4 Displaying and Exploring Images reflected immediately in the Adjust Contrast tool. For example, if you increase the brightness, the window in the Adjust Contrast moves over the histogram. The following table summarizes how these mouse motions affect the size and position of the window in the Adjust Contrast tool. Mouse Motion Effect Horizontally to the left Shrinks the window from both sides. Horizontally to the right Expands the window from both sides. Vertically up Moves the window to the right over the histogram, increasing brightness. Vertically down Moves the window to the left over the image histogram, decreasing brightness. To stop the Window/Level tool, click the Window/Level button in the Image Viewer toolbar, or click any of the navigation buttons in the toolbar. Adjust Contrast with the Window/Level Tool 1 Read an image from a sample DICOM file included with the toolbox. I = dicomread('CT-MONO2-16-ankle.dcm'); 2 View the image data using the Image Viewer. Because the image data is signed 16-bit data, this example uses the autoscaling syntax. imtool(I,'DisplayRange',[]) 3 Click the Window/Level button to start the tool, or select Window/Level from the Tools menu in the Image Viewer. 4-48 Adjusting Image Contrast Using the Adjust Contrast Tool Window/Level tool button 4 Move the pointer over the image. The pointer changes to the Window/Level cursor . 5 Click and drag the left (or right) mouse button and move the pointer horizontally to the left or right to adjust the contrast, or vertically up or down to change the brightness. 4-49 4 Displaying and Exploring Images Modifying Image Data By default, the Adjust Contrast tool adjusts the values of the pixels used to display the image in the Image Viewer but does not change the actual image data. To modify pixel values in the image to reflect the contrast adjustments you made, you must click the Adjust Data button. The following example illustrates this process. 1 Display an image in the Image Viewer. The example opens an image from a file. imtool('moon.tif'); 2 Start the Adjust Contrast tool by clicking the Adjust contrast button, , or by selecting Adjust Contrast from the Tools menu in the Image Viewer. 3 Adjust the contrast of the image. Use one of the mechanisms provided by Adjust Contrast tool, such as resizing the window over the histogram. See “Using the Histogram Window to Adjust Image Contrast” on page 4-46. You can also adjust contrast using the Window/Level tool, moving the pointer over the image. 4 Adjust the image data to reflect the contrast adjustment you just made. Click the Adjust Data button in the Adjust Contrast Tool. When you click the Adjust Data button, the histogram will update. You can then adjust the contrast again, if necessary. If you have other interactive modular tool windows open, they will update automatically to reflect the contrast adjustment. Note The Adjust Data button is unavailable until you make a change to the contrast of the image. Saving the Modified Image Data By default, if you close the Image Viewer, it does not save the modified image data. To save these changed values, use the Save As option from the Image 4-50 Adjusting Image Contrast Using the Adjust Contrast Tool Viewer File menu to store the modified data in a file or use the Export to Workspace option to save the modified data in a workspace variable. 4-51 4 Displaying and Exploring Images Crop an Image Using the Image Viewer App Cropping an image means creating a new image from a part of an original image. To crop an image using the Image Viewer, use the Crop Image tool. To use the Crop Image tool, follow this procedure. By default, if you close the Image Viewer, it does not save the modified image data. To save the cropped image, you can use the Save As option from the Image Viewer File menu to store the modified data in a file or use the Export to Workspace option to save the modified data in the workspace variable. 1 View an image in the Image Viewer. I = imread('moon.tif'); imtool(I) 2 Start the Crop Image tool by clicking Crop Image in the Image Viewer toolbar or selecting Crop Image from the Image Viewer Tools menu. (Another option is to open a figure window with imshow and call imcrop from the command line.) When you move the pointer over the image, the pointer changes to cross hairs . 3 Define the rectangular crop region, by clicking and dragging the mouse over the image. You can fine-tune the crop rectangle by moving and resizing the crop rectangle using the mouse. Or, if you want to crop a different region, move to the new location and click and drag again. To zoom in or out on the image while the Crop Image tool is active, use Ctrl+Plus or Ctrl+Minus keys. Note that these are the Plus(+) and Minus(-) keys on the numeric keypad of your keyboard. The following figure shows a crop rectangle being defined using the Crop Image tool. 4-52 Crop an Image Using the Image Viewer App Crop Image button Crop rectangle Resize handles 4 When you are finished defining the crop region, perform the crop operation. Double-click the left mouse button or right-click inside the region and select Crop Image from the context menu. The Image Viewer displays the cropped image. If you have other modular interactive tools open, they will update to show the newly cropped image. 4-53 4 Displaying and Exploring Images 5 To save the cropped image, use the Save as option or the Export to Workspace option on the Image Viewer File menu. 4-54 Viewing Image Sequences Viewing Image Sequences In this section... “Image Sequences” on page 4-55 “View Image Sequences in the Video Viewer App” on page 4-55 “Viewing Image Sequences as a Montage” on page 4-64 “Converting a Multiframe Image to a Movie” on page 4-66 Image Sequences Some applications create collections of images related by time, such as frames in a movie, or by (spatial location, such as magnetic resonance imaging (MRI) slices. These collections of images are referred to by a variety of names, such as image sequences, image stacks, or videos. The toolbox represents image sequences as four-dimensional arrays, where each separate image is called a frame, all frames are the same size, and the frames are concatenated along the fourth dimension. The Image Viewer and imshow can display one frame at a time, using standard MATLAB array indexing syntax, but cannot animate the sequence or provide any navigation within the sequence. A better choice to view image sequences is the Video Viewer app (implay). The Video Viewer app can animate the display of frames in an image sequence and provides playback controls that you can use to navigate among the frames in the sequence. To get a static view of all the frames in an image sequence at one time, use the montage function. For more information, see these additional topics. • “View Image Sequences in the Video Viewer App” on page 4-55 • “Viewing Image Sequences as a Montage” on page 4-64. • “Converting a Multiframe Image to a Movie” on page 4-66 View Image Sequences in the Video Viewer App This section describes how to use the Video Viewer app to view image sequences and provides information about configuring the Video Viewer app. • “View a Sequence of MRI Images Using the Video Viewer App” on page 4-56 4-55 4 Displaying and Exploring Images • “Configuring the Video Viewer App” on page 4-59 • “Specifying the Frame Rate” on page 4-62 • “Specifying the Color Map” on page 4-63 • “Getting Information about the Image Frame” on page 4-64 View a Sequence of MRI Images Using the Video Viewer App 1 Load the image sequence into the MATLAB workspace. For this example, load the MRI data from the file mristack.mat, which is included in the imdemos directory. load mristack This places a variable named mristack in your workspace. The variable is an array of 21 grayscale frames containing MRI images of the brain. Each frame is a 256-by-256 array of uint8 data. mristack 256x256x21 1276256 uint8 2 Click the Video Viewer app in the apps gallery and select the Import from workspace option on the File menu. You can also call implay, specifying the name of the image sequence variable as an argument. implay(mristack) The Video Viewer opens, displaying the first frame of the image sequence. Note how the Video Viewer displays information about the image sequence, such as the size of each frame and the total number of frames, at the bottom of the window. 4-56 Viewing Image Sequences Toolbar Playback toolbar Movie frames Player status Frame type (I or RGB) Frame size Current frame/ Frame rate and percentage total frames Note: + and of frame rate indicate playback achieved direction. 3 Explore the image sequence using Video Viewer Playback controls. To view the image sequence or video as an animation, click the Play button in the Playback toolbar, select Play from the Playback menu, or press P or the Space bar. By default, the Video Viewer plays the image sequence forward, once in its entirety, but you can view the frames in the image sequence in many ways, described in this table. As you view an image sequence, note how the Video Viewer updates the Status Bar at the bottom of the window. 4-57 4 Displaying and Exploring Images Viewing Option Playback Control Keyboard Shortcut Specify the direction in which to play the image sequence. Click the Playback mode button in the Playback toolbar or select Playback Modes from the Playback menu. You can select forward, backward, or autoreverse. As you click the playback mode button, it cycles through these options and the appearance changes to indicate the current selection. A View the sequence repeatedly. Click the Repeat button in the Playback toolbar or select Playback Modes > Repeat from the Playback menu. You toggle this option on or off. R Jump to a specific frame in the sequence. Click the Jump to button in the Playback toolbar or select Jump to from the Playback menu. This option opens a dialog box in which you can specify the number of the frame. J Stop the sequence. Click the Stop button in the Playback toolbar or select Stop from the Playback menu. This button is only enabled when an image sequence is playing. S Step through the sequence, one frame at a time, or jump to the beginning or end of the sequence (rewind). Click one of the navigation buttons Arrow keysPage Up/Page Down in the Playback toolbar, in the desired direction, or select an option, such as Fast Forward or Rewind from the Playback menu. L (last frame) F (first frame) 4 Change the view of the image sequence or examine a frame more closely. 4-58 Viewing Image Sequences The Video Viewer supports several tools listed in the Tools menu and on the Toolbar that you can use to examine the frames in the image sequence more closely. Viewing Option Playback Control Zoom in or out on the image, and pan to change the view. in the Click one of the zoom buttons toolbar or select Zoom In or Zoom Out from in the the Tools menu. Click the Pan button toolbar or select Pan from the Tools menu. If in you click Maintain fit to window button the toolbar or select Maintain fit to window or from the Tools menu, the zoom and pan buttons are disabled. Examine an area of the current frame in detail. Export frame to Image Viewer Click the Pixel region button in the Playback toolbar or select Pixel Region from the Tools menu. Click the Export to Image Tool button in the Playback toolbar or select Export to Image Tool from the File menu. The Video Viewer app opens an Image Viewer containing the current frame. Configuring the Video Viewer App The Video Viewer app Configuration dialog box enables you to change the appearance and behavior of the player. To open the Configuration dialog box, select File > Configuration > Edit. (To load a preexisting configuration set, select File > Configuration > Load.) The Configuration dialog box contains four tabs: Core, Sources, Visuals, and Tools. On each tab, select a category and then click Properties to view configuration settings. 4-59 4 Displaying and Exploring Images The following table lists the options that are available for each category on every pane. 4-60 Viewing Image Sequences Pane Option Category Option Descriptions Core General UI Display the full source path in the title bar check box — Select to display the full path to the video data source in the title bar. By default, Movie Player displays a shortened name in the title bar. Open message log menu — Specify when the Message log window opens. You can use the Message log window to debug issues with video playback. By default, the window only opens for failure messages. Core Source UI Keyboard commands respect playback mode check box — Select to make keyboard shortcut keys aware of your playback mode selection. If you clear this check box, the keyboard shortcut keys behave as if the playback mode is set to Forward play and Repeat is set to off. Recently used sources list parameter — Specifies the number of sources listed in the File menu. Sources Simulink Select the Enabled check box to enable connections to Simulink models. You must have Simulink installed. Sources File Select the Enabled check box to enable connections to files (the default). Default open file path parameter — Specify the directory that is displayed in the Connect to File dialog box when you click File > Open. Sources Workspace Select the Enabled check box to enable connections to variables in the workspace (the default). There are no options associated with this selection. 4-61 4 Displaying and Exploring Images Pane Option Category Option Descriptions Visuals Video Select the Enabled check box to use video visualization. Tools Image Tool Select the Enabled check box to include the Image Viewer. Open new Image Tool window for each export check box — Opens a new Image Viewer for each exported frame. Tools Pixel Region Select the Enabled check box to include the Pixel Region tool in the Video Viewer app (the default). Tools Image Navigation Tools Select the Enabled check box to include the zoom and pan tools in the Video Viewer app (the default). Tools Instrumentation Sets Select the Enabled check box to include instrumentation sets in the Video Viewer app. Provides a way to save your current configuration. Saving Your Configuration Settings. To save your configuration settings for future use, select File > Configuration Set > Save as. Note By default, the Video Viewer uses the configuration settings from the file implay.cfg. If you want to store your configuration settings in this file, you should first create a backup copy of the file. Specifying the Frame Rate To decrease or increase the playback rate, select Frame Rate from the Playback menu, or use the keyboard shortcut T. The Frame Rate dialog box displays the frame rate of the source, lets you change the rate at which the Video Viewer app plays the image sequence or video, and displays the actual playback rate. The playback rate is the number of frames the Video Viewer processes per second. 4-62 Viewing Image Sequences If you want to increase the actual playback rate, but your system’s hardware cannot keep up with the desired rate, select the Allow frame drop to achieve desired playback rate check box. This parameter enables the Video Viewer app to achieve the playback rate by dropping frames. When you select this option, the Frame Rate dialog box displays several additional options that you can use to specify the minimum and maximum refresh rates. If your hardware allows it, increase the refresh rate to achieve a smoother playback. However, if you specify a small range for the refresh rate, the computed frame replay schedule may lead to a choppy replay, and a warning will appear. Specifying the Color Map To specify the colormap to apply to the intensity values, select Colormap from the Tools menu, or use the keyboard shortcut C. The Video Viewer displays a dialog box that enables you to change the colormap. Use the Colormap parameter to specify a particular colormap. 4-63 4 Displaying and Exploring Images If you know that the pixel values do not use the entire data type range, you can select the Specify range of displayed pixel values check box and enter the range for your data. The dialog box automatically displays the range based on the data type of the pixel values. Getting Information about the Image Frame To view basic information about the image data, click the Video Information in the Video Viewer toolbar or select Video Information from button the Tools menu. The Video Viewer displays a dialog box containing basic information about the image sequence, such as the size of each frame, the frame rate, and the total number of frames. Viewing Image Sequences as a Montage To view multiple frames in a multiframe array at one time, use the montage function. montage displays all the image frames, arranging them into a rectangular grid. The montage of images is a single image object. The image frames can be grayscale, indexed, or truecolor images. If you specify indexed images, they all must use the same colormap. This example creates an array of truecolor images and uses montage to display them all at once. Note how montage displays the images in a 2-by-2 4-64 Viewing Image Sequences grid. The first image frame is displayed in the first position of the first row, the next frame in the second position of the first row, and so on. onion = imread('onion.png'); onionArray = repmat(onion, [ 1 1 1 4 ]); montage(onionArray); montage supports several optional parameters that you can use to customize the display. For example, using the 'size' parameter, you can specify the number of rows and columns montage uses to display the images. To display the onion images in one horizontal row, specify the 'size' parameter with the value [1 NaN]. When you specify NaN for a dimension, montage calculates the number of images to display along that dimension. Using montage parameters you can also specify which images in the image array you want to display, and adjust the contrast of the images displayed. See montage for more information. 4-65 4 Displaying and Exploring Images Converting a Multiframe Image to a Movie To create a MATLAB movie from a multiframe image array, use the immovie function. This example creates a movie from a multiframe indexed image. mov = immovie(X,map); In the example, X is a four-dimensional array of images that you want to use for the movie. To play the movie, use the implay function. implay(mov); This example loads the multiframe image mri.tif and makes a movie out of it. It won’t do any good to show the results here, so try it out; it’s fun to watch. mri = uint8(zeros(128,128,1,27)); for frame=1:27 [mri(:,:,:,frame),map] = imread('mri.tif',frame); end mov = immovie(mri,map); implay(mov); Note To view a MATLAB movie, you must have MATLAB software installed. To make a movie that can be run outside the MATLAB environment, use the VideoWriter class to create a movie in a standard video format, such as, AVI. 4-66 Displaying Different Image Types Displaying Different Image Types In this section... “Displaying Indexed Images” on page 4-67 “Displaying Grayscale Images” on page 4-68 “Displaying Binary Images” on page 4-69 “Displaying Truecolor Images” on page 4-71 If you need help determining what type of image you are working with, see “Image Types in the Toolbox” on page 2-10. Displaying Indexed Images To display an indexed image, using either imshow or imtool, specify both the image matrix and the colormap. This documentation uses the variable name X to represent an indexed image in the workspace, and map to represent the colormap. imshow(X,map) or imtool(X,map) For each pixel in X, these functions display the color stored in the corresponding row of map. If the image matrix data is of class double, the value 1 points to the first row in the colormap, the value 2 points to the second row, and so on. However, if the image matrix data is of class uint8 or uint16, the value 0 (zero) points to the first row in the colormap, the value 1 points to the second row, and so on. This offset is handled automatically by the imtool and imshow functions. If the colormap contains a greater number of colors than the image, the functions ignore the extra colors in the colormap. If the colormap contains fewer colors than the image requires, the functions set all image pixels over the limits of the colormap’s capacity to the last color in the colormap. For example, if an image of class uint8 contains 256 colors, and you display it 4-67 4 Displaying and Exploring Images with a colormap that contains only 16 colors, all pixels with a value of 15 or higher are displayed with the last color in the colormap. Displaying Grayscale Images To display a grayscale image, call the imshow function or open the Image Viewer app. This documentation uses the variable name I to represent a grayscale image in the workspace. Both functions display the image by scaling the intensity values to serve as indices into a grayscale colormap. If I is double, a pixel value of 0.0 is displayed as black, a pixel value of 1.0 is displayed as white, and pixel values in between are displayed as shades of gray. If I is uint8, then a pixel value of 255 is displayed as white. If I is uint16, then a pixel value of 65535 is displayed as white. Grayscale images are similar to indexed images in that each uses an m-by-3 RGB colormap, but you normally do not specify a colormap for a grayscale image. MATLAB displays grayscale images by using a grayscale system colormap (where R=G=B). By default, the number of levels of gray in the colormap is 256 on systems with 24-bit color, and 64 or 32 on other systems. (See “Displaying Colors” on page 14-2 for a detailed explanation.) Displaying Grayscale Images That Have Unconventional Ranges In some cases, the image data you want to display as a grayscale image could have a display range that is outside the conventional toolbox range (i.e., [0,1] for single or double arrays, [0,255] for uint8 arrays, [0,65535] for uint16 arrays, or [-32767,32768] for int16 arrays). For example, if you filter a grayscale image, some of the output data could fall outside the range of the original data. To display unconventional range data as an image, you can specify the display range directly, using this syntax for both the imshow and imtool functions. imshow(I,'DisplayRange',[low high]) or 4-68 Displaying Different Image Types imtool(I,'DisplayRange',[low high]) If you use an empty matrix ([]) for the display range, these functions scale the data automatically, setting low and high to the minimum and maximum values in the array. The next example filters a grayscale image, creating unconventional range data. The example calls imtool to display the image in the Image Viewer, using the automatic scaling option. If you execute this example, note the display range specified in the lower right corner of the Image Viewer window. I = imread('testpat1.png'); J = filter2([1 2;-1 -2],I); imtool(J,'DisplayRange',[]); Displaying Binary Images In MATLAB, a binary image is of class logical. Binary images contain only 0’s and 1’s. Pixels with the value 0 are displayed as black; pixels with the value 1 are displayed as white. 4-69 4 Displaying and Exploring Images Note For the toolbox to interpret the image as binary, it must be of class logical. Grayscale images that happen to contain only 0’s and 1’s are not binary images. To display a binary image, call the imshow function or open the Image Viewer app. For example, this code reads a binary image into the MATLAB workspace and then displays the image. This documentation uses the variable name BW to represent a binary image in the workspace BW = imread('circles.png'); imshow(BW) Changing the Display Colors of a Binary Image You might prefer to invert binary images when you display them, so that 0 values are displayed as white and 1 values are displayed as black. To do this, use the NOT (~) operator in MATLAB. (In this figure, a box is drawn around the image to show the image boundary.) For example: imshow(~BW) 4-70 Displaying Different Image Types You can also display a binary image using the indexed image colormap syntax. For example, the following command specifies a two-row colormap that displays 0’s as red and 1’s as blue. imshow(BW,[1 0 0; 0 0 1]) Displaying Truecolor Images Truecolor images, also called RGB images, represent color values directly, rather than through a colormap. A truecolor image is an m-by-n-by-3 array. For each pixel (r,c) in the image, the color is represented by the triplet (r,c,1:3). To display a truecolor image, call the imshow function or open the Image Viewer app. For example, this code reads a truecolor image into the MATLAB workspace and then displays the image. This documentation uses the variable name RGB to represent a truecolor image in the workspace 4-71 4 Displaying and Exploring Images RGB = imread('peppers.png'); imshow(RGB) Systems that use 24 bits per screen pixel can display truecolor images directly, because they allocate 8 bits (256 levels) each to the red, green, and blue color planes. On systems with fewer colors, imshow displays the image using a combination of color approximation and dithering. See “Displaying Colors” on page 14-2 for more information. Note If you display a color image and it appears in black and white, check if the image is an indexed image. With indexed images, you must specify the colormap associated with the image. For more information, see “Displaying Indexed Images” on page 4-67. 4-72 Adding a Colorbar to a Displayed Image Adding a Colorbar to a Displayed Image To display an image with a colorbar that indicates the range of intensity values, first use the imshow function to display the image in a MATLAB figure window and then call the colorbar function to add the colorbar to the image. When you add a colorbar to an axes object that contains an image object, the colorbar indicates the data values that the different colors in the image correspond to. If you want to add a colorbar to an image displayed in the Image Viewer, select the Print to Figure option from the File menu. The Image Viewer displays the image in a separate figure window to which you can add a colorbar. Seeing the correspondence between data values and the colors displayed by using a colorbar is especially useful if you are displaying unconventional range data as an image, as described under “Displaying Grayscale Images That Have Unconventional Ranges” on page 4-68. In the example below, a grayscale image of class uint8 is filtered, resulting in data that is no longer in the range [0,255]. RGB = imread('saturn.png'); I = rgb2gray(RGB); h = [1 2 1; 0 0 0; -1 -2 -1]; I2 = filter2(h,I); imshow(I2,'DisplayRange',[]), colorbar 4-73 4 4-74 Displaying and Exploring Images Printing Images Printing Images If you want to output a MATLAB image to use in another application (such as a word-processing program or graphics editor), use imwrite to create a file in the appropriate format. See “Writing Image Data to a File” on page 3-5 for details. If you want to print an image, use imshow to display the image in a MATLAB figure window. If you are using the Image Viewer, you must use the Print to Figure option on the File menu. When you choose this option, the Image Viewer opens a separate figure window and displays the image in it. You can access the standard MATLAB printing capabilities in this figure window. You can also use the Print to Figure option to print the image displayed in the Overview tool and the Pixel Region tool. Once the image is displayed in a figure window, you can use either the MATLAB print command or the Print option from the File menu of the figure window to print the image. When you print from the figure window, the output includes nonimage elements such as labels, titles, and other annotations. Printing and Handle Graphics Object Properties The output reflects the settings of various properties of Handle Graphic objects. In some cases, you might need to change the settings of certain properties to get the results you want. Here are some tips that could be helpful when you print images: • Image colors print as shown on the screen. This means that images are not affected by the figure object’s InvertHardcopy property. • To ensure that printed images have the proper size and aspect ratio, set the figure object’s PaperPositionMode property to auto. When PaperPositionMode is set to auto, the width and height of the printed figure are determined by the figure’s dimensions on the screen. By default, the value of PaperPositionMode is manual. If you want the default value of PaperPositionMode to be auto, you can add this line to your startup.m file. set(0,'DefaultFigurePaperPositionMode','auto') 4-75 4 Displaying and Exploring Images For detailed information about printing with File/Print or the print command (and for information about Handle Graphics), see “Overview of Printing and Exporting” in the MATLAB Graphics documentation. For a complete list of options for the print command, enter help print at the MATLAB command-line prompt or see the print command reference page in the MATLAB documentation. 4-76 Setting Toolbox Preferences Setting Toolbox Preferences In this section... “Viewing and Changing Preferences Using the Preferences Dialog Box” on page 4-77 “Retrieving the Values of Toolbox Preferences Programmatically” on page 4-77 “Setting the Values of Toolbox Preferences Programmatically” on page 4-78 Viewing and Changing Preferences Using the Preferences Dialog Box You can view and change Image Processing Toolbox Preferences in the Preferences dialog box. To open this dialog box, select Preferences > Image Processing in the File menu in the MATLAB desktop or in the Image Viewer, or type iptprefs at the command line. Retrieving the Values of Toolbox Preferences Programmatically You can use Image Processing Toolbox preferences to control certain characteristics of how imshow and imtool display images on your screen. For example, using toolbox preferences, you can specify the initial magnification used by imtool and imshow. To determine the current value of a preference, use the iptgetpref function. This example uses iptgetpref to determine the value of the ImtoolInitialMagnification preference. iptgetpref('ImtoolInitialMagnification') ans = 100 Preference names are case insensitive and can be abbreviated. For a complete list of toolbox preferences, see the iptprefs reference page. 4-77 4 Displaying and Exploring Images Setting the Values of Toolbox Preferences Programmatically To specify the value of a toolbox preference, use the iptsetpref function. This example calls iptsetpref to specify that imshow resize the figure window so that it fits tightly around displayed images. iptsetpref('ImshowBorder', 'tight'); For a table of the available preferences, see the iptprefs reference page. 4-78 5 Building GUIs with Modular Tools This chapter describes how to use the toolbox modular tools to create custom image processing applications. • “Modular Interactive Tools” on page 5-2 • “Displaying the Target Image” on page 5-10 • “Creating the Modular Tools” on page 5-11 • “Customizing Modular Tool Interactivity” on page 5-28 • “Creating Your Own Modular Tools” on page 5-33 5 Building GUIs with Modular Tools Modular Interactive Tools The toolbox includes several modular interactive tools that you can activate from the command line and use with images displayed in a MATLAB figure window, called the target image in this documentation. The tools are modular because they can be used independently or in combination to create custom graphical user interfaces (GUIs) for image processing applications. Using the tools typically involves the following steps. Step Description Notes 1 Display the image to be processed (called the target image) in a figure window. Use the imshow function to display the target image, see “Displaying the Target Image” on page 5-10. 2 Create the modular tool, associating it with the target image. You use the modular tool creation functions to create the tools — see Summary of Modular Tools on page 5-3 Most of the tools associate themselves with the image in the current axes, by default, but you can specify the handle to a specific image object, or a handle to a figure, axes, or uipanel object that contains an image. See “Creating the Modular Tools” on page 5-11. Depending on how you designed your GUI, you might also want to specify the parent object of the modular tool itself. This is optional; by default, the tools either use the same parent as the target image or open in a separate figure window. See “Specifying the Parent of a Modular Tool” on page 5-15 for more information. You might need to specify the position of the graphics objects in 5-2 Modular Interactive Tools Notes Step Description the GUI, including the modular tools. See “Positioning the Modular Tools in a GUI” on page 5-18 for more information. 3 Set up interactivity between the tool and the target image. (Optional) The modular tools all set up their interactive connections to the target image automatically. However, you can also specify custom connectivity using modular tool APIs. See “Customizing Modular Tool Interactivity” on page 5-28 for more information. The following table lists the modular tools in alphabetical order. The table includes an illustration of each tool and the function you use to create it. Note The Image Processing Toolbox GUI, Image Tool, uses these modular tools — see “Using the Image Viewer App to Explore Images” on page 4-11. Summary of Modular Tools Modular Tool Adjust Contrast tool Example Description Displays a histogram of the target image and enables interactive adjustment of contrast and brightness by manipulation of the display range. Use the imcontrast function to create the tool in a separate figure 5-3 5 Building GUIs with Modular Tools Summary of Modular Tools (Continued) Modular Tool Example Description window and associate it with an image. Choose Colormap tool Allows you to change the colormap of the target figure. You can select one of the MATLAB colormaps, select a colormap variable from the MATLAB workspace, or enter a custom MATLAB expression. Use the imcolormaptool function to launch the tool in a separate figure window. Crop Image tool Displays a draggable, resizable rectangle on an image. You can move and resize the rectangle to define the crop region. Double-click to perform the crop operation or select Crop Image from the context menu. Use the imcrop function to create the tool and associate it with an image. 5-4 Modular Interactive Tools Summary of Modular Tools (Continued) Modular Tool Display Range tool Example Description Displays a text string identifying the display range values of the associated image. Use the imdisplayrange function to create the tool, associate it with an image, and embed it in a figure or uipanel. Distance tool Displays a draggable, resizable line on an image. Superimposed on the line is the distance between the two endpoints of the line. The distance is measured in units specified by the XData and YData properties, which is pixels by default. Use the imdistline function to create the tool and associate it with an image. 5-5 5 Building GUIs with Modular Tools Summary of Modular Tools (Continued) Modular Tool Image Information tool Example Description Displays basic attributes about the target image. If the image displayed was specified as a graphics file, the tool displays any metadata that the image file might contain. Use the imageinfo function to create the tool in a separate figure window and associate it with an image. Magnification box Creates a text edit box containing the current magnification of the target image. Users can change the magnification of the image by entering a new magnification value. Use immagbox to create the tool, associate it with an image, and embed it in a figure or uipanel. Note The target image must be contained in a scroll panel. 5-6 Modular Interactive Tools Summary of Modular Tools (Continued) Modular Tool Overview tool Example Description Displays the target image in its entirety with the portion currently visible in the scroll panel outlined by a rectangle superimposed on the image. Moving the rectangle changes the portion of the target image that is currently visible in the scroll panel. Use imoverview to create the tool in a separate figure window and associate it with an image. Use imoverviewpanel to create the tool in a uipanel that can be embedded within another figure or uipanel. Note The target image must be contained in a scroll panel. 5-7 5 Building GUIs with Modular Tools Summary of Modular Tools (Continued) Modular Tool Pixel Information tool Example Description Displays information about the pixel the mouse is over in the target image. Use impixelinfo to create the tool, associate it with an image, and display it in a figure or uipanel. If you want to display only the pixel values, without the Pixel info label, use impixelinfoval. Pixel Region tool Display pixel values for a specified region in the target image. Use impixelregion to create the tool in a separate figure window and associate it with an image. Use impixelregionpanel to create the tool as a uipanel that can be embedded within another figure or uipanel. 5-8 Modular Interactive Tools Summary of Modular Tools (Continued) Modular Tool Save Image tool Example Description Display the Save Image dialog box. Use this to specify the name of an output image and choose the file format used to store the image. Use imsave to create the tool in a separate figure window and associate it with an image. Scroll Panel tool Display target image in a scrollable panel. Use imscrollpanel to add a scroll panel to an image displayed in a figure window. 5-9 5 Building GUIs with Modular Tools Displaying the Target Image As the foundation for any image processing GUI you create, use imshow to display the target image (or images) in a MATLAB figure window. (You can also use the MATLAB image or imagesc functions.) Once the image is displayed in the figure, you can associate any of the modular tools with the image displayed in the figure. This example uses imshow to display an image in a figure window. himage = imshow('pout.tif'); Because some of the modular tools add themselves to the figure window containing the image, make sure that the Image Processing Toolbox ImshowBorder preference is set to 'loose', if you are using the imshow function. (This is the default setting.) By including a border, you ensure that the modular tools are not displayed over the image in the figure. 5-10 Creating the Modular Tools Creating the Modular Tools In this section... “Overview” on page 5-11 “Associating Modular Tools with a Particular Image” on page 5-12 “Getting the Handle of the Target Image” on page 5-14 “Specifying the Parent of a Modular Tool” on page 5-15 “Positioning the Modular Tools in a GUI” on page 5-18 “Build a Pixel Information GUI” on page 5-19 “Adding Navigation Aids to a GUI” on page 5-22 Overview To associate a modular tool with a target image displayed in a MATLAB figure window, you must create the tool using the appropriate tool creation function. You specify a handle to the target image as an argument to the tool creation function. The function creates the tool and automatically sets up the interactivity connection between the tool and the target image. By default, most of the modular tool creation functions support a no-argument syntax that uses the image in the current figure as the target image. If the current figure contains multiple images, the tools associate themselves with the first image in the figure object’s children (the last image created). impixelinfo, impixelinfoval and imdisplayrange can work with multiple images in a figure. For example, to use the Pixel Information tool with a target image, display the image in a figure window, using imshow, and then call the impixelinfo function to create the tool. In this example, the image in the current figure is the target image. imshow('pout.tif'); impixelinfo 5-11 5 Building GUIs with Modular Tools The following figure shows the target image in a figure with the Pixel Information tool in the lower left corner of the window. The Pixel Information tool automatically sets up a connection to the target image: when you move the pointer over the image, the tool displays the x- and y-coordinates and value of the pixel under the pointer. Figure Window with Pixel Information Tool Associating Modular Tools with a Particular Image You can specify the target image of the modular tool when you create it by passing a handle to the target image as an argument to the modular tool creation function. You can also specify a handle to a figure, axes, or uipanel object that contains the target image. Continuing the example in the previous section, you might want to add the Display Range tool to the figure window that already contains the Pixel Information tool. To do this, call the imdisplayrange function, specifying the 5-12 Creating the Modular Tools handle to the target image. You could also have specified the handle of the figure, axes, or uipanel object containing the target image. himage = imshow('pout.tif'); hpixelinfopanel = impixelinfo(himage); hdrangepanel = imdisplayrange(himage); Note that the example retrieves handles to the uipanel objects created by the impixelinfo and imdisplayrange functions; both tools are uipanel objects. It can be helpful to get handles to the tools if you want to change their positioning. See “Positioning the Modular Tools in a GUI” on page 5-18 for more information. The following figure shows the target image in a figure with the Pixel Information tool in the lower left corner and the Display Range tool in the lower right corner of the window. The Display Range tool automatically sets up a connection to the target image: when you move the pointer over the image (or images) in the figure, the Display Range tool shows the display range of the image. 5-13 5 Building GUIs with Modular Tools Figure Window with Pixel Information and Display Range Tools Getting the Handle of the Target Image The examples in the previous section use the optional imshow syntax that returns a handle to the image displayed, himage. When creating GUIs with the modular tools, having a handle to the target image can be useful. You can get the handle when you first display the image, using this optional imshow syntax. You can also get a handle to the target image using the imhandles function. The imhandles function returns all the image objects that are children of a specified figure, axes, uipanel, or image object. 5-14 Creating the Modular Tools For example, imshow returns a handle to the image in this syntax. hfig = figure; himage = imshow('moon.tif') himage = 152.0055 When you call the imhandles function, specifying a handle to the figure (or axes) containing the image, it returns a handle to the same image. himage2 = imhandles(hfig) himage2 = 152.0055 Specifying the Parent of a Modular Tool When you create a modular tool, in addition to specifying the target image, you can optionally specify the object that you want to be the parent of the tool. By specifying the parent, you determine where the tool appears on your screen. Using this syntax of the modular tool creation functions, you can add the tool to the figure window containing the target image, open the tool in a separate figure window, or create some other combination. Specifying the parent is optional; the modular tools all have a default behavior. Some of the smaller tools, such as the Pixel Information tool, use the parent of the target image as their parent, inserting themselves in the same figure window as the target image. Other modular tools, such as the Pixel Region tool or the Overview tool, open in separate figures of their own. Tools With Separate Creation Functions Two of the tools, the Pixel Region tool and the Overview tool, have a separate creation function to provide this capability. Their primary creation functions, imoverview and impixelregion, open the tools in a separate figure window. To specify a different parent, you must use the imoverviewpanel and impixelregionpanel functions. 5-15 5 Building GUIs with Modular Tools Note The Overview tool and the Pixel Region tool provide additional capabilities when created in their own figure windows. For example, both tools include zoom buttons that are not part of their uipanel versions. Example: Embedding the Pixel Region Tool in an Existing Figure This example shows the default behavior when you create the Pixel Region tool using the impixelregion function. The tool opens in a separate figure window, as shown in the following figure. himage = imshow('pout.tif') hpixelinfopanel = impixelinfo(himage); hdrangepanel = imdisplayrange(himage); hpixreg = impixelregion(himage); Pixel Region tool Pixel Region rectangle Target Image with Pixel Region Tool in Separate Window (Default) 5-16 Creating the Modular Tools To embed the Pixel Region tool in the same window as the target image, you must specify the handle of the target image’s parent figure as the parent of the Pixel Region tool when you create it. The following example creates a figure and an axes object, getting handles to both objects. The example needs these handles to perform some repositioning of the objects in the figure to ensure their visibility. See “Positioning the Modular Tools in a GUI” on page 5-18 for more information. The example then creates the modular tools, specifying the figure containing the target image as the parent of the Pixel Region tool. Note that the example uses the impixelregionpanel function to create the tool. hfig = figure; hax = axes('units','normalized','position',[0 .5 1 .5]); himage = imshow('pout.tif') hpixelinfopanel = impixelinfo(himage); hdrangepanel = imdisplayrange(himage); hpixreg = impixelregionpanel(hfig,himage); set(hpixreg, 'Units','normalized','Position',[0 .08 1 .4]); 5-17 5 Building GUIs with Modular Tools The following figure shows the Pixel Region embedded in the same figure as the target image. Pixel Region tool embedded in figure window Target Image with Embedded Pixel Region Tool Positioning the Modular Tools in a GUI When you create the modular tools, they have default positioning behavior. For example, the impixelinfo function creates the tool as a uipanel object that is the full width of the figure window, positioned in the lower left corner of the target image figure window. Because the modular tools are constructed from standard Handle Graphics objects, such as uipanel objects, you can use properties of the objects to change their default positioning or other characteristics. For example, in “Specifying the Parent of a Modular Tool” on page 5-15, when the Pixel Region tool was embedded in the same figure window as the target 5-18 Creating the Modular Tools image, the example had to reposition both the image object and the Pixel Region tool uipanel object to make them both visible in the figure window. Specifying the Position with a Position Vector To specify the position of a modular tool or other graphics object, set the value of the Position property of the object. As the value of this property, you specify a four-element position vector [left bottom width height], where left and bottom specify the distance from the lower left corner of the parent container object, such as a figure. The width and height specify the dimensions of the object. When you use a position vector, you can specify the units of the values in the vector by setting the value of the Units property of the object. To allow better resizing behavior, use normalized units because they specify the relative position, not the exact location in pixels. See the reference page for the Handle Graphics object for more details. For example, when you first create an embedded Pixel Region tool in a figure, it appears to take over the entire figure because, by default, the position vector is set to [0 0 1 1], in normalized units. This position vector tells the tool to align itself with the bottom left corner of its parent and fill the entire object. To accommodate the image and the Pixel Information tool and Display Range tools, change the position of the Pixel Region tool in the lower half of the figure window, leaving room at the bottom for the Pixel Information and Display Range tools. Here is the position vector for the Pixel Region tool. set(hpixreg, 'Units','normalized','Position',[0 .08 1 .4]) To accommodate the Pixel Region tool, reposition the target image so that it fits in the upper half of the figure window, using the following position vector. To reposition the image, you must specify the Position property of the axes object that contains it; image objects do not have a Position property. set(hax,'Units','normalized','Position',[0 0.5 1 0.5]) Build a Pixel Information GUI This example shows how to use the tools to create a simple GUI that provides information and pixels and features in an image. The GUI displays an image and includes the following modular pixel information tools: 5-19 5 Building GUIs with Modular Tools • Display Range tool • Distance tool • Pixel Information tool • Pixel Region tool panel The example suppresses the figure window toolbar and menu bar because the standard figure zoom tools are not compatible with the toolbox modular navigation tools — see “Adding Navigation Aids to a GUI” on page 5-22. function my_pixinfotool(im) % Create figure, setting up properties hfig = figure('Toolbar','none',... 'Menubar', 'none',... 'Name','My Pixel Info Tool',... 'NumberTitle','off',... 'IntegerHandle','off'); % Create axes and reposition the axes % to accommodate the Pixel Region tool panel hax = axes('Units','normalized',... 'Position',[0 .5 1 .5]); % Display image in the axes and get a handle to the image himage = imshow(im); % Add Distance tool, specifying axes as parent hdist = imdistline(hax); % Add Pixel Information tool, specifying image as parent hpixinfo = impixelinfo(himage); % Add Display Range tool, specifying image as parent hdrange = imdisplayrange(himage); % Add Pixel Region tool panel, specifying figure as parent % and image as target hpixreg = impixelregionpanel(hfig,himage); % Reposition the Pixel Region tool to fit in the figure 5-20 Creating the Modular Tools % window, leaving room for the Pixel Information and % Display Range tools. set(hpixreg, 'units','normalized','position',[0 .08 1 .4]) To use the tool, pass it an image that is already in the MATLAB workspace. pout = imread('pout.tif'); my_pixinfotool(pout); The tool opens a figure window, displaying the image in the upper half, with the Distance tool overlaid on the image, and the Pixel Information tool, Display Range tool, and the Pixel Region tool panel in the lower half of the figure. Custom Image Display Tool with Pixel Information 5-21 5 Building GUIs with Modular Tools Adding Navigation Aids to a GUI Note The toolbox modular navigation tools are incompatible with standard MATLAB figure window navigation tools. When using these tools in a GUI, suppress the toolbar and menu bar in the figure windows to avoid conflicts between the tools. The toolbox includes several modular tools that you can use to add navigation aids to a GUI application: • Scroll Panel • Overview tool • Magnification box The Scroll Panel is the primary navigation tool; it is a prerequisite for the other navigation tools. When you display an image in a Scroll Panel, the tool displays only a portion of the image, if it is too big to fit into the figure window. When only a portion of the image is visible, the Scroll Panel adds horizontal and vertical scroll bars, to enable viewing of the parts of the image that are not currently visible. Once you create a Scroll Panel, you can optionally add the other modular navigation tools: the Overview tool and the Magnification tool. The Overview tool displays a view of the entire image, scaled to fit, with a rectangle superimposed over it that indicates the part of the image that is currently visible in the scroll panel. The Magnification Box displays the current magnification of the image and can be used to change the magnification. The following sections provide more details. • “Understanding Scroll Panels” on page 5-23 — Adding a scroll panel to an image display changes the relationship of the graphics objects used in the display. This section provides some essential background. • “Example: Building a Navigation GUI for Large Images” on page 5-25 — This section shows how to add a scroll panel to an image display. 5-22 Creating the Modular Tools Understanding Scroll Panels When you display an image in a scroll panel, it changes the object hierarchy of your displayed image. This diagram illustrates the typical object hierarchy for an image displayed in an axes object in a figure object. hfig = figure; himage = imshow('concordaerial.png'); The following figure shows this object hierarchy. Object Hierarchy of Image Displayed in a Figure When you call the imscrollpanel function to put the target image in a scrollable window, this object hierarchy changes. For example, this code adds a scroll panel to an image displayed in a figure window, specifying the parent of the scroll panel and the target image as arguments. The example suppresses the figure window toolbar and menu bar because they are not compatible with the scroll panel navigation tools. hfig = figure('Toolbar','none',... 'Menubar', 'none'); himage = imshow('concordaerial.png'); hpanel = imscrollpanel(hfig,himage); 5-23 5 Building GUIs with Modular Tools The following figure shows the object hierarchy after the call to imscrollpanel. Note how imscrollpanel inserts new objects (shaded in gray) into the hierarchy between the figure object and the axes object containing the image. (To change the image data displayed in the scroll bar, use the replaceImage function in the imscrollpanel API.) Object Hierarchy of Image Displayed in Scroll Panel 5-24 Creating the Modular Tools The following figure shows how these graphics objects appear in the scrollable image as it is displayed on the screen. Components of a Scroll Panel Example: Building a Navigation GUI for Large Images If your work typically requires that you view large images, you might want to create a custom image display function that includes the modular navigation tools. This example creates a tool that accepts an image as an argument and displays the image in a scroll panel with an Overview tool and a Magnification box. 5-25 5 Building GUIs with Modular Tools Note Because the toolbox scrollable navigation is incompatible with standard MATLAB figure window navigation tools, the example suppresses the toolbar and menu bar in the figure window. function my_large_image_display(im) % Create a figure without toolbar and menubar. hfig = figure('Toolbar','none',... 'Menubar', 'none',... 'Name','My Large Image Display Tool',... 'NumberTitle','off',... 'IntegerHandle','off'); % Display the image in a figure with imshow. himage = imshow(im); % Add the scroll panel. hpanel = imscrollpanel(hfig,himage); % Position the scroll panel to accommodate the other tools. set(hpanel,'Units','normalized','Position',[0 .1 1 .9]); % Add the Magnification box. hMagBox = immagbox(hfig,himage); % Position the Magnification box pos = get(hMagBox,'Position'); set(hMagBox,'Position',[0 0 pos(3) pos(4)]); % Add the Overview tool. hovervw = imoverview(himage); To use the tool, pass it a large image that is already in the MATLAB workspace. big_image = imread('peppers.png'); my_large_image_display(big_image) 5-26 Creating the Modular Tools The tool opens a figure window, displaying the image in a scroll panel with the Overview tool and the Magnification Box tool. Overview Tool Magnification Box Custom Image Display Tool with Navigation Aids 5-27 5 Building GUIs with Modular Tools Customizing Modular Tool Interactivity In this section... “Overview” on page 5-28 “Build Image Comparison Tool” on page 5-29 Overview When you create a modular tool and associate it with a target image, the tool automatically makes the necessary connections to the target image to do its job. For example, the Pixel Information tool sets up a connection to the target image so that it can display the location and value of the pixel currently under the pointer. As another example, the Overview tool sets up a two-way connection to the target image: • Target image to the Overview tool — If the visible portion of the image changes, by scrolling, panning, or by changing the magnification, the Overview tool changes the size and location of the detail rectangle to the indicate the portion of the image that is now visible. • Overview tool to the target image — If a user moves the detail rectangle in the Overview tool, the portion of the target image visible in the scroll panel is updated. The modular tools accomplish this interactivity by using callback properties of the graphics objects. For example, the figure object supports a WindowButtonMotionFcn callback that executes whenever the mouse button is depressed. You can customize the connectivity of a modular tool by using the application programmer interface (API) associated with the tool to set up callbacks to get notification of events. For example, the Magnification box supports a single API function: setMagnification. You can use this API function to set the magnification value displayed in the Magnification box. The Magnification box automatically notifies the scroll panel to change the magnification of the image based on the value. The scroll panel also supports an extensive set of API functions. To get information about these APIs, see the reference page for the modular tool. 5-28 Customizing Modular Tool Interactivity Build Image Comparison Tool To illustrate how to use callbacks to make the connections required for interactions between tools, this example uses the Scroll Panel API to build a simple image comparison GUI. This custom tool displays two images side by side in scroll panels that are synchronized in location and magnification. The custom tool also includes an Overview tool and a Magnification box. function my_image_compare_tool(left_image, right_image) % Create the figure hFig = figure('Toolbar','none',... 'Menubar','none',... 'Name','My Image Compare Tool',... 'NumberTitle','off',... 'IntegerHandle','off'); % Display left image subplot(121) hImL = imshow(left_image); % Display right image subplot(122) hImR = imshow(right_image); % Create a scroll panel for left image hSpL = imscrollpanel(hFig,hImL); set(hSpL,'Units','normalized',... 'Position',[0 0.1 .5 0.9]) % Create scroll panel for right image hSpR = imscrollpanel(hFig,hImR); set(hSpR,'Units','normalized',... 'Position',[0.5 0.1 .5 0.9]) % Add a Magnification box hMagBox = immagbox(hFig,hImL); pos = get(hMagBox,'Position'); set(hMagBox,'Position',[0 0 pos(3) pos(4)]) %% Add an Overview tool 5-29 5 Building GUIs with Modular Tools imoverview(hImL) %% Get APIs from the scroll panels apiL = iptgetapi(hSpL); apiR = iptgetapi(hSpR); %% Synchronize left and right scroll panels apiL.setMagnification(apiR.getMagnification()) apiL.setVisibleLocation(apiR.getVisibleLocation()) % When magnification changes on left scroll panel, % tell right scroll panel apiL.addNewMagnificationCallback(apiR.setMagnification); % When magnification changes on right scroll panel, % tell left scroll panel apiR.addNewMagnificationCallback(apiL.setMagnification); % When location changes on left scroll panel, % tell right scroll panel apiL.addNewLocationCallback(apiR.setVisibleLocation); % When location changes on right scroll panel, % tell left scroll panel apiR.addNewLocationCallback(apiL.setVisibleLocation); The tool sets up a complex interaction between the scroll panels with just a few calls to Scroll Panel API functions. In the code, the tool specifies a callback function to execute every time the magnification changes. The function specified is the setMagnification API function of the other scroll panel. Thus, whenever the magnification changes in one of the scroll panels, the other scroll panel changes its magnification to match. The tool sets up a similar connection for position changes. The following figure is a sequence diagram that shows the interaction between the two scroll panels set up by the comparison tool for both changes in magnification and location. 5-30 Customizing Modular Tool Interactivity Scroll Panel Connections in Custom Image Comparison Tool To use the image comparison tool, pass it two images as arguments. left_image = imread('peppers.png'); right_image = edge(left_image(:,:,1),'canny'); my_image_compare_tool(left_image,right_image); 5-31 5 Building GUIs with Modular Tools The tool opens a figure window, displaying the two images side by side, in separate scroll panels. The custom compare tool also includes an Overview tool and a Magnification box. When you move the detail rectangle in the Overview tool or change the magnification in one image, both images respond. Custom Image Comparison Tool with Synchronized Scroll Panels 5-32 Creating Your Own Modular Tools Creating Your Own Modular Tools In this section... “Overview” on page 5-33 “Create Angle Measurement Tool” on page 5-35 Overview Because the toolbox uses an open architecture for the modular interactive tools, you can extend the toolbox by creating your own modular interactive tools, using standard Handle Graphics concepts and techniques. To help you create tools that integrate well with the existing modular interactive tools, the toolbox includes many utility functions that perform commonly needed tasks. The utility functions can help check the input arguments to your tool, add callback functions to a callback list or remove them from a list, and align figure windows in relation to a fixed window. The toolbox also provides a set of functions that you can use to define a region-of-interest of various shapes, including points, lines, rectangles, ellipses, polygons, and freehand shapes — see “Create Angle Measurement Tool” on page 5-35 for more information. The following table lists these utility functions in alphabetical order. See the function’s reference page for more detailed information. Utility Function Description getimagemodel Retrieve image model objects from image handles getrangefromclass Get default display range of image, based on its class imagemodel Access to properties of an image relevant to its display imattributes Return information about image attributes imellipse Create draggable, resizable ellipse imfreehand Create draggable freehand region imgca Get handle to current axes containing an image 5-33 5 Building GUIs with Modular Tools Utility Function Description imgcf Get handle to most recent current figure containing an image imgetfile Display Open Image dialog box imhandles Get all image handles imline Create draggable, resizable line impoint Create draggable point impoly Create draggable, resizable polygon imputfile Display Save Image dialog box imrect Create draggable, resizable rectangle iptaddcallback Add function handle to a callback list iptcheckconn Check validity of connectivity argument iptcheckhandle Check validity of image handle argument iptcheckinput Check validity of input argument iptcheckmap Check validity of colormap argument iptchecknargin Check number of input arguments iptcheckstrs Check validity of string argument iptgetapi Get application programmer interface (API) for a handle iptGetPointerBehavior Retrieve pointer behavior from HG object ipticondir Return names of directories containing IPT and MATLAB icons iptnum2ordinal Convert positive integer to ordinal string iptPointerManager Install mouse pointer manager in figure iptremovecallback Delete function handle from callback list iptSetPointerBehavior Store pointer behavior in HG object iptwindowalign 5-34 Align figure windows Creating Your Own Modular Tools Create Angle Measurement Tool The toolbox includes a set of functions that you can use to enable users of your image processing GUI to define a region-of-interest (ROI) on the target image. The functions implement drawing of various shapes of ROI, such as rectangles, ellipses, and polygons, and returning information about the coordinates that define the ROI. These ROI objects support methods that you can use to control aspects of its appearance and behavior. To illustrate how to use these ROI tools, this example creates a simple angle measurement tool This custom tool uses impoly to create a two-segment polyline on an image and displays the angle created by the two line segments in a title in the figure. Users of the tool can move the polyline anywhere on the image and view the angle formed by the two line segments. function my_angle_measurement_tool(im) % Create figure, setting up properties figure('Name','My Angle Measurement Tool',... 'NumberTitle','off',... 'IntegerHandle','off'); % Display image in the axes imshow(im) % Get size of image. m = size(im,1); n = size(im,2); % Get center point of image for initial positioning. midy = ceil(m/2); midx = ceil(n/2); % Position first point vertically above the middle. firstx = midx; firsty = midy - ceil(m/4); lastx = midx + ceil(n/4); lasty = midy; % Create a two-segment right-angle polyline centered in the image. h = impoly(gca,[firstx,firsty;midx,midy;lastx,lasty],'Closed',false); api = iptgetapi(h); initial_position = api.getPosition() % Display initial position updateAngle(initial_position) % set up callback to update angle in title. api.addNewPositionCallback(@updateAngle); 5-35 5 Building GUIs with Modular Tools fcn = makeConstrainToRectFcn('impoly',get(gca,'XLim'),get(gca,'YLim')); api.setPositionConstraintFcn(fcn); % % Callback function that calculates the angle and updates the title. % Function receives an array containing the current x,y position of % the three vertices. function updateAngle(p) % Create two vectors from the vertices. % v1 = [x1 - x2, y1 - y2] % v2 = [x3 - x2, Y3 - y2] v1 = [p(1,1)-p(2,1), p(1,2)-p(2,2)]; v2 = [p(3,1)-p(2,1), p(3,2)-p(2,2)]; % Find the angle. theta = acos(dot(v1,v2)/(norm(v1)*norm(v2))); % Convert it to degrees. angle_degrees = (theta * (180/pi)); % Display the angle in the title of the figure. title(sprintf('(%1.0f) degrees',angle_degrees)) To use the angle measurement tool, pass it an image. I = imread('gantrycrane.png'); my_angle_measurement_tool(I); The tool opens a figure window, displaying the image with the angle measure tool centered over the image in a right angle. Move the pointer over any of the vertices of the tool to measure any angle in the image. In the following figure, the tool is measuring an angle in the image. Note the size of the angle displayed in the title of the figure. 5-36 Creating Your Own Modular Tools Angle displayed in title. Angle measurement tool Custom Angle Measurement Tool 5-37 5 5-38 Building GUIs with Modular Tools 6 Geometric Transformations A geometric transformation (also known as a spatial transformation) modifies the spatial relationship between pixels in an image, mapping pixel locations in an moving image to new locations in an output image. The toolbox includes functions that perform certain specialized geometric transformations, such as resizing and rotating an image. In addition, the toolbox includes functions that you can use to perform many types of 2-D and N-D geometric transformations, including custom transformations. • “Resize an Image” on page 6-2 • “Rotate an Image” on page 6-5 • “Crop an Image” on page 6-6 • “2-D Geometric Transformations” on page 6-8 • “Perform a 2-D Translation” on page 6-15 • “N-Dimensional Spatial Transformations” on page 6-20 • “Register an Image Using Spatial Referencing Objects to Enhance the Display” on page 6-22 6 Geometric Transformations Resize an Image In this section... “Overview” on page 6-2 “Specifying the Interpolation Method” on page 6-3 “Preventing Aliasing by Using Filters” on page 6-4 Overview To resize an image, use the imresize function. When you resize an image, you specify the image to be resized and the magnification factor. To enlarge an image, specify a magnification factor greater than 1. To reduce an image, specify a magnification factor between 0 and 1. . For example, the command below increases the size of an image by 1.25 times. I = imread('circuit.tif'); J = imresize(I,1.25); imshow(I) figure, imshow(J) 6-2 Resize an Image You can specify the size of the output image by passing a vector that contains the number of rows and columns in the output image. If the specified size does not produce the same aspect ratio as the input image, the output image will be distorted. If you specify one of the elements in the vector as NaN, imresize calculates the value for that dimension to preserve the aspect ratio of the image. This example creates an output image with 100 rows and 150 columns. I = imread('circuit.tif'); J = imresize(I,[100 150]); imshow(I) figure, imshow(J) To perform the resizing required for multiresolution processing, use the impyramid function. Specifying the Interpolation Method Interpolation is the process used to estimate an image value at a location in between image pixels. When imresize enlarges an image, the output image contains more pixels than the original image. The imresize function uses interpolation to determine the values for the additional pixels. Interpolation methods determine the value for an interpolated pixel by finding the point in the input image that corresponds to a pixel in the output image and then calculating the value of the output pixel by computing a weighted average of some set of pixels in the vicinity of the point. The weightings are based on the distance each pixel is from the point. By default, imresize uses bicubic interpolation to determine the values of pixels in the output image, but you can specify other interpolation methods and interpolation kernels. In the following example, imresize uses the bilinear interpolation method. See the imresize reference page for a complete list of interpolation methods and interpolation kernels available. You can also specify your own custom interpolation kernel. Y = imresize(X,[100 150],'bilinear') 6-3 6 Geometric Transformations Preventing Aliasing by Using Filters When you reduce the size of an image, you lose some of the original pixels because there are fewer pixels in the output image and this can cause aliasing. Aliasing that occurs as a result of size reduction normally appears as “stair-step“ patterns (especially in high-contrast images), or as moiré (ripple-effect) patterns in the output image. By default, imresize uses antialiasing to limit the impact of aliasing on the output image for all interpolation types except nearest neighbor. To turn off antialiasing, specify the 'Antialiasing' parameter and set the value to false. Note Even with antialiasing, resizing an image can introduce artifacts, because information is always lost when you reduce the size of an image. For more information, see the reference page for imresize. 6-4 Rotate an Image Rotate an Image To rotate an image, use the imrotate function. When you rotate an image, you specify the image to be rotated and the rotation angle, in degrees. If you specify a positive rotation angle, imrotate rotates the image counterclockwise; if you specify a negative rotation angle, imrotate rotates the image clockwise. By default, imrotate creates an output image large enough to include the entire original image. Pixels that fall outside the boundaries of the original image are set to 0 and appear as a black background in the output image. You can, however, specify that the output image be the same size as the input image, using the 'crop' argument. Similarly, imrotate uses nearest-neighbor interpolation by default to determine the value of pixels in the output image, but you can specify other interpolation methods. See the imrotate reference page for a list of supported interpolation methods. This example rotates an image 35° counterclockwise and specifies bilinear interpolation. I = imread('circuit.tif'); J = imrotate(I,35,'bilinear'); imshow(I) figure, imshow(J) 6-5 6 Geometric Transformations Crop an Image Note You can also crop an image interactively using the Image Tool — see “Crop an Image Using the Image Viewer App” on page 4-52. To extract a rectangular portion of an image, use the imcrop function. Using imcrop, you can specify the crop region interactively using the mouse or programmatically by specifying the size and position of the crop region. This example illustrates an interactive syntax. The example reads an image into the MATLAB workspace and calls imcrop specifying the image as an argument. imcrop displays the image in a figure window and waits for you to draw the crop rectangle on the image. When you move the pointer over the image, the shape of the pointer changes to cross hairs . Click and drag the pointer to specify the size and position of the crop rectangle. You can move and adjust the size of the crop rectangle using the mouse. When you are satisfied with the crop rectangle, double-click to perform the crop operation, or right-click inside the crop rectangle and select Crop Image from the context menu. imcrop returns the cropped image in J. I = imread('circuit.tif') J = imcrop(I); 6-6 Crop an Image Resize handle Crop rectangle Crop Image tool context menu You can also specify the size and position of the crop rectangle as parameters when you call imcrop. Specify the crop rectangle as a four-element position vector, [xmin ymin width height]. In this example, you call imcrop specifying the image to crop, I, and the crop rectangle. imcrop returns the cropped image in J. I = imread('circuit.tif'); J = imcrop(I,[60 40 100 90]); 6-7 6 Geometric Transformations 2-D Geometric Transformations In this section... “Defining the Geometric Transformation” on page 6-9 “Performing the Geometric Transformation” on page 6-11 “Understanding Geometric Transformation” on page 6-12 “Specifying Fill Values” on page 6-13 To perform a general 2-D geometric transformation: 1 Define the parameters of the geometric transformation, creating a geometric transformation object. The toolbox defines several geometric transformation objects for different types of transformations, such as affine and projective. 2 Perform the transformation. To do this, you pass the image to be transformed and the geometric transformation object to the imwarp function. The following figure illustrates this process. 6-8 2-D Geometric Transformations Defining the Geometric Transformation Before you can perform a geometric transformation, you must first define the parameters of the transformation in a geometric transformation object. The following sections describe two ways you can do this: • “Using a Transformation Matrix” on page 6-9 • “Using Sets of Points” on page 6-11 Using a Transformation Matrix If you know the transformation matrix for the geometric transformation you want to perform, you can create one of the geometric transformation objects directly, passing the transformation matrix as a parameter. 6-9 6 Geometric Transformations For example, you can use a 3-by-3 matrix to specify any of the affine transformations. For affine transformations, the last column must contain 0 0 1 ([zeros(N,1); 1]). The following table lists affine transformations with the transformation matrix used to define them. You can combine multiple affine transformations into a single matrix. Affine Transform Example Transformation Matrix Translation tx specifies the displacement along the x axis ty specifies the displacement along the y axis. Scale sx specifies the scale factor along the x axis sy specifies the scale factor along the y axis. Shear shx specifies the shear factor along the x axis shy specifies the shear factor along the y axis. Rotation q specifies the angle of rotation. The following example defines the transformation matrix for a translation and creates an affine2d geometric transformation object. xform = [ 1 0 0 0 1 0 40 40 1 ]; tform_translate = affine2d(xform); 6-10 2-D Geometric Transformations tform_translate = affine2d with properties: T: [3x3 double] Dimensionality: 2 Using Sets of Points You can create a geometric transformation object by passing two sets of control point pairs to the fitgeotrans function. The fitgeotrans function estimates the transformation from these points and returns one of the geometric transformation objects. Different transformations require a varying number of points. For example, affine transformations require three non-collinear points in each image (a triangle) and projective transformations require four points (a quadrilateral). This example passes two sets of control points to fitgeotrans, which returns an affine geometric transformation object. movingPoints = [11 11;21 11; 21 21]; fixedPoints = [51 51;61 51;61 61]; tform = fitgeotrans(movingPoints,fixedPoints,'affine') tform = affine2d with properties: T: [3x3 double] Dimensionality: 2 Performing the Geometric Transformation Once you specify the transformation in a geometric transformation object, you can perform the transformation by calling the imwarp function, passing it the image to be transformed and a geometric transformation object. The imwarp function performs the specified transformation on the coordinates of the input image and creates an output image. 6-11 6 Geometric Transformations For example, to perform a transformation of the checkerboard image using the geometric transformation object created in “Defining the Geometric Transformation” on page 6-9, you would call imwarp this way: cb_trans = imwarp(cb, tform_translate); Understanding Geometric Transformation imwarp determines the value of pixels in the output image by mapping the new locations back to the corresponding locations in the input image (inverse mapping). imwarp interpolates within the input image to compute the output pixel value. See imwarp for more information about supported interpolation methods. The following figure illustrates a translation transformation. By convention, the axes in input space are labeled u and v and the axes in output space are labelled x and y. In the figure, note how imwarp modifies the spatial coordinates that define the locations of pixels in the input image. The pixel at (1,1) is now positioned at (41,41). In the checkerboard image, each black, white, and gray square is 10 pixels high and 10 pixels wide. (For more information about the distinction between spatial coordinates and pixel coordinates, see “Expressing Image Locations” on page 2-3. ) Input Image Translated 6-12 2-D Geometric Transformations Specifying Fill Values When you perform a transformation, there are often pixels in the output image that are not part of the original input image. These pixels must be assigned some value, called a fill value. By default, imwarp sets these pixels to zero and they are displayed as black. Using the FillValues parameter with the imwarp function, you can specify a different color. If the image being transformed is a grayscale image, you must specify a scalar value that specifies a shade of gray. For example, in , where the example displays the translated checkerboard image in relation to the original coordinate space, you can specify a fill value that matches the color of the gray squares, rather than the default black color. cb_fill = imwarp(cb, tform_translate,'FillValues', .7 ); figure, imshow(cb_fill) Translated Image with Gray Fill Value If the image being transformed is an RGB image, you can use either a scalar value or a 1-by-3 vector. If you specify a scalar, imwarp uses that shade of gray for each plane of the RGB image. If you specify a 1-by-3 vector, imwarp interprets the values as an RGB color value. For example, this code translates an RGB image, specifying an RGB color value as the fill value. The example specifies one of the light green values in the image as the fill value. 6-13 6 Geometric Transformations rgb = imread('onion.png'); xform = [ 1 0 0 0 1 0 40 40 1 ] tform_translate = affine2d(xform); cb_rgb = imwarp(rgb,tform_translate,'FillValues',[187;192;57]); figure, imshow(cb_rgb) Translated RGB Image with Color Fill Value If you are transforming multiple RGB images, you can specify different fill values for each RGB image. For example, if you want to transform a series of 10 RGB images, a 4-D array with dimensions 200-by-200-by-3-by-10, you can specify a 3-by-10 array containing RGB color values for each plane. 6-14 Perform a 2-D Translation Perform a 2-D Translation This example shows how to perform a simple affine transformation called a translation. In a translation, you shift an image in coordinate space by adding a specified value to the x- and y-coordinates. Import the image to be transformed. This example creates a checkerboard image, using the checkerboard function. By default, checkerboard creates an 80-by-80 pixel image. cb = checkerboard; imshow(cb) Get spatial referencing information about the image. This information is useful when you want to display the result of the transformation. R = imref2d(size(cb)) R = 6-15 6 Geometric Transformations imref2d with properties: XWorldLimits: YWorldLimits: ImageSize: PixelExtentInWorldX: PixelExtentInWorldY: ImageExtentInWorldX: ImageExtentInWorldY: XIntrinsicLimits: YIntrinsicLimits: [0.5000 [0.5000 [80 80] 1 1 80 80 [0.5000 [0.5000 80.5000] 80.5000] 80.5000] 80.5000] Create a geometric transformation object that defines the translation you want to perform. This example implements a translation transformation which is a type of 2-D affine transformation so it uses the affine2d geometric transformation object. You can use a 3-by-3 transformation matrix to define the transformation. In this matrix, A(3,1) specifies the number of pixels to shift the image in the horizontal direction and A(3,2) specifies the number of pixels to shift the image in the vertical direction. Now create a geometric transformation object using the transformation matrix. tform = affine2d([1 0 0; 0 1 0; 20 20 1]); tform = affine2d with properties: T: [3x3 double] Dimensionality: 2 Perform the transformation. Call the imwarp function specifying the image you want to transform and the geometric transformation object. imwarp returns the transformed image. This example gets the optional spatial referencing object return value which contains information about the transformed image. View the original and the transformed image side-by-side using the subplot function in conjunction with imshow. [out,Rout] = imwarp(cb,tform); figure; subplot(1,2,1); imshow(cb,Rcb); 6-16 Perform a 2-D Translation subplot(1,2,2); imshow(out,Rout) When viewing the transformed image, especially for a translation operation, it might appear that the transformation had no effect. The transformed image looks identical to the original image. The reason that no change is apparent in the visualization is because imwarp sizes the output image to be just large enough to contain the entire transformed image but not the entire output coordinate space. Notice, however, that the coordinate values have been changed by the transformation. Customize your view of the output image. Instead of the default view, you might want to see the entirety of the transformed image in the same relation 6-17 6 Geometric Transformations to the origin of the coordinate space as the original image. To do this, use the 'OutputView' parameter, specifying a spatial referencing object that resets the image output limits. This example makes a copy of the spatial referencing object associated with the original image and then modifies the world coordinate limits to accommodate the full size of the transformed image. imwarp changes the locations of pixels between input space and output space. The pixel located at (1,1) in the input image is now located at (21,21) in the output image. Note, however, that the value at that pixel location has not changed. Pixel (1,1) in the input image is black and so is pixel (21,21) in the output image. To get another view of the translation in relation to the original image, you can use the 'OutputView' parameters that specifies the size of output image and how much of the output coordinate space is included in the output image. The example sets the limits of the output image in world coordinates to include the origin from the input image. Rout = Rcb; Rout.XWorldLimits(2) = Rout.XWorldLimits(2)+20; Rout.YWorldLimits(2) = Rout.YWorldLimits(2)+20; [out,Rout] = imwarp(cb,tform,'OutputView',Rout); figure, subplot(1,2,1); imshow(cb,Rcb); subplot(1,2,2); imshow(out,Rout) 6-18 Perform a 2-D Translation 6-19 6 Geometric Transformations N-Dimensional Spatial Transformations The following functions, when used in combination, provide a vast array of options for defining and working with 2-D, N-D, and mixed-D spatial transformations: • maketform • fliptform • tformfwd • tforminv • findbounds • makeresampler • tformarray • imtransform The imtransform, findbounds, and tformarray functions use the tformfwd and tforminv functions internally to encapsulate the forward transformations needed to determine the extent of an output image or array and/or to map the output pixels/array locations back to input locations. You can use tformfwd and tforminv to explore the geometric effects of a transformation by applying them to points and lines and plotting the results. They support a consistent handling of both image and pointwise data. The following example, “Performing the Geometric Transformation” on page 6-11, uses the makeresampler function with a standard interpolation method. You can also use it to obtain special effects or custom processing. For example, you could specify your own separable filtering/interpolation kernel, build a custom resampler around the MATLAB interp2 or interp3 functions, or even implement an advanced antialiasing technique. And, as noted, you can use tformarray to work with arbitrary-dimensional array transformations. The arrays do not even need to have the same dimensions. The output can have either a lower or higher number of dimensions than the input. 6-20 N-Dimensional Spatial Transformations For example, if you are sampling 3-D data on a 2-D slice or manifold, the input array might have a lower dimensionality. The output dimensionality might be higher, for example, if you combine multiple 2-D transformations into a single 2-D to 3-D operation. For example, this code uses imtransform to perform a projective transformation of a checkerboard image. I = checkerboard(20,1,1); figure; imshow(I) T = maketform('projective',[1 1; 41 1; 41 41; 1 41],... [5 5; 40 5; 35 30; -10 30]); R = makeresampler('cubic','circular'); K = imtransform(I,T,R,'Size',[100 100],'XYScale',1); figure, imshow(K) The imtransform function options let you control many aspects of the transformation. For example, note how the transformed image appears to contain multiple copies of the original image. This is accomplished by using the 'Size' option, to make the output image larger than the input image, and then specifying a padding method that extends the input image by repeating the pixels in a circular pattern. The Image Processing Toolbox Image Transformation demos provide more examples of using the imtransform function and related functions to perform different types of spatial transformations. 6-21 6 Geometric Transformations Register an Image Using Spatial Referencing Objects to Enhance the Display This example shows how to use spatial referencing objects to understand the spatial relationship between two images in image registration. Read the two images of the same scene that are slightly misaligned. This example brings one of the images, called the moving image, into alignment with the other image, called the fixed image. These two images are included in the toolbox as sample data files. fixed = imread('westconcordorthophoto.png'); moving = imread('westconcordaerial.png'); Display the moving (unregistered) image. iptsetpref('ImshowAxesVisible','on') imshow(moving) text(size(moving,2),size(moving,1)+30, ... 'Image courtesy of mPower3/Emerge', ... 'FontSize',7,'HorizontalAlignment','right'); 6-22 Register an Image Using Spatial Referencing Objects to Enhance the Display Fit a geometric transformation to control points. Create the transformation using preselected control points. Load the MAT-file that contains the control points for the fixed and moving images. 6-23 6 Geometric Transformations load westconcordpoints tform = fitgeotrans(movingPoints, fixedPoints, 'projective'); tform = projective2d with properties: T: [3x3 double] Dimensionality: 2 Transform the moving image. Use imwarp to perform the transformation necessary to register the moving image with the fixed image. This example uses the optional FillValues parameter to specify a fill value (white). The white background will help when the fixed image is displayed over the transformed moving image to check registration. registered = imwarp(moving, tform,'FillValues', 255); figure, imshow(registered); 6-24 Register an Image Using Spatial Referencing Objects to Enhance the Display Notice that the full content of the moving image is present, although it has been geometrically transformed. Also note that there are no blank rows or columns. Overlay a blended version of the fixed image over the moving image. Notice how the two images appear misregistered. This happens because the example assumes that the images are both in the default intrinsic coordinate system. The next steps provide two ways to remedy this display problem. 6-25 6 Geometric Transformations figure, imshowpair(fixed,registered,'blend'); Specifying the 'OutputView' parameter with imwarp. One way to ensure that the registered image appears registered with the fixed image is to truncate the registered image by discarding any areas that would extrapolate beyond the extent of the fixed image. You use spatial referencing objects and the 'OutputView' name/value pair of imwarp to accomplish this. Create a default spatial referencing object that specifies the size and location of the fixed image. 6-26 Register an Image Using Spatial Referencing Objects to Enhance the Display Rfixed = imref2d(size(fixed)) Rfixed = imref2d with properties: XWorldLimits: YWorldLimits: ImageSize: PixelExtentInWorldX: PixelExtentInWorldY: ImageExtentInWorldX: ImageExtentInWorldY: XIntrinsicLimits: YIntrinsicLimits: [0.5000 364.5000] [0.5000 366.5000] [366 364] 1 1 364 366 [0.5000 364.5000] [0.5000 366.5000] Specify the 'OutputView' parameter to imwarp using the spatial referencing object, Rfixed. You use spatial referencing object to created a resampled image registered1 that is constrained to the same number of rows and columns and same spatial limits as the fixed image. registered1 = imwarp(moving,tform,'FillValues', 255,'OutputView',Rfixed); Display the registered image, overlaying a semitransparent version of the base image for comparison. In this view, you can see that the images have been registered, but part of the unregistered image has been discarded. The next step provides another solution in which the entire registered image is visible. figure, imshowpair(fixed,registered1,'blend'); 6-27 6 Geometric Transformations View the full extent of the registered image. Use the optional imwarp syntax that returns the output spatial referencing object that indicates the full transformed image’s position the same default intrinsic coordinate system as the fixed image. [registered2, Rregistered] = imwarp(moving, tform,'FillValues', 255); Display the registered image, overlaying a semitransparent version of the base image for comparison. figure, imshowpair(fixed,Rfixed,registered2,Rregistered,'blend'); 6-28 Register an Image Using Spatial Referencing Objects to Enhance the Display 6-29 6 6-30 Geometric Transformations 7 Image Registration This chapter describes the image registration capabilities of the Image Processing Toolbox software. Image registration is the process of aligning two or more images of the same scene. Image registration is often used as a preliminary step in other image processing applications. • “Image Registration Techniques” on page 7-2 • “Control Point Registration” on page 7-4 • “Using cpselect in a Script” on page 7-5 • “Register an Aerial Photograph to a Digital Orthophoto” on page 7-6 • “Geometric Transformation Types” on page 7-12 • “Control Point Selection Procedure” on page 7-13 • “Start the Control Point Selection Tool” on page 7-15 • “Find Visual Elements Common to Both Images” on page 7-18 • “Select Matching Control Point Pairs” on page 7-24 • “Export Control Points to the Workspace” on page 7-30 • “Use Cross-Correlation to Improve Control Point Placement” on page 7-32 • “Intensity-Based Automatic Image Registration” on page 7-33 • “Registering Multimodal MRI Images” on page 7-35 7 Image Registration Image Registration Techniques Image registration is the process of aligning two or more images of the same scene. This process involves designating one image as the reference (also called the reference image or the fixed image), and applying geometric transformations to the other images so that they align with the reference. Images can be misaligned for a variety of reasons. Commonly, the images are captured under variable conditions that can change camera perspective. Misalignment can also be the result of lens and sensor distortions or differences between capture devices. A geometric transformation maps locations in one image to new locations in another image. The step of determining the correct geometric transformation parameters is key to the image registration process. Image registration is often used as a preliminary step in other image processing applications. For example, you can use image registration to align satellite images or to align medical images captured with different diagnostic modalities (MRI and SPECT). Image registration allows you to compare common features in different images. For example, you might discover how a river has migrated, how an area became flooded, or whether a tumor is visible in an MRI or SPECT image. Together, the Image Processing Toolbox and Computer Vision System Toolbox™ offer three image registration solutions: • “Intensity-Based Automatic Image Registration” on page 7-33 maps certain pixels in each image to the same location based on relative intensity patterns. This approach is best suited for workflows that involve a large collection of images or when you require an automated workflow. This functionality resides in the Image Processing Toolbox. • “Control Point Registration” on page 7-4 allows you to manually select common features in each image to map to the same pixel location. This method of registration is best suited for images that have distinct features. It resides in the Image Processing Toolbox. • An automated feature-based workflow automatically aligns images by selecting matching features between two images. This workflow includes feature detection, extraction, and matching, followed by transform estimation. Features can be corners or blobs and the distortion can include 7-2 Image Registration Techniques rotation and scale changes. For more information, see Finding Rotation and Scale of an Image Using Automated Feature Matching. You must have the Computer Vision System Toolbox installed to use this method. 7-3 7 Image Registration Control Point Registration The Image Processing Toolbox software provides tools to support point mapping to determine the parameters of the transformation required to bring an image into alignment with another image. In point mapping, you pick points in a pair of images that identify the same feature or landmark in the images. Then, a geometric mapping is inferred from the positions of these control points. Note You might need to perform several iterations of this process, experimenting with different types of transformations, before you achieve a satisfactory result. In some cases, you might perform successive registrations, removing gross global distortions first, and then removing smaller local distortions in subsequent passes. The following figure provides a graphic illustration of this process. This process is best understood by looking at an example. See “Register an Aerial Photograph to a Digital Orthophoto” on page 7-6 for an extended example. 7-4 Using cpselect in a Script Using cpselect in a Script If you need to perform the same kind of registration for many images, you can automate the process by putting all the steps in a script. For example, you could create a script that launches the Control Point Selection Tool with the images to be registered. The script could then use the control points selected to create a geometric transformation object and pass this object and the image to be registered to the imwarp function, outputting the registered image. When calling cpselect in a script, specify the 'Wait' option. The 'Wait' option causescpselect to block the MATLAB command line until control points have been selected and returned. If you do not use the 'Wait' option, cpselect returns control immediately and your script will continue without allowing time for control point selection. In addition, without the 'Wait' option, cpselect does not return the control points as return values. For an example, see the cpselect reference page. 7-5 7 Image Registration Register an Aerial Photograph to a Digital Orthophoto This example shows how to use point mapping to perform image registration. Read the sample images and display them. orthophoto = imread('westconcordorthophoto.png'); figure, imshow(orthophoto) unregistered = imread('westconcordaerial.png'); figure, imshow(unregistered) In this example, the fixed image is westconcordorthophoto.png, the MassGIS georegistered orthophoto. It is a panchromatic (grayscale) image, supplied by the Massachusetts Geographic Information System (MassGIS), that has been orthorectified to remove camera, perspective, and relief distortions (via a specialized image transformation process). The orthophoto is also georegistered (and geocoded) — the columns and rows of the digital orthophoto image are aligned to the axes of the Massachusetts State Plane coordinate system. In the orthophoto, each pixel center corresponds to a definite geographic location, and every pixel is 1 meter square in map units. 7-6 Register an Aerial Photograph to a Digital Orthophoto The image to be registered is westconcordaerial.png, a digital aerial photograph supplied by mPower3/Emerge, and is a visible-color RGB image. The aerial image is geometrically uncorrected: it includes camera perspective, terrain and building relief, internal (lens) distortions, and it does not have any particular alignment or registration with respect to the earth. The example reads both images into the MATLAB workspace but the cpselect function accepts file specifications for grayscale images. However, if you want to use cross-correlation to tune your control point positioning, the images must be in the workspace. Select pairs of corresponding control points in both images, using the Control Point Selection tool. Control points are landmarks that you can find in both images, like a road intersection, or a natural feature. To start this tool, enter cpselect, specifying as arguments the moving and fixed images. cpselect(unregistered, orthophoto) 7-7 7 7-8 Image Registration Register an Aerial Photograph to a Digital Orthophoto Save the control point pairs to the MATLAB workspace. In the Control Point Selection Tool, click the File menu and choose the Export Points to Workspace option. For example, the following set of control points in the moving image represent spatial coordinates; the left column lists x-coordinates, the right column lists y-coordinates. moving_points = 118.0000 304.0000 358.0000 127.0000 96.0000 87.0000 281.0000 292.0000 You can optionally fine-tune the control point pair placement, using the cpcorr function. This is an optional step that uses cross-correlation to adjust the position of the control points you selected with cpselect. To use cross-correlation, features in the two images must be at the same scale and have the same orientation. They cannot be rotated relative to each other. Because the Concord image is rotated in relation to the fixed image, cpcorr cannot tune the control points. Specify the type of transformation and infer its parameters, using fitgeotrans. fitgeotrans is a data-fitting function that determines the transformation needed to bring the image into alignment, based on the geometric relationship of the control points. fitgeotrans returns the parameters in a geometric transformation object. mytform = fitgeotrans(movingPoints, fixedPoints, 'projective'); mytform = projective2d with properties: T: [3x3 double] Dimensionality: 2 When you use fitgeotrans, you must specify the type of transformation you want to perform. The fitgeotrans function can infer the parameters for 7-9 7 Image Registration several types of transformations. You must choose which transformation will correct the type of distortion present in the moving image. Images can contain more than one type of distortion. The predominant distortion in the aerial image of West Concord (the moving image) results from the camera perspective. Ignoring terrain relief, which is minor in this area, image registration can correct for camera perspective distortion by using a projective transformation. The projective transformation also rotates the image into alignment with the map coordinate system underlying the fixed digital orthophoto image. Transform the moving image (unregistered) to bring it into alignment with the fixed image. You use imwarp to perform the transformation, passing it the moving image and the geometric transformation object returned by fitgeotrans. imwarp returns the transformed image. registered = imwarp(unregistered, mytform); The following figure shows the transformed image transparently overlaid on the fixed image to show the results of the registration. 7-10 Register an Aerial Photograph to a Digital Orthophoto 7-11 7 Image Registration Geometric Transformation Types The Image Processing Toolbox provides functionality for applying geometric transformations to register images. For control point registration, the fitgeotrans function can infer the parameters for the following types of transformations, listed in order of complexity. • 'nonreflective similarity' • 'affine' • 'projective' • 'polynomial' (Order 2, 3, or 4) • 'piecewise linear' • 'lwm' The first four transformations, 'nonreflective similarity', 'affine', 'projective', and 'polynomial' are global transformations. In these transformations, a single mathematical expression applies to an entire image. The last two transformations, 'piecewise linear' and 'lwm' (local weighted mean), are local transformations. In these transformations, different mathematical expressions apply to different regions within an image. When exploring how different transformations affect the images you are working with, try the global transformations first. If these transformations are not satisfactory, try the local transformations: the piecewise linear transformation first, and then the local weighted mean transformation. Your choice of transformation type affects the number of control point pairs you need to select. For example, a nonreflective similarity transformation requires at least two control point pairs. A polynomial transformation of order 4 requires 15 control point pairs. For more information about these transformation types, and the special syntaxes they require, see cpselect. For information about the specific transformation types available for intensity-based automatic image registration, see the imregister function reference page. 7-12 Control Point Selection Procedure Control Point Selection Procedure To specify control points in a pair of images you want to register, use the Control Point Selection Tool, cpselect. The tool displays the image you want to register, called the moving image, next to the image you want to compare it to, called the fixed image. Specifying control points is a four-step process: 1 Start the tool, specifying the moving image and the fixed image. 2 Use navigation aids to explore the image, looking for visual elements that you can identify in both images. cpselect provides many ways to navigate around the image, panning and zooming to view areas of the image in more detail. 3 Specify matching control point pairs in the moving image and the fixed image. 4 Save the control points in the MATLAB workspace. The following figure shows the default appearance of the tool when you first start it. 7-13 7 7-14 Image Registration Start the Control Point Selection Tool Start the Control Point Selection Tool To use the Control Point Selection Tool, enter the cpselect command at the MATLAB prompt. As arguments, specify the image you want to register (the moving image) and the image you want to compare it to (the fixed image). For simplicity, this section uses the same image as the moving and the fixed image. To walk through an example of an actual registration, see “Register an Aerial Photograph to a Digital Orthophoto” on page 7-6. moon_fixed = imread('moon.tif'); moon_moving = moon_fixed; cpselect(moon_moving, moon_fixed); The cpselect command has other optional arguments. For example, you can restart a control point selection session by including a cpstruct structure as the third argument. For more information about restarting sessions, see “Export Control Points to the Workspace” on page 7-30. For complete details, see the cpselect reference page. When the Control Point Selection Tool starts, it contains three primary components: • Details windows—The two windows displayed at the top of the tool are called the Detail windows. These windows show a close-up view of a portion of the images you are working with. The moving image is on the left and the fixed image is on the right. • Overview windows—The two windows displayed at the bottom of the tool are called the Overview windows. These windows show the images in their entirety, at the largest scale that fits the window. The moving image is on the left and the fixed image is on the right. You can control whether the Overview window appears by using the View menu. • Details rectangle—Superimposed on the images displayed in the two Overview windows is a rectangle, called the Detail rectangle. This rectangle controls the part of the image that is visible in the Detail window. By default, at startup, the detail rectangle covers one quarter of the entire image and is positioned over the center of the image. You can move the Detail rectangle to change the portion of the image displayed in the Detail windows. 7-15 7 Image Registration The following figure shows these components of the Control Point Selection Tool. 7-16 Start the Control Point Selection Tool 7-17 7 Image Registration Find Visual Elements Common to Both Images To find visual elements that are common to both images, you might want to change the section of the image displayed in the detail view or zoom in on a part of the image to view it in more detail. The following sections describe the different ways to change your view of the images: In this section... “Using Scroll Bars to View Other Parts of an Image” on page 7-18 “Using the Detail Rectangle to Change the View” on page 7-18 “Panning the Image Displayed in the Detail Window” on page 7-20 “Zooming In and Out on an Image” on page 7-20 “Specifying the Magnification of the Images” on page 7-21 “Locking the Relative Magnification of the Moving and Fixed Images” on page 7-22 Using Scroll Bars to View Other Parts of an Image To view parts of an image that are not visible in the Detail or Overview windows, use the scroll bars provided for each window. As you scroll the image in the Detail window, note how the Detail rectangle moves over the image in the Overview window. The position of the Detail rectangle always shows the portion of the image in the Detail window. Using the Detail Rectangle to Change the View To get a closer view of any part of the image, move the Detail rectangle in the Overview window over that section of the image. cpselect displays that section of the image in the Detail window at a higher magnification than the Overview window. To move the detail rectangle, 1 Move the pointer into the Detail rectangle. The cursor changes to the fleur shape, 7-18 . Find Visual Elements Common to Both Images 2 Press and hold the mouse button to drag the detail rectangle anywhere on the image. Note As you move the Detail rectangle over the image in the Overview window, the view of the image displayed in the Detail window changes. 7-19 7 Image Registration Panning the Image Displayed in the Detail Window To change the section of the image displayed in the Detail window, use the pan tool to move the image in the window. To use the pan tool, 1 Click the Pan button in the Control Point Selection Tool toolbar or select Pan from the Tools menu. 2 Move the pointer over the image in the Detail window. The cursor changes to the hand shape, . 3 Press and hold the mouse button. The cursor changes to a closed fist shape, . Use the mouse to move the image in the Detail window. Note As you move the image in the Detail window, the Detail rectangle in the Overview window moves. Zooming In and Out on an Image To enlarge an image to get a closer look or shrink an image to see the whole image in context, you can zoom in or zoom out on the images displayed. (You can also zoom in or out on an image by changing the magnification. See “Specifying the Magnification of the Images” on page 7-21 for more information.) To zoom in or zoom out on the fixed or moving images, 1 Click the appropriate magnifying glass button on the Control Point Selection Tool toolbar or select Zoom In or Zoom Out from the Tools menu. Zoom in 7-20 Zoom out Find Visual Elements Common to Both Images 2 Move the pointer over the image in the Detail window that you want to zoom in or out on. The cursor changes to the appropriate magnifying glass shape, such as . Position the cursor over a location in the image and click the mouse. With each click, cpselect changes the magnification of the image by a preset amount. (See“Specifying the Magnification of the Images” on page 7-21 for a list of some of these magnifications.) cpselect centers the new view of the image on the spot where you clicked. Another way to use the Zoom tool to zoom in on an image is to position the cursor over a location in the image and, while pressing and holding the mouse button, draw a rectangle defining the area you want to zoom in on. cpselect magnifies the image so that the chosen section fills the Detail window. cpselect resizes the detail rectangle in the Overview window as well. The size of the Detail rectangle in the Overview window changes as you zoom in or out on the image in the Detail window. To keep the relative magnifications of the fixed and moving images synchronized as you zoom in or out, click the Lock ratio check box. See “Locking the Relative Magnification of the Moving and Fixed Images” on page 7-22 for more information. Specifying the Magnification of the Images To enlarge an image to get a closer look or to shrink an image to see the whole image in context, use the magnification edit box. (You can also use the Zoom buttons to enlarge or shrink an image. See “Zooming In and Out on an Image” on page 7-20 for more information.) To change the magnification of an image, 1 Move the cursor into the magnification edit box of the window you want to change. The cursor changes to the text entry cursor. 2 Type a new value in the magnification edit box and press Enter, or click the menu associated with the edit box and choose from a list of preset magnifications. cpselect changes the magnification of the image and displays the new view in the appropriate window. To keep the relative magnifications of the fixed and moving images synchronized as you change the magnification, 7-21 7 Image Registration click the Lock ratio check box. See “Locking the Relative Magnification of the Moving and Fixed Images” on page 7-22 for more information. Locking the Relative Magnification of the Moving and Fixed Images To keep the relative magnification of the moving and fixed images automatically synchronized in the Detail windows, click the Lock Ratio check box. 7-22 Find Visual Elements Common to Both Images When the Lock Ratio check box is selected, cpselect changes the magnification of both the moving and fixed images when you zoom in or out on either one of the images or specify a magnification value for either of the images. Lock magnification ratio check box 7-23 7 Image Registration Select Matching Control Point Pairs The primary function of the Control Point Selection Tool is to enable you to pick control points in the image to be registered (the moving image) and the image to which you are comparing it (the fixed image). When you start cpselect, point selection is enabled, by default. You specify control points by pointing and clicking in the moving and fixed images, in either the Detail or the Overview windows. Each point you specify in the moving image must have a match in the fixed image. The following sections describe the ways you can use the Control Point Selection Tool to choose control point pairs: In this section... “Picking Control Point Pairs Manually” on page 7-24 “Using Control Point Prediction” on page 7-26 “Moving Control Points” on page 7-29 “Deleting Control Points” on page 7-29 Picking Control Point Pairs Manually To specify a pair of control points in your images, 1 Click the Control Point Selection button in the Control Point Selection Tool toolbar or select Add Points from the Tools menu. (Control point selection mode is active by default.) The cursor changes to a crosshairs shape 2 Position the cursor over a feature you have visually selected in any of the images displayed and click the mouse button. cpselect places a control , at the position you specified, in both the Detail window point symbol, and the corresponding Overview window. cpselect numbers the points as you select them. The appearance of the control point symbol indicates its current state. The circle around the point indicates that it is the currently selected point. The number identifies control point pairs. 7-24 Select Matching Control Point Pairs Note Depending on where in the image you pick control points, the symbol for the point might be visible in the Overview window, but not in the Detail window. 3 You can select another point in the same image or you can move to the corresponding image and create a match for the point. To create the match for this control point, position the cursor over the same feature in the corresponding Detail or Overview window and click the mouse button. cpselect places a control point symbol at the position you specified, in both the Detail and Overview windows. You can work in either direction: picking control points in either of the Detail windows, moving or fixed, or in either of the Overview windows, moving or fixed. To match an unmatched control point, select it, and then pick a point in the corresponding window. You can move or delete control points after you create them. The following figure illustrates control points in several states. 7-25 7 Image Registration Matched pair of points Selected, unmatched point Using Control Point Prediction Instead of picking matching control points yourself, you can let the Control Point Selection Tool estimate the match for the control points you specify, automatically. The Control Point Selection Tool determines the position of the matching control point based on the geometric relationship of the previously selected control points, not on any feature of the underlying images. To illustrate point prediction, this figure shows four control points selected in the moving image, where the points form the four corners of a square. (The control point selections in the figure do not attempt to identify any landmarks in the image.) The figure shows the picking of a fourth point, in the left window, and the corresponding predicted point in the right window. 7-26 Select Matching Control Point Pairs Note how the Control Point Selection Tool places the predicted point at the same location relative to the other control points, forming the bottom right corner of the square. Predicted point 7-27 7 Image Registration Note By default, the Control Point Selection Tool does not include predicted points in the set of valid control points returned in movingPoints or fixedPoints. To include predicted points, you must accept them by selecting the points and fine-tuning their position with the cursor. When you move a predicted point, the Control Point Selection Tool changes the symbol to indicate that it has changed to a standard control point. For more information, see “Moving Control Points” on page 7-29. To use control point prediction, 1 Click the Control Point Prediction button . Note Because the Control Point Selection Tool predicts control point locations based on the locations of the previous control points, you cannot use point prediction until you have a minimum of two pairs of matched points. Until this minimum is met, the Control Point Prediction button is disabled. 2 Position the cursor anywhere in any of the images displayed. The cursor changes to the crosshairs shape, . You can pick control points in either of the Detail windows, moving or fixed, or in either of the Overview windows, moving or fixed. You also can work in either direction: moving-to-fixed image or fixed-to-moving image. 3 Click either mouse button. The Control Point Selection Tool places a control point symbol at the position you specified and places another control point symbol for a matching point in all the other windows. The symbol for the predicted point contains the letter P, control point, indicating that it’s a predicted 4 To accept a predicted point, select it with the cursor and move it. The Control Point Selection Tool removes the P from the point. 7-28 Select Matching Control Point Pairs Moving Control Points To move a control point, 1 Click the Control Point Selection button . 2 Position the cursor over the control point you want to move. The cursor changes to the fleur shape, 3 Press and hold the mouse button and drag the control point. The state of the control point changes to selected when you move it. If you move a predicted control point, the state of the control point changes to a regular (nonpredicted) control point. Deleting Control Points To delete a control point, and its matching point, if one exists 1 Click the Control Point Selection button . 2 Click the control point you want to delete. Its state changes to selected. If the control point has a match, both points become active. 3 Delete the point (or points) using one of these methods: • Pressing the Backspace key • Pressing the Delete key • Choosing one of the delete options from the Edit menu Using this menu you can delete individual points or pairs of matched points, in the moving or fixed images. 7-29 7 Image Registration Export Control Points to the Workspace After you specify control point pairs, you must save them in the MATLAB workspace to make them available for the next step in image registration, processing by fitgeotrans. To save control points to the MATLAB workspace, 1 Select File on the Control Point Selection Tool menu bar. 2 Choose the Export Points to Workspace option. The Control Point Selection Tool displays this dialog box: By default, the Control Point Selection Tool saves the x-coordinates and y-coordinates that specify the locations of the control points you selected in two arrays named movingPoints and fixedPoints, although you can specify other names. These are n-by-2 arrays, where n is the number of valid control point pairs you selected. This example shows the movingPoints array containing four pairs of control points. The values in the left column represent the x-coordinates; the values in the right column represent the y-coordinates. movingPoints = 215.6667 225.7778 156.5556 270.8889 262.3333 311.3333 340.1111 368.8889 Whenever you exit the Control Point Selection Tool, it asks if you want to save your control points. Saving Your Control Point Selection Session To save the current state of the Control Point Selection Tool, choose the Export Points to Workspace option from the File menu. In the Export Points to Workspace dialog box, select the Structure with all points check box. 7-30 Export Control Points to the Workspace This option saves the positions of all the control points you specified and their current states in a cpstruct structure. cpstruct = inputPoints: basePoints: inputBasePairs: ids: inputIdPairs: baseIdPairs: isInputPredicted: isBasePredicted: [2x2 [2x2 [2x2 [2x1 [2x2 [2x2 [2x1 [2x1 double] double] double] double] double] double] double] double] You can use the cpstruct to restart a control point selection session at the point where you left off. This option is useful if you are picking many points over a long time and want to preserve unmatched and predicted points when you resume work. The Control Point Selection Tool does not include unmatched and predicted points in the movingPoints and fixedPoints arrays. To extract the arrays of valid control point coordinates from a cpstruct, use the cpstruct2pairs function. 7-31 7 Image Registration Use Cross-Correlation to Improve Control Point Placement You might want to fine-tune the control points you selected using cpselect. Using cross-correlation, you can sometimes improve the points you selected by eye using the Control Point Selection Tool. To use cross-correlation, pass sets of control points in the moving and fixed images, along with the images themselves, to the cpcorr function. moving_pts_adj= cpcorr(movingPoints, fixedPoints, moving, fixed); The cpcorr function defines 11-by-11 regions around each control point in the moving image and around the matching control point in the fixed image, and then calculates the correlation between the values at each pixel in the region. Next, the cpcorr function looks for the position with the highest correlation value and uses this as the optimal position of the control point. The cpcorr function only moves control points up to 4 pixels based on the results of the cross-correlation. Note Features in the two images must be at the same scale and have the same orientation. They cannot be rotated relative to each other. If cpcorr cannot correlate some of the control points, it returns their values in movingPoints unmodified. 7-32 Intensity-Based Automatic Image Registration Intensity-Based Automatic Image Registration Intensity-based automatic image registration is an iterative process. It requires that you specify a pair of images, a metric, an optimizer, and a transformation type. The metric defines the image similarity metric for evaluating the accuracy of the registration. This image similarity metric takes two images and returns a scalar value that describes how similar the images are. The optimizer defines the methodology for minimizing or maximizing the similarity metric. The transformation type defines the type of 2-D transformation that brings the misaligned image (called the moving image) into alignment with the reference image (called the fixed image). The process begins with the transform type you specify and an internally determined transformation matrix. Together, they determine the specific image transformation that is applied to the moving image with bilinear interpolation. Next, the metric compares the transformed moving image to the fixed image and a metric value is computed. Finally, the optimizer checks for a stop condition. A stop condition is anything that warrants the termination of the process. In most cases, the process has reached a point of diminishing returns or it has reached the specified maximum number of iterations. If there is no stop condition, the optimizer adjusts the transformation matrix to begin the next iteration. 7-33 7 Image Registration Perform intensity-based image registration with the following steps: 1 Read the images into the workspace with imread. 2 Create the optimizer and metric with imregconfig. 3 Register the images with imregister. 4 View the results with imshowpair or save a copy of an image showing the results with imfuse. The example, “Registering Multimodal MRI Images” on page 7-35, demonstrates this workflow in detail. 7-34 Registering Multimodal MRI Images Registering Multimodal MRI Images This example shows how you can use imregister to automatically align two magnetic resonance images (MRI) to a common coordinate system using intensity-based image registration. Unlike some other techniques, it does not find features or use control points. Intensity-based registration is often well-suited for medical and remotely sensed imagery. Step 1: Load Images This example uses two magnetic resonance (MRI) images of a knee. The fixed image is a spin echo image, while the moving image is a spin echo image with inversion recovery. The two sagittal slices were acquired at the same time but are slightly out of alignment. fixed = dicomread('knee1.dcm'); moving = dicomread('knee2.dcm'); The imshowpair function is a useful function for visualizing images during every part of the registration process. Use it to see the two images individually in a montage fashion or display them stacked to show the amount of misregistration. figure, imshowpair(moving, fixed, 'montage') title('Unregistered') 7-35 7 Image Registration In the overlapping image from imshowpair, gray areas correspond to areas that have similar intensities, while magenta and green areas show places where one image is brighter than the other. In some imager pairs, green and magenta areas don’t always indicate misregistration, but in this example it’s easy to use the color information to see where they do. figure, imshowpair(moving, fixed) title('Unregistered') 7-36 Registering Multimodal MRI Images Step 2: Set up the Initial Registration The imregconfig function makes it easy to pick the correct optimizer and metric configuration to use with imregister. These two images have different intensity distributions, which suggests a multimodal configuration. 7-37 7 Image Registration [optimizer,metric] = imregconfig('multimodal'); The distortion between the two images includes scaling, rotation, and (possibly) shear. Use an affine transformation to register the images. It’s very, very rare that imregister will align images perfectly with the default settings. Nevertheless, using them is a useful way to decide which properties to tune first. tic movingRegisteredDefault = imregister(moving, fixed, 'affine', optimizer, me timeDefault = toc figure, imshowpair(movingRegisteredDefault, fixed) title('A: Default registration') timeDefault = 2.2974 7-38 Registering Multimodal MRI Images Step 3: Improve the Registration The initial registration was pretty good, but there are still some areas that don’t line up. It’s easiest to see this along the left and right edges of the image and in the small bright bands that run through the right-hand part. Try to 7-39 7 Image Registration improve the registration by adjusting the optimizer and metric configuration properties. The optimizer and metric variables are objects whose properties control the registration. optimizer metric optimizer = registration.optimizer.OnePlusOneEvolutionary Properties: GrowthFactor: Epsilon: InitialRadius: MaximumIterations: 1.050000e+00 1.500000e-06 6.250000e-03 100 metric = registration.metric.MattesMutualInformation Properties: NumberOfSpatialSamples: 500 NumberOfHistogramBins: 50 UseAllPixels: 1 Because the registration improved with the default parameters, perhaps it will continue to improve if the optimization runs longer. optimizer.MaximumIterations = 300; movingRegistered = imregister(moving, fixed, 'affine', optimizer, metric); figure, imshowpair(movingRegistered, fixed) title('MaximumIterations = 300') 7-40 Registering Multimodal MRI Images Does it continue to improve if run even longer? optimizer.MaximumIterations = 500; tic 7-41 7 Image Registration movingRegistered500 = imregister(moving, fixed, 'affine', optimizer, metric time500 = toc figure, imshowpair(movingRegistered500, fixed) title('B: MaximumIterations = 500') time500 = 9.9225 7-42 Registering Multimodal MRI Images Step 4: Improve the Speed of Registration The previous section showed that it’s often possible to improve a registration with the default parameters simply by letting it run longer. Although 7-43 7 Image Registration increasing ’MaximumIterations’ will likely lead to convergence, it’s also likely that running for a longer time will yield diminishing returns. It’s often possible to force the optimizer to be more aggressive in its initial steps. Changing parameters that control step size might move the registration closer to the correct solution more quickly, but it could result in treating a local extrema as the best answer, when the best answer is elsewhere in the optimization space. The ’InitialRadius’ property controls the initial search radius for the optimizer. optimizer.MaximumIterations = 100; optimizer.InitialRadius = 0.009; movingRegistered = imregister(moving, fixed, 'affine', optimizer, metric); figure, imshowpair(movingRegistered, fixed) title('MaximumIterations = 100, InitialRadius = 0.009') 7-44 Registering Multimodal MRI Images Compared with the default configuration, the results are worse. While ’InitialRadius specifies the upper bound of the search radius, ’Epsilon’ sets the lower bound. [optimizer,metric] = imregconfig('multimodal'); 7-45 7 Image Registration optimizer.Epsilon = 1.5e-4; movingRegistered = imregister(moving, fixed, 'affine', optimizer, metric); figure, imshowpair(movingRegistered, fixed) title('MaximumIterations = 100, Epsilon = 1.5e-4') 7-46 Registering Multimodal MRI Images This configuration yields almost exactly the same registration as the default parameters with almost no difference in performance. The only remaining optimizer property to tweak independently is ’GrowthFactor’, which controls the rate at which the search radius grows in parameter space. A larger growth factor causes a more aggressive optimization. [optimizer,metric] = imregconfig('multimodal'); optimizer.GrowthFactor = 1.1; movingRegistered = imregister(moving, fixed, 'affine', optimizer, metric); figure, imshowpair(movingRegistered, fixed) title('MaximumIterations = 100, GrowthFactor = 1.1') 7-47 7 Image Registration That seemed too aggressive. Perhaps the default value is too large. Try a smaller ’GrowthFactor’ setting. optimizer.GrowthFactor = 1.01; 7-48 Registering Multimodal MRI Images tic movingRegisteredGrowth = imregister(moving, fixed, 'affine', optimizer, met timeGrowth = toc figure, imshowpair(movingRegisteredGrowth, fixed) title('C: MaximumIterations = 100, GrowthFactor = 1.01') timeGrowth = 2.2227 7-49 7 Image Registration Step 5: Further Refinement Usually a combination of changes to the step-size parameters and number of iterations to run yields the best results. [optimizer,metric] = imregconfig('multimodal'); 7-50 Registering Multimodal MRI Images optimizer.GrowthFactor = 1.01; optimizer.InitialRadius = 0.009; optimizer.Epsilon = 1.5e-4; optimizer.MaximumIterations = 300; tic movingRegisteredTuned = imregister(moving, fixed, 'affine', optimizer, metr timeTuned = toc figure, imshowpair(movingRegisteredTuned, fixed) title('D: MaximumIterations = 300, GrowthFactor = 1.01, Epsilon = 1.5e-4, I timeTuned = 6.5000 7-51 7 Image Registration Step 6: Deciding When Enough is Enough Comparing the results of running imregister with different configurations, it becomes apparent that there’s a trade-off between performance and accuracy. 7-52 Registering Multimodal MRI Images The difference in execution time and quality of the default registration run for 100 iterations (A) and the most highly tuned set of properties (B) is quite large. The difference between running imregister with a nonstandard growth factor for 100 iterations (C) and the best result (B) is obvious, too. It becomes more of a trade-off between the quality of the highly tuned registration executed to 300 iterations (D) and the default registration run to 500 iterations (B), given the comparatively small amount of time that it took to get there. figure imshowpair(movingRegisteredDefault, fixed) title(sprintf('A - Default settings - %0.2f sec', timeDefault)) figure imshowpair(movingRegistered500, fixed) title(sprintf('B - Default settings, 500 iterations - %0.2f sec', time500)) figure imshowpair(movingRegisteredGrowth, fixed) title(sprintf('C - Growth factor, 100 iterations - %0.2f sec', timeGrowth)) figure imshowpair(movingRegisteredTuned, fixed) title(sprintf('D - Highly tuned, 300 iterations - %0.2f sec', timeTuned)) 7-53 7 7-54 Image Registration Registering Multimodal MRI Images 7-55 7 7-56 Image Registration Registering Multimodal MRI Images Step 7: Alternate Visualizations Often as the quality of multimodal registrations improve it becomes more difficult to judge the quality of registration visually. This is because the intensity differences can obscure areas of misalignment. Sometimes switching 7-57 7 Image Registration to a different display mode for imshowpair exposes hidden details. (This is not always the case.) 7-58 8 Designing and Implementing 2-D Linear Filters for Image Data The Image Processing Toolbox software provides a number of functions for designing and implementing two-dimensional linear filters for image data. This chapter describes these functions and how to use them effectively. • “Designing and Implementing Linear Filters in the Spatial Domain” on page 8-2 • “Designing Linear Filters in the Frequency Domain” on page 8-15 8 Designing and Implementing 2-D Linear Filters for Image Data Designing and Implementing Linear Filters in the Spatial Domain In this section... “Overview” on page 8-2 “Convolution” on page 8-2 “Correlation” on page 8-4 “Performing Linear Filtering of Images Using imfilter” on page 8-5 “Filtering an Image with Predefined Filter Types” on page 8-13 For information about designing linear filters in the frequency domain, see “Designing Linear Filters in the Frequency Domain” on page 8-15. Overview Filtering is a technique for modifying or enhancing an image. For example, you can filter an image to emphasize certain features or remove other features. Image processing operations implemented with filtering include smoothing, sharpening, and edge enhancement. Filtering is a neighborhood operation, in which the value of any given pixel in the output image is determined by applying some algorithm to the values of the pixels in the neighborhood of the corresponding input pixel. A pixel’s neighborhood is some set of pixels, defined by their locations relative to that pixel. (See“Neighborhood and Block Processing” for a general discussion of neighborhood operations.) Linear filtering is filtering in which the value of an output pixel is a linear combination of the values of the pixels in the input pixel’s neighborhood. Convolution Linear filtering of an image is accomplished through an operation called convolution. Convolution is a neighborhood operation in which each output pixel is the weighted sum of neighboring input pixels. The matrix of weights is called the convolution kernel, also known as the filter. A convolution kernel is a correlation kernel that has been rotated 180 degrees. For example, suppose the image is 8-2 Designing and Implementing Linear Filters in the Spatial Domain A = [17 23 4 10 11 24 5 6 12 18 1 7 13 19 25 8 14 20 21 2 15 16 22 3 9] and the convolution kernel is h = [8 3 4 1 5 9 6 7 2] The following figure shows how to compute the (2,4) output pixel using these steps: 1 Rotate the convolution kernel 180 degrees about its center element. 2 Slide the center element of the convolution kernel so that it lies on top of the (2,4) element of A. 3 Multiply each weight in the rotated convolution kernel by the pixel of A underneath. 4 Sum the individual products from step 3. Hence the (2,4) output pixel is 8-3 8 Designing and Implementing 2-D Linear Filters for Image Data Computing the (2,4) Output of Convolution Correlation The operation called correlation is closely related to convolution. In correlation, the value of an output pixel is also computed as a weighted sum of neighboring pixels. The difference is that the matrix of weights, in this case called the correlation kernel, is not rotated during the computation. The Image Processing Toolbox filter design functions return correlation kernels. The following figure shows how to compute the (2,4) output pixel of the correlation of A, assuming h is a correlation kernel instead of a convolution kernel, using these steps: 1 Slide the center element of the correlation kernel so that lies on top of the (2,4) element of A. 2 Multiply each weight in the correlation kernel by the pixel of A underneath. 3 Sum the individual products from step 3. The (2,4) output pixel from the correlation is 8-4 Designing and Implementing Linear Filters in the Spatial Domain Computing the (2,4) Output of Correlation Performing Linear Filtering of Images Using imfilter Filtering of images, either by correlation or convolution, can be performed using the toolbox function imfilter. This example filters an image with a 5-by-5 filter containing equal weights. Such a filter is often called an averaging filter. I = imread('coins.png'); h = ones(5,5) / 25; I2 = imfilter(I,h); imshow(I), title('Original Image'); figure, imshow(I2), title('Filtered Image') 8-5 8 Designing and Implementing 2-D Linear Filters for Image Data Data Types The imfilter function handles data types similarly to the way the image arithmetic functions do, as described in “Image Arithmetic Saturation Rules” on page 2-30. The output image has the same data type, or numeric class, as the input image. The imfilter function computes the value of each output pixel using double-precision, floating-point arithmetic. If the result exceeds the range of the data type, the imfilter function truncates the result to that data type’s allowed range. If it is an integer data type, imfilter rounds fractional values. Because of the truncation behavior, you might sometimes want to consider converting your image to a different data type before calling imfilter. In this example, the output of imfilter has negative values when the input is of class double. A = magic(5) A = 17 23 4 10 11 8-6 24 5 6 12 18 1 7 13 19 25 8 14 20 21 2 15 16 22 3 9 Designing and Implementing Linear Filters in the Spatial Domain h = [-1 0 1] h = -1 0 1 imfilter(A,h) ans = 24 5 6 12 18 -16 -16 9 9 14 -16 9 14 9 -16 14 9 9 -16 -16 -8 -14 -20 -21 -2 Notice that the result has negative values. Now suppose A is of class uint8, instead of double. A = uint8(magic(5)); imfilter(A,h) ans = 24 5 6 12 18 0 0 9 9 14 0 9 14 9 0 14 9 9 0 0 0 0 0 0 0 Since the input to imfilter is of class uint8, the output also is of class uint8, and so the negative values are truncated to 0. In such cases, it might be appropriate to convert the image to another type, such as a signed integer type, single, or double, before calling imfilter. Correlation and Convolution Options The imfilter function can perform filtering using either correlation or convolution. It uses correlation by default, because the filter design functions, described in “Designing Linear Filters in the Frequency Domain” on page 8-15, and the fspecial function, described in “Filtering an Image with Predefined Filter Types” on page 8-13, produce correlation kernels. 8-7 8 Designing and Implementing 2-D Linear Filters for Image Data However, if you want to perform filtering using convolution instead, you can pass the string 'conv' as an optional input argument to imfilter. For example: A = magic(5); h = [-1 0 1] imfilter(A,h) ans = 24 5 6 12 18 -16 -16 9 9 14 % filter using correlation -16 9 14 9 -16 imfilter(A,h,'conv') 14 9 9 -16 -16 -8 -14 -20 -21 -2 % filter using convolution ans = -24 -5 -6 -12 -18 16 16 -9 -9 -14 16 -9 -14 -9 16 -14 -9 -9 16 16 8 14 20 21 2 Boundary Padding Options When computing an output pixel at the boundary of an image, a portion of the convolution or correlation kernel is usually off the edge of the image, as illustrated in the following figure. 8-8 Designing and Implementing Linear Filters in the Spatial Domain When the Values of the Kernel Fall Outside the Image The imfilter function normally fills in these off-the-edge image pixels by assuming that they are 0. This is called zero padding and is illustrated in the following figure. Zero Padding of Outside Pixels 8-9 8 Designing and Implementing 2-D Linear Filters for Image Data When you filter an image, zero padding can result in a dark band around the edge of the image, as shown in this example. I = imread('eight.tif'); h = ones(5,5) / 25; I2 = imfilter(I,h); imshow(I), title('Original Image'); figure, imshow(I2), title('Filtered Image with Black Border') To eliminate the zero-padding artifacts around the edge of the image, imfilter offers an alternative boundary padding method called border replication. In border replication, the value of any pixel outside the image is determined by replicating the value from the nearest border pixel. This is illustrated in the following figure. 8-10 Designing and Implementing Linear Filters in the Spatial Domain Replicated Boundary Pixels To filter using border replication, pass the additional optional argument 'replicate' to imfilter. I3 = imfilter(I,h,'replicate'); figure, imshow(I3); title('Filtered Image with Border Replication') 8-11 8 Designing and Implementing 2-D Linear Filters for Image Data The imfilter function supports other boundary padding options, such as 'circular' and 'symmetric'. See the reference page for imfilter for details. Multidimensional Filtering The imfilter function can handle both multidimensional images and multidimensional filters. A convenient property of filtering is that filtering a three-dimensional image with a two-dimensional filter is equivalent to filtering each plane of the three-dimensional image individually with the same two-dimensional filter. This example shows how easy it is to filter each color plane of a truecolor image with the same filter: 1 Read in an RGB image and display it. rgb = imread('peppers.png'); imshow(rgb); 2 Filter the image and display it. h = ones(5,5)/25; rgb2 = imfilter(rgb,h); 8-12 Designing and Implementing Linear Filters in the Spatial Domain figure, imshow(rgb2) Relationship to Other Filtering Functions MATLAB has several two-dimensional and multidimensional filtering functions. The function filter2 performs two-dimensional correlation, conv2 performs two-dimensional convolution, and convn performs multidimensional convolution. Each of these filtering functions always converts the input to double, and the output is always double. These other filtering functions always assume the input is zero padded, and they do not support other padding options. In contrast, the imfilter function does not convert input images to double. The imfilter function also offers a flexible set of boundary padding options, as described in “Boundary Padding Options” on page 8-8. Filtering an Image with Predefined Filter Types The fspecial function produces several kinds of predefined filters, in the form of correlation kernels. After creating a filter with fspecial, you can apply it directly to your image data using imfilter. This example illustrates applying 8-13 8 Designing and Implementing 2-D Linear Filters for Image Data an unsharp masking filter to a grayscale image. The unsharp masking filter has the effect of making edges and fine detail in the image more crisp. I = imread('moon.tif'); h = fspecial('unsharp'); I2 = imfilter(I,h); imshow(I), title('Original Image') figure, imshow(I2), title('Filtered Image') 8-14 Designing Linear Filters in the Frequency Domain Designing Linear Filters in the Frequency Domain In this section... “FIR Filters” on page 8-16 “Frequency Transformation Method” on page 8-16 “Frequency Sampling Method” on page 8-18 “Windowing Method” on page 8-19 “Creating the Desired Frequency Response Matrix” on page 8-21 “Computing the Frequency Response of a Filter” on page 8-22 For information about designing linear filters in the spatial domain, see “Designing and Implementing Linear Filters in the Spatial Domain” on page 8-2. Note Most of the design methods described in this section work by creating a two-dimensional filter from a one-dimensional filter or window created using Signal Processing Toolbox functions. Although this toolbox is not required, you might find it difficult to design filters if you do not have the Signal Processing Toolbox software. 8-15 8 Designing and Implementing 2-D Linear Filters for Image Data FIR Filters The Image Processing Toolbox software supports one class of linear filter: the two-dimensional finite impulse response (FIR) filter. FIR filters have a finite extent to a single point, or impulse. All the Image Processing Toolbox filter design functions return FIR filters. FIR filters have several characteristics that make them ideal for image processing in the MATLAB environment: • FIR filters are easy to represent as matrices of coefficients. • Two-dimensional FIR filters are natural extensions of one-dimensional FIR filters. • There are several well-known, reliable methods for FIR filter design. • FIR filters are easy to implement. • FIR filters can be designed to have linear phase, which helps prevent distortion. Another class of filter, the infinite impulse response (IIR) filter, is not as suitable for image processing applications. It lacks the inherent stability and ease of design and implementation of the FIR filter. Therefore, this toolbox does not provide IIR filter support. Frequency Transformation Method The frequency transformation method transforms a one-dimensional FIR filter into a two-dimensional FIR filter. The frequency transformation method preserves most of the characteristics of the one-dimensional filter, particularly the transition bandwidth and ripple characteristics. This method uses a transformation matrix, a set of elements that defines the frequency transformation. The toolbox function ftrans2 implements the frequency transformation method. This function’s default transformation matrix produces filters with nearly circular symmetry. By defining your own transformation matrix, you can obtain different symmetries. (See Jae S. Lim, Two-Dimensional Signal and Image Processing, 1990, for details.) 8-16 Designing Linear Filters in the Frequency Domain The frequency transformation method generally produces very good results, as it is easier to design a one-dimensional filter with particular characteristics than a corresponding two-dimensional filter. For instance, the next example designs an optimal equiripple one-dimensional FIR filter and uses it to create a two-dimensional filter with similar characteristics. The shape of the one-dimensional frequency response is clearly evident in the two-dimensional response. b = remez(10,[0 0.4 0.6 1],[1 1 0 0]); h = ftrans2(b); [H,w] = freqz(b,1,64,'whole'); colormap(jet(64)) plot(w/pi-1,fftshift(abs(H))) figure, freqz2(h,[32 32]) 1.4 1.2 1 0.8 0.6 0.4 0.2 0 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 One-Dimensional Frequency Response 8-17 8 Designing and Implementing 2-D Linear Filters for Image Data Magnitude 1.5 1 0.5 0 1 0.5 1 0.5 0 0 −0.5 Fy −0.5 −1 −1 Fx Corresponding Two-Dimensional Frequency Response Frequency Sampling Method The frequency sampling method creates a filter based on a desired frequency response. Given a matrix of points that define the shape of the frequency response, this method creates a filter whose frequency response passes through those points. Frequency sampling places no constraints on the behavior of the frequency response between the given points; usually, the response ripples in these areas. (Ripples are oscillations around a constant value. The frequency response of a practical filter often has ripples where the frequency response of an ideal filter is flat.) The toolbox function fsamp2 implements frequency sampling design for two-dimensional FIR filters. fsamp2 returns a filter h with a frequency response that passes through the points in the input matrix Hd. The example below creates an 11-by-11 filter using fsamp2 and plots the frequency response of the resulting filter. (The freqz2 function in this example calculates the two-dimensional frequency response of a filter. See “Computing the Frequency Response of a Filter” on page 8-22 for more information.) 8-18 Designing Linear Filters in the Frequency Domain Hd = zeros(11,11); Hd(4:8,4:8) = 1; [f1,f2] = freqspace(11,'meshgrid'); mesh(f1,f2,Hd), axis([-1 1 -1 1 0 1.2]), colormap(jet(64)) h = fsamp2(Hd); figure, freqz2(h,[32 32]), axis([-1 1 -1 1 0 1.2]) Desired Two-Dimensional Frequency Response (left) and Actual Two-Dimensional Frequency Response (right) Notice the ripples in the actual frequency response, compared to the desired frequency response. These ripples are a fundamental problem with the frequency sampling design method. They occur wherever there are sharp transitions in the desired response. You can reduce the spatial extent of the ripples by using a larger filter. However, a larger filter does not reduce the height of the ripples, and requires more computation time for filtering. To achieve a smoother approximation to the desired frequency response, consider using the frequency transformation method or the windowing method. Windowing Method The windowing method involves multiplying the ideal impulse response with a window function to generate a corresponding filter, which tapers the ideal impulse response. Like the frequency sampling method, the windowing method produces a filter whose frequency response approximates a desired frequency response. The windowing method, however, tends to produce better results than the frequency sampling method. 8-19 8 Designing and Implementing 2-D Linear Filters for Image Data The toolbox provides two functions for window-based filter design, fwind1 and fwind2. fwind1 designs a two-dimensional filter by using a two-dimensional window that it creates from one or two one-dimensional windows that you specify. fwind2 designs a two-dimensional filter by using a specified two-dimensional window directly. fwind1 supports two different methods for making the two-dimensional windows it uses: • Transforming a single one-dimensional window to create a two-dimensional window that is nearly circularly symmetric, by using a process similar to rotation • Creating a rectangular, separable window from two one-dimensional windows, by computing their outer product The example below uses fwind1 to create an 11-by-11 filter from the desired frequency response Hd. The example uses the Signal Processing Toolbox hamming function to create a one-dimensional window, which fwind1 then extends to a two-dimensional window. Hd = zeros(11,11); Hd(4:8,4:8) = 1; [f1,f2] = freqspace(11,'meshgrid'); mesh(f1,f2,Hd), axis([-1 1 -1 1 0 1.2]), colormap(jet(64)) h = fwind1(Hd,hamming(11)); figure, freqz2(h,[32 32]), axis([-1 1 -1 1 0 1.2]) Desired Two-Dimensional Frequency Response (left) and Actual Two-Dimensional Frequency Response (right) 8-20 Designing Linear Filters in the Frequency Domain Creating the Desired Frequency Response Matrix The filter design functions fsamp2, fwind1, and fwind2 all create filters based on a desired frequency response magnitude matrix. Frequency response is a mathematical function describing the gain of a filter in response to different input frequencies. You can create an appropriate desired frequency response matrix using the freqspace function. freqspace returns correct, evenly spaced frequency values for any size response. If you create a desired frequency response matrix using frequency points other than those returned by freqspace, you might get unexpected results, such as nonlinear phase. For example, to create a circular ideal lowpass frequency response with cutoff at 0.5, use [f1,f2] = freqspace(25,'meshgrid'); Hd = zeros(25,25); d = sqrt(f1.^2 + f2.^2) < 0.5; Hd(d) = 1; mesh(f1,f2,Hd) Ideal Circular Lowpass Frequency Response Note that for this frequency response, the filters produced by fsamp2, fwind1, and fwind2 are real. This result is desirable for most image processing applications. To achieve this in general, the desired frequency response should be symmetric about the frequency origin (f1 = 0, f2 = 0). 8-21 8 Designing and Implementing 2-D Linear Filters for Image Data Computing the Frequency Response of a Filter The freqz2 function computes the frequency response for a two-dimensional filter. With no output arguments, freqz2 creates a mesh plot of the frequency response. For example, consider this FIR filter, h =[0.1667 0.6667 0.1667 0.6667 -3.3333 0.6667 0.1667 0.6667 0.1667]; This command computes and displays the 64-by-64 point frequency response of h. freqz2(h) Frequency Response of a Two-Dimensional Filter To obtain the frequency response matrix H and the frequency point vectors f1 and f2, use output arguments [H,f1,f2] = freqz2(h); 8-22 Designing Linear Filters in the Frequency Domain freqz2 normalizes the frequencies f1 and f2 so that the value 1.0 corresponds to half the sampling frequency, or π radians. For a simple m-by-n response, as shown above, freqz2 uses the two-dimensional fast Fourier transform function fft2. You can also specify vectors of arbitrary frequency points, but in this case freqz2 uses a slower algorithm. See “Fourier Transform” on page 9-2 for more information about the fast Fourier transform and its application to linear filtering and filter design. 8-23 8 8-24 Designing and Implementing 2-D Linear Filters for Image Data 9 Transforms The usual mathematical representation of an image is a function of two spatial variables: f(x,y). The value of the function at a particular location (x,y) represents the intensity of the image at that point. This is called the spatial domain. The term transform refers to an alternative mathematical representation of an image. For example, the Fourier transform is a representation of an image as a sum of complex exponentials of varying magnitudes, frequencies, and phases. This is called the frequency domain. Transforms are useful for a wide range of purposes, including convolution, enhancement, feature detection, and compression. This chapter defines several important transforms and shows examples of their application to image processing. • “Fourier Transform” on page 9-2 • “Discrete Cosine Transform” on page 9-15 • “Radon Transform” on page 9-19 • “The Inverse Radon Transformation” on page 9-29 • “Fan-Beam Projection Data” on page 9-36 9 Transforms Fourier Transform In this section... “Definition of Fourier Transform” on page 9-2 “Discrete Fourier Transform” on page 9-7 “Applications of the Fourier Transform” on page 9-10 Definition of Fourier Transform The Fourier transform is a representation of an image as a sum of complex exponentials of varying magnitudes, frequencies, and phases. The Fourier transform plays a critical role in a broad range of image processing applications, including enhancement, analysis, restoration, and compression. If f(m,n) is a function of two discrete spatial variables m and n, then the two-dimensional Fourier transform of f(m,n) is defined by the relationship ∞ F (1 , 2 ) = ∞ f (m, n) e− j1m e− j2 n . ∑ ∑ m =−∞ n=−∞ The variables ω1 and ω2 are frequency variables; their units are radians per sample. F(ω1,ω2) is often called the frequency-domain representation of f(m,n). F(ω1,ω2) is a complex-valued function that is periodic both in ω1 and ω2, with period 2 . Because of the periodicity, usually only the range − ≤ 1 , 2 ≤ is displayed. Note that F(0,0) is the sum of all the values of f(m,n). For this reason, F(0,0) is often called the constant component or DC component of the Fourier transform. (DC stands for direct current; it is an electrical engineering term that refers to a constant-voltage power source, as opposed to a power source whose voltage varies sinusoidally.) The inverse of a transform is an operation that when performed on a transformed image produces the original image. The inverse two-dimensional Fourier transform is given by f (m, n) = 9-2 1 ∫ ∫ 4 2 1 =− 2 =− F (1 , 2 )e j1m e j2 n d1 d2 . Fourier Transform Roughly speaking, this equation means that f(m,n) can be represented as a sum of an infinite number of complex exponentials (sinusoids) with different frequencies. The magnitude and phase of the contribution at the frequencies (ω1,ω2) are given by F(ω1,ω2). Visualizing the Fourier Transform To illustrate, consider a function f(m,n) that equals 1 within a rectangular region and 0 everywhere else. To simplify the diagram, f(m,n) is shown as a continuous function, even though the variables m and n are discrete. Rectangular Function The following figure shows, as a mesh plot, the magnitude of the Fourier transform, F(1 , 2 ) , of the rectangular function shown in the preceding figure. The mesh plot of the magnitude is a common way to visualize the Fourier transform. 9-3 9 Transforms Magnitude Image of a Rectangular Function The peak at the center of the plot is F(0,0), which is the sum of all the values in f(m,n). The plot also shows that F(ω1,ω2) has more energy at high horizontal frequencies than at high vertical frequencies. This reflects the fact that horizontal cross sections of f(m,n) are narrow pulses, while vertical cross sections are broad pulses. Narrow pulses have more high-frequency content than broad pulses. Another common way to visualize the Fourier transform is to display log F (1 , 2 ) as an image, as shown. 9-4 Fourier Transform Log of the Fourier Transform of a Rectangular Function Using the logarithm helps to bring out details of the Fourier transform in regions where F(ω1,ω2) is very close to 0. Examples of the Fourier transform for other simple shapes are shown below. 9-5 9 Transforms Fourier Transforms of Some Simple Shapes 9-6 Fourier Transform Discrete Fourier Transform Working with the Fourier transform on a computer usually involves a form of the transform known as the discrete Fourier transform (DFT). A discrete transform is a transform whose input and output values are discrete samples, making it convenient for computer manipulation. There are two principal reasons for using this form of the transform: • The input and output of the DFT are both discrete, which makes it convenient for computer manipulations. • There is a fast algorithm for computing the DFT known as the fast Fourier transform (FFT). The DFT is usually defined for a discrete function f(m,n) that is nonzero only over the finite region 0 ≤ m ≤ M − 1 and 0 ≤ n ≤ N − 1 . The two-dimensional M-by-N DFT and inverse M-by-N DFT relationships are given by F ( p, q) = M −1 N −1 ∑ ∑ f (m, n) e− j 2 pm / M e− j 2 qn / N m =0 n =0 p = 0, 1, ..., M − 1 q = 0, 1, ..., N − 1 and f (m, n) = 1 MN M −1 N −1 ∑ ∑ F ( p, q)e j 2 pm / M e j 2 qn / N p= 0 q = 0 m = 0, 1, ..., M − 1 n = 0, 1, ..., N − 1 The values F(p,q) are the DFT coefficients of f(m,n). The zero-frequency coefficient, F(0,0), is often called the "DC component." DC is an electrical engineering term that stands for direct current. (Note that matrix indices in MATLAB always start at 1 rather than 0; therefore, the matrix elements f(1,1) and F(1,1) correspond to the mathematical quantities f(0,0) and F(0,0), respectively.) The MATLAB functions fft, fft2, and fftn implement the fast Fourier transform algorithm for computing the one-dimensional DFT, two-dimensional DFT, and N-dimensional DFT, respectively. The functions ifft, ifft2, and ifftn compute the inverse DFT. 9-7 9 Transforms Relationship to the Fourier Transform The DFT coefficients F(p,q) are samples of the Fourier transform F(ω1,ω2). F ( p, q ) = F (1 , 2 )|1 = 2 p / M 2 = 2 q / N p = 0,1,..., M − 1 q = 0,1,..., N − 1 Visualizing the Discrete Fourier Transform 1 Construct a matrix f that is similar to the function f(m,n) in the example in “Definition of Fourier Transform” on page 9-2. Remember that f(m,n) is equal to 1 within the rectangular region and 0 elsewhere. Use a binary image to represent f(m,n). f = zeros(30,30); f(5:24,13:17) = 1; imshow(f,'InitialMagnification','fit') 2 Compute and visualize the 30-by-30 DFT of f with these commands. F = fft2(f); F2 = log(abs(F)); imshow(F2,[-1 5],'InitialMagnification','fit'); colormap(jet); colorbar 9-8 Fourier Transform Discrete Fourier Transform Computed Without Padding This plot differs from the Fourier transform displayed in “Visualizing the Fourier Transform” on page 9-3. First, the sampling of the Fourier transform is much coarser. Second, the zero-frequency coefficient is displayed in the upper left corner instead of the traditional location in the center. 3 To obtain a finer sampling of the Fourier transform, add zero padding to f when computing its DFT. The zero padding and DFT computation can be performed in a single step with this command. F = fft2(f,256,256); This command zero-pads f to be 256-by-256 before computing the DFT. imshow(log(abs(F)),[-1 5]); colormap(jet); colorbar 9-9 9 Transforms Discrete Fourier Transform Computed with Padding 4 The zero-frequency coefficient, however, is still displayed in the upper left corner rather than the center. You can fix this problem by using the function fftshift, which swaps the quadrants of F so that the zero-frequency coefficient is in the center. F = fft2(f,256,256);F2 = fftshift(F); imshow(log(abs(F2)),[-1 5]); colormap(jet); colorbar The resulting plot is identical to the one shown in “Visualizing the Fourier Transform” on page 9-3. Applications of the Fourier Transform This section presents a few of the many image processing-related applications of the Fourier transform. Frequency Response of Linear Filters The Fourier transform of the impulse response of a linear filter gives the frequency response of the filter. The function freqz2 computes and displays a filter’s frequency response. The frequency response of the Gaussian convolution kernel shows that this filter passes low frequencies and attenuates high frequencies. h = fspecial('gaussian'); freqz2(h) 9-10 Fourier Transform 1 Magnitude 0.8 0.6 0.4 0.2 1 0.5 1 0.5 0 0 −0.5 Fy −0.5 −1 −1 Fx Frequency Response of a Gaussian Filter See “Designing Linear Filters in the Frequency Domain” on page 8-15 for more information about linear filtering, filter design, and frequency responses. Fast Convolution A key property of the Fourier transform is that the multiplication of two Fourier transforms corresponds to the convolution of the associated spatial functions. This property, together with the fast Fourier transform, forms the basis for a fast convolution algorithm. Note The FFT-based convolution method is most often used for large inputs. For small inputs it is generally faster to use imfilter. To illustrate, this example performs the convolution of A and B, where A is an M-by-N matrix and B is a P-by-Q matrix: 1 Create two matrices. 9-11 9 Transforms A = magic(3); B = ones(3); 2 Zero-pad A and B so that they are at least (M+P-1)-by-(N+Q-1). (Often A and B are zero-padded to a size that is a power of 2 because fft2 is fastest for these sizes.) The example pads the matrices to be 8-by-8. A(8,8) = 0; B(8,8) = 0; 3 Compute the two-dimensional DFT of A and B using fft2, multiply the two DFTs together, and compute the inverse two-dimensional DFT of the result using ifft2 C = ifft2(fft2(A).*fft2(B)); 4 Extract the nonzero portion of the result and remove the imaginary part caused by roundoff error. C = C(1:5,1:5); C = real(C) This example produces the following result. C = 8.0000 11.0000 15.0000 7.0000 4.0000 9.0000 17.0000 30.0000 21.0000 13.0000 15.0000 30.0000 45.0000 30.0000 15.0000 7.0000 19.0000 30.0000 23.0000 11.0000 6.0000 13.0000 15.0000 9.0000 2.0000 Locating Image Features The Fourier transform can also be used to perform correlation, which is closely related to convolution. Correlation can be used to locate features within an image; in this context correlation is often called template matching. This example illustrates how to use correlation to locate occurrences of the letter "a" in an image containing text: 1 Read in the sample image. 9-12 Fourier Transform bw = imread('text.png'); 2 Create a template for matching by extracting the letter "a" from the image. a = bw(32:45,88:98); You can also create the template image by using the interactive version of imcrop. The following figure shows both the original image and the template. imshow(bw); figure, imshow(a); Image (left) and the Template to Correlate (right) 3 Compute the correlation of the template image with the original image by rotating the template image by 180o and then using the FFT-based convolution technique described in “Fast Convolution” on page 9-11. (Convolution is equivalent to correlation if you rotate the convolution kernel by 180o.) To match the template to the image, use the fft2 and ifft2 functions. C = real(ifft2(fft2(bw) .* fft2(rot90(a,2),256,256))); The following image shows the result of the correlation. Bright peaks in the image correspond to occurrences of the letter. 9-13 9 Transforms figure, imshow(C,[]) % Scale image to appropriate display range. Correlated Image 4 To view the locations of the template in the image, find the maximum pixel value and then define a threshold value that is less than this maximum. The locations of these peaks are indicated by the white spots in the thresholded correlation image. (To make the locations easier to see in this figure, the thresholded image has been dilated to enlarge the size of the points.) max(C(:)) ans = 68.0000 thresh = 60; % Use a threshold that's a little less than max. figure, imshow(C > thresh) % Display pixels over threshold. Correlated, Thresholded Image Showing Template Locations 9-14 Discrete Cosine Transform Discrete Cosine Transform In this section... “DCT Definition” on page 9-15 “The DCT Transform Matrix” on page 9-17 “DCT and Image Compression” on page 9-17 DCT Definition The discrete cosine transform (DCT) represents an image as a sum of sinusoids of varying magnitudes and frequencies. The dct2 function computes the two-dimensional discrete cosine transform (DCT) of an image. The DCT has the property that, for a typical image, most of the visually significant information about the image is concentrated in just a few coefficients of the DCT. For this reason, the DCT is often used in image compression applications. For example, the DCT is at the heart of the international standard lossy image compression algorithm known as JPEG. (The name comes from the working group that developed the standard: the Joint Photographic Experts Group.) The two-dimensional DCT of an M-by-N matrix A is defined as follows. Bpq = p q M −1 N −1 ∑ ∑ m=0 n=0 Amn cos ( 2m + 1 ) p ( 2n + 1 ) q 0 ≤ p ≤ M − 1 cos , 0 ≤ q ≤ N −1 2M 2N ⎪⎧1 / M , p = 0 ⎪⎧1 / N , q = 0 p = ⎨ = q ⎨ 1 ≤ p ≤ M −1 1 ≤ q ≤ N −1 ⎪⎩ 2 / N , ⎩⎪ 2 / M , The values Bpq are called the DCT coefficients of A. (Note that matrix indices in MATLAB always start at 1 rather than 0; therefore, the MATLAB matrix elements A(1,1) and B(1,1) correspond to the mathematical quantities A00 and B00, respectively.) The DCT is an invertible transform, and its inverse is given by 9-15 9 Transforms Amn = M −1 N −1 ∑ ∑ p q Bpq cos p= 0 q=0 ( 2m + 1 ) p ( 2n + 1 ) q 0 ≤ m ≤ M − 1 cos , 0 ≤ n ≤ N −1 2M 2N ⎪⎧1 / M , p = 0 ⎪⎧1 / N , q = 0 p = ⎨ = q ⎨ 1 ≤ p ≤ M −1 1 ≤ q ≤ N −1 ⎪⎩ 2 / N , ⎩⎪ 2 / M , The inverse DCT equation can be interpreted as meaning that any M-by-N matrix A can be written as a sum of MN functions of the form p q cos (2m + 1) p (2n + 1) q cos , 2M 2N 0 ≤ p ≤ M −1 0 ≤ q ≤ N −1 These functions are called the basis functions of the DCT. The DCT coefficients Bpq, then, can be regarded as the weights applied to each basis function. For 8-by-8 matrices, the 64 basis functions are illustrated by this image. The 64 Basis Functions of an 8-by-8 Matrix Horizontal frequencies increase from left to right, and vertical frequencies increase from top to bottom. The constant-valued basis function at the upper left is often called the DC basis function, and the corresponding DCT coefficient B00 is often called the DC coefficient. 9-16 Discrete Cosine Transform The DCT Transform Matrix There are two ways to compute the DCT using Image Processing Toolbox software. The first method is to use the dct2 function. dct2 uses an FFT-based algorithm for speedy computation with large inputs. The second method is to use the DCT transform matrix, which is returned by the function dctmtx and might be more efficient for small square inputs, such as 8-by-8 or 16-by-16. The M-by-M transform matrix T is given by Tpq p = 0, 0 ≤ q ≤ M −1 ⎧ 1 ⎪ M ⎪ =⎨ ⎪ 2 cos ( 2q + 1 ) p 1 ≤ p ≤ M − 1, 0 ≤ q ≤ M − 1 ⎪⎩ M 2M For an M-by-M matrix A, T*A is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of A. The two-dimensional DCT of A can be computed as B=T*A*T'. Since T is a real orthonormal matrix, its inverse is the same as its transpose. Therefore, the inverse two-dimensional DCT of B is given by T'*B*T. DCT and Image Compression In the JPEG image compression algorithm, the input image is divided into 8-by-8 or 16-by-16 blocks, and the two-dimensional DCT is computed for each block. The DCT coefficients are then quantized, coded, and transmitted. The JPEG receiver (or JPEG file reader) decodes the quantized DCT coefficients, computes the inverse two-dimensional DCT of each block, and then puts the blocks back together into a single image. For typical images, many of the DCT coefficients have values close to zero; these coefficients can be discarded without seriously affecting the quality of the reconstructed image. The example code below computes the two-dimensional DCT of 8-by-8 blocks in the input image, discards (sets to zero) all but 10 of the 64 DCT coefficients in each block, and then reconstructs the image using the two-dimensional inverse DCT of each block. The transform matrix computation method is used. 9-17 9 Transforms I = imread('cameraman.tif'); I = im2double(I); T = dctmtx(8); dct = @(block_struct) T * block_struct.data * T'; B = blockproc(I,[8 8],dct); mask = [1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]; B2 = blockproc(B,[8 8],@(block_struct) mask .* block_struct.data); invdct = @(block_struct) T' * block_struct.data * T; I2 = blockproc(B2,[8 8],invdct); imshow(I), figure, imshow(I2) Although there is some loss of quality in the reconstructed image, it is clearly recognizable, even though almost 85% of the DCT coefficients were discarded. 9-18 Radon Transform Radon Transform In this section... “Radon Transformation Definition” on page 9-19 “Plotting the Radon Transform” on page 9-22 “Viewing the Radon Transform as an Image” on page 9-24 “Detecting Lines Using the Radon Transform” on page 9-25 Note For information about creating projection data from line integrals along paths that radiate from a single source, called fan-beam projections, see “Fan-Beam Projection Data” on page 9-36. To convert parallel-beam projection data to fan-beam projection data, use the para2fan function. Radon Transformation Definition The radon function computes projections of an image matrix along specified directions. A projection of a two-dimensional function f(x,y) is a set of line integrals. The radon function computes the line integrals from multiple sources along parallel paths, or beams, in a certain direction. The beams are spaced 1 pixel unit apart. To represent an image, the radon function takes multiple, parallel-beam projections of the image from different angles by rotating the source around the center of the image. The following figure shows a single projection at a specified rotation angle. 9-19 9 Transforms Parallel-Beam Projection at Rotation Angle Theta For example, the line integral of f(x,y) in the vertical direction is the projection of f(x,y) onto the x-axis; the line integral in the horizontal direction is the projection of f(x,y) onto the y-axis. The following figure shows horizontal and vertical projections for a simple two-dimensional function. Horizontal and Vertical Projections of a Simple Function 9-20 Radon Transform Projections can be computed along any angle [[THETA]]. In general, the Radon transform of f(x,y) is the line integral of f parallel to the y´-axis R ( x′) = ∫ ∞ −∞ f ( x′ cos − y′ sin , x′ sin + y′ cos ) dy′ where ⎡ x′ ⎤ ⎡ cos ⎢ y′⎥ = ⎢ − sin ⎣ ⎦ ⎣ sin ⎤ ⎡ x ⎤ cos ⎥⎦ ⎢⎣ y ⎥⎦ The following figure illustrates the geometry of the Radon transform. Geometry of the Radon Transform 9-21 9 Transforms Plotting the Radon Transform You can compute the Radon transform of an image I for the angles specified in the vector theta using the radon function with this syntax. [R,xp] = radon(I,theta); The columns of R contain the Radon transform for each angle in theta. The vector xp contains the corresponding coordinates along the x′-axis. The center pixel of I is defined to be floor((size(I)+1)/2); this is the pixel on the x′-axis corresponding to x′ = 0 . The commands below compute and plot the Radon transform at 0° and 45° of an image containing a single square object. xp is the same for all projection angles. I = zeros(100,100); I(25:75, 25:75) = 1; imshow(I) [R,xp] = radon(I,[0 45]); figure; plot(xp,R(:,1)); title('R_{0^o} (x\prime)') 9-22 Radon Transform R0o (x′) 60 50 40 30 20 10 0 −80 −60 −40 −20 0 20 40 60 80 Radon Transform of a Square Function at 0 Degrees figure; plot(xp,R(:,2)); title('R_{45^o} (x\prime)') 9-23 9 Transforms R45o (x′) 80 70 60 50 40 30 20 10 0 −80 −60 −40 −20 0 20 40 60 80 Radon Transform of a Square Function at 45 Degrees Viewing the Radon Transform as an Image The Radon transform for a large number of angles is often displayed as an image. In this example, the Radon transform for the square image is computed at angles from 0° to 180°, in 1° increments. theta = 0:180; [R,xp] = radon(I,theta); imagesc(theta,xp,R); title('R_{\theta} (X\prime)'); xlabel('\theta (degrees)'); ylabel('X\prime'); set(gca,'XTick',0:20:180); colormap(hot); colorbar 9-24 Radon Transform Radon Transform Using 180 Projections Detecting Lines Using the Radon Transform The Radon transform is closely related to a common computer vision operation known as the Hough transform. You can use the radon function to implement a form of the Hough transform used to detect straight lines. The steps are 1 Compute a binary edge image using the edge function. I = fitsread('solarspectra.fts'); I = mat2gray(I); BW = edge(I); imshow(I), figure, imshow(BW) 9-25 9 Transforms 2 Compute the Radon transform of the edge image. theta = 0:179; [R,xp] = radon(BW,theta); figure, imagesc(theta, xp, R); colormap(hot); xlabel('\theta (degrees)'); ylabel('x\prime'); title('R_{\theta} (x\prime)'); colorbar 9-26 Radon Transform Radon Transform of an Edge Image 3 Find the locations of strong peaks in the Radon transform matrix. The locations of these peaks correspond to the locations of straight lines in the original image. In the following figure, the strongest peaks in R correspond to = 1 and x′ = −80 . The line perpendicular to that angle and located at x′ = −80 is shown below, superimposed in red on the original image. The Radon transform geometry is shown in black. Notice that the other strong lines parallel to the red line also appear as peaks at = 1 in the transform. Also, the lines perpendicular to this line appear as peaks at = 91 . 9-27 9 Transforms Radon Transform Geometry and the Strongest Peak (Red) 9-28 The Inverse Radon Transformation The Inverse Radon Transformation In this section... “Inverse Radon Transform Definition” on page 9-29 “Reconstructing an Image from Parallel Projection Data” on page 9-32 Inverse Radon Transform Definition The iradon function inverts the Radon transform and can therefore be used to reconstruct images. As described in “Radon Transform” on page 9-19, given an image I and a set of angles theta, the radon function can be used to calculate the Radon transform. R = radon(I,theta); The function iradon can then be called to reconstruct the image I from projection data. IR = iradon(R,theta); In the example above, projections are calculated from the original image I. Note, however, that in most application areas, there is no original image from which projections are formed. For example, the inverse Radon transform is commonly used in tomography applications. In X-ray absorption tomography, projections are formed by measuring the attenuation of radiation that passes through a physical specimen at different angles. The original image can be thought of as a cross section through the specimen, in which intensity values represent the density of the specimen. Projections are collected using special purpose hardware, and then an internal image of the specimen is reconstructed by iradon. This allows for noninvasive imaging of the inside of a living body or another opaque object. iradon reconstructs an image from parallel-beam projections. In parallel-beam geometry, each projection is formed by combining a set of line integrals through an image at a specific angle. 9-29 9 Transforms The following figure illustrates how parallel-beam geometry is applied in X-ray absorption tomography. Note that there is an equal number of n emitters and n sensors. Each sensor measures the radiation emitted from its corresponding emitter, and the attenuation in the radiation gives a measure of the integrated density, or mass, of the object. This corresponds to the line integral that is calculated in the Radon transform. The parallel-beam geometry used in the figure is the same as the geometry that was described in “Radon Transform” on page 9-19. f(x,y) denotes the brightness of the image and R ( x′) is the projection at angle theta. Parallel-Beam Projections Through an Object 9-30 The Inverse Radon Transformation Another geometry that is commonly used is fan-beam geometry, in which there is one source and n sensors. For more information, see “Fan-Beam Projection Data” on page 9-36. To convert parallel-beam projection data into fan-beam projection data, use the para2fan function. Improving the Results iradon uses the filtered backprojection algorithm to compute the inverse Radon transform. This algorithm forms an approximation of the image I based on the projections in the columns of R. A more accurate result can be obtained by using more projections in the reconstruction. As the number of projections (the length of theta) increases, the reconstructed image IR more accurately approximates the original image I. The vector theta must contain monotonically increasing angular values with a constant incremental angle Dtheta. When the scalar Dtheta is known, it can be passed to iradon instead of the array of theta values. Here is an example. IR = iradon(R,Dtheta); The filtered backprojection algorithm filters the projections in R and then reconstructs the image using the filtered projections. In some cases, noise can be present in the projections. To remove high frequency noise, apply a window to the filter to attenuate the noise. Many such windowed filters are available in iradon. The example call to iradon below applies a Hamming window to the filter. See the iradon reference page for more information. To get unfiltered backprojection data, specify 'none' for the filter parameter. IR = iradon(R,theta,'Hamming'); iradon also enables you to specify a normalized frequency, D, above which the filter has zero response. D must be a scalar in the range [0,1]. With this option, the frequency axis is rescaled so that the whole filter is compressed to fit into the frequency range [0,D]. This can be useful in cases where the projections contain little high-frequency information but there is high-frequency noise. In this case, the noise can be completely suppressed without compromising the reconstruction. The following call to iradon sets a normalized frequency value of 0.85. IR = iradon(R,theta,0.85); 9-31 9 Transforms Reconstructing an Image from Parallel Projection Data The commands below illustrate how to reconstruct an image from parallel projection data. The test image is the Shepp-Logan head phantom, which can be generated using the phantom function. The phantom image illustrates many of the qualities that are found in real-world tomographic imaging of human heads. The bright elliptical shell along the exterior is analogous to a skull, and the many ellipses inside are analogous to brain features. 1 Create a Shepp-Logan head phantom image. P = phantom(256); imshow(P) 2 Compute the Radon transform of the phantom brain for three different sets of theta values. R1 has 18 projections, R2 has 36 projections, and R3 has 90 projections. theta1 = 0:10:170; [R1,xp] = radon(P,theta1); theta2 = 0:5:175; [R2,xp] = radon(P,theta2); theta3 = 0:2:178; [R3,xp] = radon(P,theta3); 3 Display a plot of one of the Radon transforms of the Shepp-Logan head phantom. The following figure shows R3, the transform with 90 projections. figure, imagesc(theta3,xp,R3); colormap(hot); colorbar xlabel('\theta'); ylabel('x\prime'); 9-32 The Inverse Radon Transformation Radon Transform of Head Phantom Using 90 Projections Note how some of the features of the input image appear in this image of the transform. The first column in the Radon transform corresponds to a projection at 0º that is integrating in the vertical direction. The centermost column corresponds to a projection at 90º, which is integrating in the horizontal direction. The projection at 90º has a wider profile than the projection at 0º due to the larger vertical semi-axis of the outermost ellipse of the phantom. 9-33 9 Transforms 4 Reconstruct the head phantom image from the projection data created in step 2 and display the results. I1 = iradon(R1,10); I2 = iradon(R2,5); I3 = iradon(R3,2); imshow(I1) figure, imshow(I2) figure, imshow(I3) The following figure shows the results of all three reconstructions. Notice how image I1, which was reconstructed from only 18 projections, is the least accurate reconstruction. Image I2, which was reconstructed from 36 projections, is better, but it is still not clear enough to discern clearly the small ellipses in the lower portion of the image. I3, reconstructed using 90 projections, most closely resembles the original image. Notice that when the number of projections is relatively small (as in I1 and I2), the reconstruction can include some artifacts from the back projection. 9-34 The Inverse Radon Transformation Inverse Radon Transforms of the Shepp-Logan Head Phantom 9-35 9 Transforms Fan-Beam Projection Data In this section... “Fan-Beam Projection Data Definition” on page 9-36 “Computing Fan-Beam Projection Data” on page 9-37 “Reconstructing an Image from Fan-Beam Projection Data” on page 9-39 “Reconstructing a Head Phantom Image” on page 9-40 Note For information about creating projection data from line integrals along parallel paths, see “Radon Transform” on page 9-19. To convert fan-beam projection data to parallel-beam projection data, use the fan2para function. Fan-Beam Projection Data Definition The fanbeam function computes projections of an image matrix along specified directions. A projection of a two-dimensional function f(x,y) is a set of line integrals. The fanbeam function computes the line integrals along paths that radiate from a single source, forming a fan shape. To represent an image, the fanbeam function takes multiple projections of the image from different angles by rotating the source around the center of the image. The following figure shows a single fan-beam projection at a specified rotation angle. 9-36 Fan-Beam Projection Data Fan-Beam Projection at Rotation Angle Theta Computing Fan-Beam Projection Data To compute fan-beam projection data, use the fanbeam function. You specify as arguments an image and the distance between the vertex of the fan-beam projections and the center of rotation (the center pixel in the image). The fanbeam function determines the number of beams, based on the size of the image and the settings of fanbeam parameters. The FanSensorGeometry parameter specifies how sensors are aligned. If you specify the value 'arc' for FanSensorGeometry (the default), fanbeam positions the sensors along an arc, spacing the sensors at 1 degree intervals. Using the FanSensorSpacing parameter, you can control the distance between sensors by specifying the angle between each beam. If you specify the value 'line' for FanSensorGeometry parameter, fanbeam position sensors along a straight line, rather than an arc. With 'line' geometry, the FanSensorSpacing parameter specifies the distance between the sensors, in pixels, along the x´ axis. fanbeam takes projections at different angles by rotating the source around the center pixel at 1 degree intervals. Using the FanRotationIncrement parameter you can specify a different rotation angle increment. The following figures illustrate both these geometries. The first figure illustrates geometry used by the fanbeam function when FanSensorGeometry 9-37 9 Transforms is set to 'arc' (the default). Note how you specify the distance between sensors by specifying the angular spacing of the beams. Fan-Beam Projection with Arc Geometry The following figure illustrates the geometry used by the fanbeam function when FanSensorGeometry is set to 'line'. In this figure, note how you specify the position of the sensors by specifying the distance between them in pixels along the x´ axis. 9-38 Fan-Beam Projection Data so rs y Se n x Fan rotation angle x FanSensorSpacing measured in pixels along x axis So ur c e Center pixel D Fan-Beam Projection with Line Geometry Reconstructing an Image from Fan-Beam Projection Data To reconstruct an image from fan-beam projection data, use the ifanbeam function. With this function, you specify as arguments the projection data and 9-39 9 Transforms the distance between the vertex of the fan-beam projections and the center of rotation when the projection data was created. For example, this code recreates the image I from the projection data P and distance D. I = ifanbeam(P,D); By default, the ifanbeam function assumes that the fan-beam projection data was created using the arc fan sensor geometry, with beams spaced at 1 degree angles and projections taken at 1 degree increments over a full 360 degree range. As with the fanbeam function, you can use ifanbeam parameters to specify other values for these characteristics of the projection data. Use the same values for these parameters that were used when the projection data was created. For more information about these parameters, see “Computing Fan-Beam Projection Data” on page 9-37. The ifanbeam function converts the fan-beam projection data to parallel-beam projection data with the fan2para function, and then calls the iradon function to perform the image reconstruction. For this reason, the ifanfeam function supports certain iradon parameters, which it passes to the iradon function. See “The Inverse Radon Transformation” on page 9-29 for more information about the iradon function. Reconstructing a Head Phantom Image The commands below illustrate how to use fanbeam and ifanbeam to form projections from a sample image and then reconstruct the image from the projections. The test image is the Shepp-Logan head phantom, which can be generated by the phantom function. The phantom image illustrates many of the qualities that are found in real-world tomographic imaging of human heads. 1 Generate the test image and display it. P = phantom(256); imshow(P) 9-40 Fan-Beam Projection Data 2 Compute fan-beam projection data of the test image, using the FanSensorSpacing parameter to vary the sensor spacing. The example uses the fanbeam arc geometry, so you specify the spacing between sensors by specifying the angular spacing of the beams. The first call spaces the beams at 2 degrees; the second at 1 degree; and the third at 0.25 degrees. In each call, the distance between the center of rotation and vertex of the projections is constant at 250 pixels. In addition, fanbeam rotates the projection around the center pixel at 1 degree increments. D = 250; dsensor1 = 2; F1 = fanbeam(P,D,'FanSensorSpacing',dsensor1); dsensor2 = 1; F2 = fanbeam(P,D,'FanSensorSpacing',dsensor2); dsensor3 = 0.25 [F3, sensor_pos3, fan_rot_angles3] = fanbeam(P,D,... 'FanSensorSpacing',dsensor3); 3 Plot the projection data F3. Because fanbeam calculates projection data at rotation angles from 0 to 360 degrees, the same patterns occur at an offset of 180 degrees. The same features are being sampled from both sides. Compare this plot to the plot of the parallel-beam projection data of the head phantom using 90 projections in “Reconstructing an Image from Parallel Projection Data” on page 9-32. figure, imagesc(fan_rot_angles3, sensor_pos3, F3) 9-41 9 Transforms colormap(hot); colorbar xlabel('Fan Rotation Angle (degrees)') ylabel('Fan Sensor Position (degrees)') 4 Reconstruct the image from the fan-beam projection data using ifanbeam. In each reconstruction, match the fan sensor spacing with the spacing used when the projection data was created in step 2. The example uses the OutputSize parameter to constrain the output size of each reconstruction to be the same as the size of the original image |P|. output_size = max(size(P)); Ifan1 = ifanbeam(F1,D, ... 'FanSensorSpacing',dsensor1,'OutputSize',output_size); figure, imshow(Ifan1) Ifan2 = ifanbeam(F2,D, ... 'FanSensorSpacing',dsensor2,'OutputSize',output_size); figure, imshow(Ifan2) 9-42 Fan-Beam Projection Data Ifan3 = ifanbeam(F3,D, ... 'FanSensorSpacing',dsensor3,'OutputSize',output_size); figure, imshow(Ifan3) The following figure shows the result of each transform. Note how the quality of the reconstruction gets better as the number of beams in the projection increases. The first image, Ifan1, was created using 2 degree spacing of the beams; the second image, ifan2, was created using 1 degree spacing of the beams; the third image, ifan3, was created using 0.25 spacing of the beams. Reconstructions of the Head Phantom Image from Fan-Beam Projections 9-43 9 9-44 Transforms 10 Morphological Operations This chapter describes the Image Processing Toolbox morphological functions. You can use these functions to perform common image processing tasks, such as contrast enhancement, noise removal, thinning, skeletonization, filling, and segmentation. • “Morphology Fundamentals: Dilation and Erosion” on page 10-2 • “Morphological Reconstruction” on page 10-17 • “Distance Transform” on page 10-36 • “Labeling and Measuring Objects in a Binary Image” on page 10-39 • “Lookup Table Operations” on page 10-44 10 Morphological Operations Morphology Fundamentals: Dilation and Erosion In this section... “Understanding Dilation and Erosion” on page 10-2 “Understanding Structuring Elements” on page 10-5 “Dilating an Image” on page 10-9 “Eroding an Image” on page 10-10 “Combining Dilation and Erosion” on page 10-12 “Dilation- and Erosion-Based Functions” on page 10-14 To see how morphological processing can solve an image processing problem, view the Image Processing Toolbox watershed segmentation example. Understanding Dilation and Erosion Morphology is a broad set of image processing operations that process images based on shapes. Morphological operations apply a structuring element to an input image, creating an output image of the same size. In a morphological operation, the value of each pixel in the output image is based on a comparison of the corresponding pixel in the input image with its neighbors. By choosing the size and shape of the neighborhood, you can construct a morphological operation that is sensitive to specific shapes in the input image. The most basic morphological operations are dilation and erosion. Dilation adds pixels to the boundaries of objects in an image, while erosion removes pixels on object boundaries. The number of pixels added or removed from the objects in an image depends on the size and shape of the structuring element used to process the image. In the morphological dilation and erosion operations, the state of any given pixel in the output image is determined by applying a rule to the corresponding pixel and its neighbors in the input image. The rule used to process the pixels defines the operation as a dilation or an erosion. This table lists the rules for both dilation and erosion. 10-2 Morphology Fundamentals: Dilation and Erosion Rules for Dilation and Erosion Operation Rule Dilation The value of the output pixel is the maximum value of all the pixels in the input pixel’s neighborhood. In a binary image, if any of the pixels is set to the value 1, the output pixel is set to 1. Erosion The value of the output pixel is the minimum value of all the pixels in the input pixel’s neighborhood. In a binary image, if any of the pixels is set to 0, the output pixel is set to 0. The following figure illustrates the dilation of a binary image. Note how the structuring element defines the neighborhood of the pixel of interest, which is circled. (See “Understanding Structuring Elements” on page 10-5 for more information.) The dilation function applies the appropriate rule to the pixels in the neighborhood and assigns a value to the corresponding pixel in the output image. In the figure, the morphological dilation function sets the value of the output pixel to 1 because one of the elements in the neighborhood defined by the structuring element is on. Morphological Dilation of a Binary Image The following figure illustrates this processing for a grayscale image. The figure shows the processing of a particular pixel in the input image. Note how the function applies the rule to the input pixel’s neighborhood and uses the highest value of all the pixels in the neighborhood as the value of the corresponding pixel in the output image. 10-3 10 Morphological Operations Morphological Dilation of a Grayscale Image Processing Pixels at Image Borders (Padding Behavior) Morphological functions position the origin of the structuring element, its center element, over the pixel of interest in the input image. For pixels at the edge of an image, parts of the neighborhood defined by the structuring element can extend past the border of the image. To process border pixels, the morphological functions assign a value to these undefined pixels, as if the functions had padded the image with additional rows and columns. The value of these padding pixels varies for dilation and erosion operations. The following table describes the padding rules for dilation and erosion for both binary and grayscale images. Rules for Padding Images Operation Rule Dilation Pixels beyond the image border are assigned the minimum value afforded by the data type. For binary images, these pixels are assumed to be set to 0. For grayscale images, the minimum value for uint8 images is 0. Erosion 10-4 Pixels beyond the image border are assigned the maximum value afforded by the data type. Morphology Fundamentals: Dilation and Erosion Rules for Padding Images (Continued) Operation Rule For binary images, these pixels are assumed to be set to 1. For grayscale images, the maximum value for uint8 images is 255. Note By using the minimum value for dilation operations and the maximum value for erosion operations, the toolbox avoids border effects, where regions near the borders of the output image do not appear to be homogeneous with the rest of the image. For example, if erosion padded with a minimum value, eroding an image would result in a black border around the edge of the output image. Understanding Structuring Elements An essential part of the dilation and erosion operations is the structuring element used to probe the input image. A structuring element is a matrix consisting of only 0’s and 1’s that can have any arbitrary shape and size. The pixels with values of 1 define the neighborhood. Two-dimensional, or flat, structuring elements are typically much smaller than the image being processed. The center pixel of the structuring element, called the origin, identifies the pixel of interest -- the pixel being processed. The pixels in the structuring element containing 1’s define the neighborhood of the structuring element. These pixels are also considered in dilation or erosion processing. Three-dimensional, or nonflat, structuring elements use 0’s and 1’s to define the extent of the structuring element in the x- and y-planes and add height values to define the third dimension. 10-5 10 Morphological Operations The Origin of a Structuring Element The morphological functions use this code to get the coordinates of the origin of structuring elements of any size and dimension. origin = floor((size(nhood)+1)/2) (In this code nhood is the neighborhood defining the structuring element. Because structuring elements are MATLAB objects, you cannot use the size of the STREL object itself in this calculation. You must use the STREL getnhood method to retrieve the neighborhood of the structuring element from the STREL object. For information about other STREL object methods, see the strel function reference page.) For example, the following illustrates a diamond-shaped structuring element. Origin of a Diamond-Shaped Structuring Element Creating a Structuring Element The toolbox dilation and erosion functions accept structuring element objects, called STRELs. You use the strel function to create STRELs of any arbitrary size and shape. The strel function also includes built-in support for many common shapes, such as lines, diamonds, disks, periodic lines, and balls. Note You typically choose a structuring element the same size and shape as the objects you want to process in the input image. For example, to find lines in an image, create a linear structuring element. For example, this code creates a flat, diamond-shaped structuring element. 10-6 Morphology Fundamentals: Dilation and Erosion se = strel('diamond',3) se = Flat STREL object containing 25 neighbors. Decomposition: 3 STREL objects containing a total of 13 neighbors Neighborhood: 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 Structuring Element Decomposition To enhance performance, the strel function might break structuring elements into smaller pieces, a technique known as structuring element decomposition. For example, dilation by an 11-by-11 square structuring element can be accomplished by dilating first with a 1-by-11 structuring element, and then with an 11-by-1 structuring element. This results in a theoretical speed improvement of a factor of 5.5, although in practice the actual speed improvement is somewhat less. Structuring element decompositions used for the 'disk' and 'ball' shapes are approximations; all other decompositions are exact. Decomposition is not used with an arbitrary structuring element unless it is a flat structuring element whose neighborhood matrix is all 1’s. To view the sequence of structuring elements used in a decomposition, use the STREL getsequence method. The getsequence function returns an array of the structuring elements that form the decomposition. For example, here are the structuring elements created in the decomposition of a diamond-shaped structuring element. sel = strel('diamond',4) sel = 10-7 10 Morphological Operations Flat STREL object containing 41 neighbors. Decomposition: 3 STREL objects containing a total of 13 neighbors Neighborhood: 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 seq = getsequence(sel) seq = 3x1 array of STREL objects seq(1) ans = Flat STREL object containing 5 neighbors. Neighborhood: 0 1 1 1 0 1 0 1 0 seq(2) ans = Flat STREL object containing 4 neighbors. Neighborhood: 0 1 1 0 0 1 0 1 0 seq(3) ans = Flat STREL object containing 4 neighbors. 10-8 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 Morphology Fundamentals: Dilation and Erosion Neighborhood: 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 Dilating an Image To dilate an image, use the imdilate function. The imdilate function accepts two primary arguments: • The input image to be processed (grayscale, binary, or packed binary image) • A structuring element object, returned by the strel function, or a binary matrix defining the neighborhood of a structuring element imdilate also accepts two optional arguments: SHAPE and PACKOPT. The SHAPE argument affects the size of the output image. The PACKOPT argument identifies the input image as packed binary. (Packing is a method of compressing binary images that can speed up the processing of the image. See the bwpack reference page for information.) This example dilates a simple binary image containing one rectangular object. BW = zeros(9,10); BW(4:6,4:7) = 1 BW = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 To expand all sides of the foreground component, the example uses a 3-by-3 square structuring element object. (For more information about using the strel function, see “Understanding Structuring Elements” on page 10-5.) 10-9 10 Morphological Operations SE = strel('square',3) SE = Flat STREL object containing 3 neighbors. Neighborhood: 1 1 1 1 1 1 1 1 1 To dilate the image, pass the image BW and the structuring element SE to the imdilate function. Note how dilation adds a rank of 1’s to all sides of the foreground object. BW2 = imdilate(BW,SE) Eroding an Image To erode an image, use the imerode function. The imerode function accepts two primary arguments: • The input image to be processed (grayscale, binary, or packed binary image) • A structuring element object, returned by the strel function, or a binary matrix defining the neighborhood of a structuring element imerode also accepts three optional arguments: SHAPE, PACKOPT, and M. The SHAPE argument affects the size of the output image. The PACKOPT argument identifies the input image as packed binary. If the image is packed 10-10 Morphology Fundamentals: Dilation and Erosion binary, M identifies the number of rows in the original image. (Packing is a method of compressing binary images that can speed up the processing of the image. See the bwpack reference page for more information.) The following example erodes the binary image circbw.tif: 1 Read the image into the MATLAB workspace. BW1 = imread('circbw.tif'); 2 Create a structuring element. The following code creates a diagonal structuring element object. (For more information about using the strel function, see “Understanding Structuring Elements” on page 10-5.) SE = strel('arbitrary',eye(5)); SE= Flat STREL object containing 5 neighbors. Neighborhood: 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 3 Call the imerode function, passing the image BW and the structuring element SE as arguments. BW2 = imerode(BW1,SE); Notice the diagonal streaks on the right side of the output image. These are due to the shape of the structuring element. imshow(BW1) figure, imshow(BW2) 10-11 10 Morphological Operations Combining Dilation and Erosion Dilation and erosion are often used in combination to implement image processing operations. For example, the definition of a morphological opening of an image is an erosion followed by a dilation, using the same structuring element for both operations. The related operation, morphological closing of an image, is the reverse: it consists of dilation followed by an erosion with the same structuring element. The following section uses imdilate and imerode to illustrate how to implement a morphological opening. Note, however, that the toolbox already includes the imopen function, which performs this processing. The toolbox includes functions that perform many common morphological operations. See “Dilation- and Erosion-Based Functions” on page 10-14 for a complete list. Morphological Opening You can use morphological opening to remove small objects from an image while preserving the shape and size of larger objects in the image. For example, you can use the imopen function to remove all the circuit lines from the original circuit image, circbw.tif, creating an output image that contains only the rectangular shapes of the microchips. To morphologically open the image, perform these steps: 1 Read the image into the MATLAB workspace. 10-12 Morphology Fundamentals: Dilation and Erosion BW1 = imread('circbw.tif'); 2 Create a structuring element. SE = strel('rectangle',[40 30]); The structuring element should be large enough to remove the lines when you erode the image, but not large enough to remove the rectangles. It should consist of all 1’s, so it removes everything but large contiguous patches of foreground pixels. 3 Erode the image with the structuring element. BW2 = imerode(BW1,SE); imshow(BW2) This removes all the lines, but also shrinks the rectangles. 4 To restore the rectangles to their original sizes, dilate the eroded image using the same structuring element, SE. BW3 = imdilate(BW2,SE); imshow(BW3) 10-13 10 Morphological Operations Dilation- and Erosion-Based Functions This section describes two common image processing operations that are based on dilation and erosion: • Skeletonization • Perimeter determination This table lists other functions in the toolbox that perform common morphological operations that are based on dilation and erosion. For more information about these functions, see their reference pages. Dilation- and Erosion-Based Functions 10-14 Function Morphological Definition bwhitmiss Logical AND of an image, eroded with one structuring element, and the image’s complement, eroded with a second structuring element. imbothat Subtracts the original image from a morphologically closed version of the image. Can be used to find intensity troughs in an image. imclose Dilates an image and then erodes the dilated image using the same structuring element for both operations. Morphology Fundamentals: Dilation and Erosion Dilation- and Erosion-Based Functions (Continued) Function Morphological Definition imopen Erodes an image and then dilates the eroded image using the same structuring element for both operations. imtophat Subtracts a morphologically opened image from the original image. Can be used to enhance contrast in an image. Skeletonization To reduce all objects in an image to lines, without changing the essential structure of the image, use the bwmorph function. This process is known as skeletonization. BW1 = imread('circbw.tif'); BW2 = bwmorph(BW1,'skel',Inf); imshow(BW1) figure, imshow(BW2) 10-15 10 Morphological Operations Perimeter Determination The bwperim function determines the perimeter pixels of the objects in a binary image. A pixel is considered a perimeter pixel if it satisfies both of these criteria: • The pixel is on. • One (or more) of the pixels in its neighborhood is off. For example, this code finds the perimeter pixels in a binary image of a circuit board. BW1 = imread('circbw.tif'); BW2 = bwperim(BW1); imshow(BW1) figure, imshow(BW2) 10-16 Morphological Reconstruction Morphological Reconstruction In this section... “Understanding Morphological Reconstruction” on page 10-17 “Understanding the Marker and Mask” on page 10-19 “Pixel Connectivity” on page 10-20 “Flood-Fill Operations” on page 10-23 “Finding Peaks and Valleys” on page 10-26 Understanding Morphological Reconstruction Morphological reconstruction can be thought of conceptually as repeated dilations of an image, called the marker image, until the contour of the marker image fits under a second image, called the mask image. In morphological reconstruction, the peaks in the marker image “spread out,” or dilate. This figure illustrates this processing in 1-D. Each successive dilation is constrained to lie underneath the mask. When further dilation ceases to change the image, processing stops. The final dilation is the reconstructed image. (Note: the actual implementation of this operation in the toolbox is done much more efficiently. See the imreconstruct reference page for more details.) The figure shows the successive dilations of the marker. 10-17 10 Morphological Operations Repeated Dilations of Marker Image, Constrained by Mask 10-18 Morphological Reconstruction Morphological reconstruction is based on morphological dilation, but note the following unique properties: • Processing is based on two images, a marker and a mask, rather than one image and a structuring element. • Processing is based on the concept of connectivity, rather than a structuring element. • Processing repeats until stability; i.e., the image no longer changes. Understanding the Marker and Mask Morphological reconstruction processes one image, called the marker, based on the characteristics of another image, called the mask. The high points, or peaks, in the marker image specify where processing begins. The processing continues until the image values stop changing. To illustrate morphological reconstruction, consider this simple image. It contains two primary regions, the blocks of pixels containing the values 14 and 18. The background is primarily all set to 10, with some pixels set to 11. To morphologically reconstruct this image, perform these steps: 1 Create a marker image. As with the structuring element in dilation and erosion, the characteristics of the marker image determine the processing performed in morphological reconstruction. The peaks in the marker image should identify the location of objects in the mask image that you want to emphasize. 10-19 10 Morphological Operations One way to create a marker image is to subtract a constant from the mask image, using imsubtract. marker = imsubtract(A,2) marker = 8 8 8 8 8 12 12 12 8 12 12 12 8 12 12 12 8 8 8 8 8 9 8 8 8 8 8 9 8 8 9 8 8 9 8 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 16 16 16 8 8 8 9 8 9 8 16 16 16 8 9 8 8 9 8 8 16 16 16 8 8 8 9 8 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 Call the imreconstruct function to morphologically reconstruct the image. In the output image, note how all the intensity fluctuations except the intensity peak have been removed. recon = imreconstruct(marker, mask) Pixel Connectivity Morphological processing starts at the peaks in the marker image and spreads throughout the rest of the image based on the connectivity of the pixels. Connectivity defines which pixels are connected to other pixels. A set of pixels in a binary image that form a connected group is called an object or a connected component. 10-20 Morphological Reconstruction Determining which pixels create a connected component depends on how pixel connectivity is defined. For example, this binary image contains one foreground object or two, depending on the connectivity. If the foreground is 4-connected, the image is all one object — there is no distinction between a foreground object and the background. However, if the foreground is 8-connected, the pixels set to 1 connect to form a closed loop and the image has two separate objects: the pixels in the loop and the pixels outside the loop. 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Defining Connectivity in an Image The following table lists all the standard two- and three-dimensional connectivities supported by the toolbox. See these sections for more information: • “Choosing a Connectivity” on page 10-22 • “Specifying Custom Connectivities” on page 10-23 Supported Connectivities Two-Dimensional Connectivities 4-connected Pixels are connected if their edges touch. This means that a pair of adjoining pixels are part of the same object only if they are both on and are connected along the horizontal or vertical direction. 10-21 10 Morphological Operations Supported Connectivities (Continued) 8-connected Pixels are connected if their edges or corners touch. This means that if two adjoining pixels are on, they are part of the same object, regardless of whether they are connected along the horizontal, vertical, or diagonal direction. Three-Dimensional Connectivities 6-connected Pixels are connected if their faces touch. 18-connected Pixels are connected if their faces or edges touch. 26-connected Pixels are connected if their faces, edges, or corners touch. Choosing a Connectivity The type of neighborhood you choose affects the number of objects found in an image and the boundaries of those objects. For this reason, the results of many morphology operations often differ depending upon the type of connectivity you specify. For example, if you specify a 4-connected neighborhood, this binary image contains two objects; if you specify an 8-connected neighborhood, the image has one object. 10-22 Morphological Reconstruction 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 Specifying Custom Connectivities You can also define custom neighborhoods by specifying a 3-by-3-by-...-by-3 array of 0’s and 1’s. The 1-valued elements define the connectivity of the neighborhood relative to the center element. For example, this array defines a “North/South” connectivity which can be used to break up an image into independent columns. CONN = [ 0 1 0; 0 1 0; 0 1 0 ] CONN = 0 1 0 0 1 0 0 1 0 Note Connectivity arrays must be symmetric about their center element. Also, you can use a 2-D connectivity array with a 3-D image; the connectivity affects each "page" in the 3-D image. Flood-Fill Operations The imfill function performs a flood-fill operation on binary and grayscale images. For binary images, imfill changes connected background pixels (0’s) to foreground pixels (1’s), stopping when it reaches object boundaries. For grayscale images, imfill brings the intensity values of dark areas that are surrounded by lighter areas up to the same intensity level as surrounding pixels. (In effect, imfill removes regional minima that are not connected to the image border. See “Finding Areas of High or Low Intensity” on page 10-28 for more information.) This operation can be useful in removing irrelevant artifacts from images. See these additional topics: • “Specifying Connectivity” on page 10-24 • “Specifying the Starting Point” on page 10-24 10-23 10 Morphological Operations • “Filling Holes” on page 10-25 Specifying Connectivity For both binary and grayscale images, the boundary of the fill operation is determined by the connectivity you specify. Note imfill differs from the other object-based operations in that it operates on background pixels. When you specify connectivity with imfill, you are specifying the connectivity of the background, not the foreground. The implications of connectivity can be illustrated with this matrix. BW = logical([0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0; 0; 0; 0; 0; 0; 0; 0]); If the background is 4-connected, this binary image contains two separate background elements (the part inside the loop and the part outside). If the background is 8-connected, the pixels connect diagonally, and there is only one background element. Specifying the Starting Point For binary images, you can specify the starting point of the fill operation by passing in the location subscript or by using imfill in interactive mode, selecting starting pixels with a mouse. See the reference page for imfill for more information about using imfill interactively. For example, if you call imfill, specifying the pixel BW(4,3) as the starting point, imfill only fills the inside of the loop because, by default, the background is 4-connected. imfill(BW,[4 3]) 10-24 Morphological Reconstruction ans = 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 If you specify the same starting point, but use an 8-connected background connectivity, imfill fills the entire image. imfill(BW,[4 3],8) ans = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Filling Holes A common use of the flood-fill operation is to fill holes in images. For example, suppose you have an image, binary or grayscale, in which the foreground objects represent spheres. In the image, these objects should appear as disks, but instead are donut shaped because of reflections in the original photograph. Before doing any further processing of the image, you might want to first fill in the “donut holes” using imfill. Because the use of flood-fill to fill holes is so common, imfill includes special syntax to support it for both binary and grayscale images. In this syntax, you just specify the argument 'holes'; you do not have to specify starting locations in each hole. To illustrate, this example fills holes in a grayscale image of a spinal column. 10-25 10 Morphological Operations [X,map] = imread('spine.tif'); I = ind2gray(X,map); Ifill = imfill(I,'holes'); imshow(I);figure, imshow(Ifill) Finding Peaks and Valleys Grayscale images can be thought of in three dimensions: the x- and y-axes represent pixel positions and the z-axis represents the intensity of each pixel. In this interpretation, the intensity values represent elevations, as in a topographical map. The areas of high intensity and low intensity in an image, peaks and valleys in topographical terms, can be important morphological features because they often mark relevant image objects. For example, in an image of several spherical objects, points of high intensity could represent the tops of the objects. Using morphological processing, these maxima can be used to identify objects in an image. This section covers these topics: • “Terminology” on page 10-27 • “Understanding the Maxima and Minima Functions” on page 10-27 • “Finding Areas of High or Low Intensity” on page 10-28 10-26 Morphological Reconstruction • “Suppressing Minima and Maxima” on page 10-30 • “Imposing a Minimum” on page 10-32 Terminology This section uses the following terms. Term Definition global maxima Highest regional maxima in the image. See the entry for regional maxima in this table for more information. global minima Lowest regional minima in the image. See the entry for regional minima in this table for more information. regional maxima Connected set of pixels of constant intensity from which it is impossible to reach a point with higher intensity without first descending; that is, a connected component of pixels with the same intensity value, t, surrounded by pixels that all have a value less than t. regional minima Connected set of pixels of constant intensity from which it is impossible to reach a point with lower intensity without first ascending; that is, a connected component of pixels with the same intensity value, t, surrounded by pixels that all have a value greater than t. Understanding the Maxima and Minima Functions An image can have multiple regional maxima or minima but only a single global maximum or minimum. Determining image peaks or valleys can be used to create marker images that are used in morphological reconstruction. This figure illustrates the concept in 1-D. 10-27 10 Morphological Operations Finding Areas of High or Low Intensity The toolbox includes functions that you can use to find areas of high or low intensity in an image: • The imregionalmax and imregionalmin functions identify all regional minima or maxima. • The imextendedmax and imextendedmin functions identify regional minima or maxima that are greater than or less than a specified threshold. The functions accept a grayscale image as input and return a binary image as output. In the output binary image, the regional minima or maxima are set to 1; all other pixels are set to 0. For example, this simple image contains two primary regional maxima, the blocks of pixels containing the value 13 and 18, and several smaller maxima, set to 11. 10-28 Morphological Reconstruction The binary image returned by imregionalmax pinpoints all these regional maxima. B = imregionalmax(A) You might want only to identify areas of the image where the change in intensity is extreme; that is, the difference between the pixel and neighboring pixels is greater than (or less than) a certain threshold. For example, to find only those regional maxima in the sample image, A, that are at least two units higher than their neighbors, use imextendedmax. B = imextendedmax(A,2) 10-29 10 Morphological Operations Suppressing Minima and Maxima In an image, every small fluctuation in intensity represents a regional minimum or maximum. You might only be interested in significant minima or maxima and not in these smaller minima and maxima caused by background texture. To remove the less significant minima and maxima but retain the significant minima and maxima, use the imhmax or imhmin function. With these functions, you can specify a contrast criteria or threshold level, h, that suppresses all maxima whose height is less than h or whose minima are greater than h. Note The imregionalmin, imregionalmax, imextendedmin, and imextendedmax functions return a binary image that marks the locations of the regional minima and maxima in an image. The imhmax and imhmin functions produce an altered image. For example, this simple image contains two primary regional maxima, the blocks of pixels containing the value 14 and 18, and several smaller maxima, set to 11. 10-30 Morphological Reconstruction To eliminate all regional maxima except the two significant maxima, use imhmax, specifying a threshold value of 2. Note that imhmax only affects the maxima; none of the other pixel values are changed. The two significant maxima remain, although their heights are reduced. B = imhmax(A,2) This figure takes the second row from the sample image to illustrate in 1-D how imhmax changes the profile of the image. 10-31 10 Morphological Operations Imposing a Minimum You can emphasize specific minima (dark objects) in an image using the imimposemin function. The imimposemin function uses morphological reconstruction to eliminate all minima from the image except the minima you specify. To illustrate the process of imposing a minimum, this code creates a simple image containing two primary regional minima and several other regional minima. mask = uint8(10*ones(10,10)); mask(6:8,6:8) = 2; mask(2:4,2:4) = 7; mask(3,3) = 5; mask(2,9) = 9; mask(3,8) = 9; mask(9,2) = 9; mask(8,3) = 9 10-32 Morphological Reconstruction Creating a Marker Image To obtain an image that emphasizes the two deepest minima and removes all others, create a marker image that pinpoints the two minima of interest. You can create the marker image by explicitly setting certain pixels to specific values or by using other morphological functions to extract the features you want to emphasize in the mask image. This example uses imextendedmin to get a binary image that shows the locations of the two deepest minima. marker = imextendedmin(mask,1) Applying the Marker Image to the Mask Now use imimposemin to create new minima in the mask image at the points specified by the marker image. Note how imimposemin sets the values of pixels specified by the marker image to the lowest value supported by the datatype (0 for uint8 values). imimposemin also changes the values of all the other pixels in the image to eliminate the other minima. 10-33 10 Morphological Operations I = imimposemin(mask,marker) I = 11 11 11 11 11 11 8 8 8 11 11 8 0 8 11 11 8 8 8 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 0 0 0 11 11 11 11 11 11 11 0 0 0 11 11 11 11 11 11 11 0 0 0 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 This figure illustrates in 1-D how imimposemin changes the profile of row 2 of the image. 10-34 Morphological Reconstruction Imposing a Minimum 10-35 10 Morphological Operations Distance Transform The distance transform provides a metric or measure of the separation of points in the image. The bwdist function calculates the distance between each pixel that is set to off (0) and the nearest nonzero pixel for binary images. The bwdist function supports several distance metrics, listed in the following table. Distance Metrics Distance Metric Description Euclidean The Euclidean distance is the straight-line distance between two pixels. Illustration 0 0 0 1.41 1.0 1.41 0 1 0 1.0 0.0 1.0 0 0 0 1.41 1.0 1.41 Image City Block 10-36 The city block distance metric measures the path between the pixels based on a 4-connected neighborhood. Pixels whose edges touch are 1 unit apart; pixels diagonally touching are 2 units apart. Distance Transform 0 0 0 2 1 2 0 1 0 1 0 1 0 0 0 2 1 2 Image Distance Transform Distance Transform Distance Metrics (Continued) Distance Metric Description Chessboard The chessboard distance metric measures the path between the pixels based on an 8-connected neighborhood. Pixels whose edges or corners touch are 1 unit apart. Quasi-Euclidean The quasi-Euclidean metric measures the total Euclidean distance along a set of horizontal, vertical, and diagonal line segments. Illustration 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 Image Distance Transform 0 0 0 0 0 2.8 2.4 2.0 2.4 2.8 0 0 0 0 0 2.4 1.4 1.0 1.4 2.4 0 0 1 0 0 2.0 1.0 0 1.0 2.0 0 0 0 0 0 2.4 1.4 1.0 1.4 2.4 0 0 0 0 0 2.8 2.4 2.0 2.4 2.8 Image Distance Transform This example creates a binary image containing two intersecting circular objects. center1 = -10; center2 = -center1; dist = sqrt(2*(2*center1)^2); radius = dist/2 * 1.4; lims = [floor(center1-1.2*radius) ceil(center2+1.2*radius)]; [x,y] = meshgrid(lims(1):lims(2)); bw1 = sqrt((x-center1).^2 + (y-center1).^2) <= radius; bw2 = sqrt((x-center2).^2 + (y-center2).^2) <= radius; bw = bw1 | bw2; figure, imshow(bw), title('bw') 10-37 10 Morphological Operations To compute the distance transform of the complement of the binary image, use the bwdist function. In the image of the distance transform, note how the centers of the two circular areas are white. D = bwdist(~bw); figure, imshow(D,[]), title('Distance transform of ~bw') 10-38 Labeling and Measuring Objects in a Binary Image Labeling and Measuring Objects in a Binary Image In this section... “Understanding Connected-Component Labeling” on page 10-39 “Selecting Objects in a Binary Image” on page 10-41 “Finding the Area of the Foreground of a Binary Image” on page 10-42 “Finding the Euler Number of a Binary Image” on page 10-43 Understanding Connected-Component Labeling A connected component in a binary image is a set of pixels that form a connected group. For example, the binary image below has three connected components. Connected component labeling is the process of identifying the connected components in an image and assigning each one a unique label, like this: 10-39 10 Morphological Operations The matrix above is called a label matrix. bwconncomp computes connected components, as shown in the example: cc = bwconncomp(BW) cc = Connectivity: ImageSize: NumObjects: PixelIdxList: 8 [8 9] 3 {[6x1 double] [6x1 double] [5x1 double]} The PixelIdxList identifies the list of pixels belonging to each connected component. For visualizing connected components, it is useful to construct a label matrix. Use the labelmatrix function. To inspect the results, display the label matrix as a pseudo-color image using label2rgb. Construct a label matrix: labeled = labelmatrix(cc); Create a pseudo-color image, where the label identifying each object in the label matrix maps to a different color in the associated colormap matrix. Use label2rgb to choose the colormap, the background color, and how objects in the label matrix map to colors in the colormap: 10-40 Labeling and Measuring Objects in a Binary Image RGB_label = label2rgb(labeled, @copper, 'c', 'shuffle'); imshow(RGB_label,'InitialMagnification','fit') Remarks The functions bwlabel, bwlabeln, and bwconncomp all compute connected components for binary images. bwconncomp replaces the use of bwlabel and bwlabeln. It uses significantly less memory and is sometimes faster than the older functions. Function Input Dimension Output Form Memory Use Connectivity bwlabel 2-D Double-precision label matrix High 4 or 8 bwlabeln N-D Double-precision label matrix High Any bwconncomp N-D CC struct Low Any Selecting Objects in a Binary Image You can use the bwselect function to select individual objects in a binary image. You specify pixels in the input image, and bwselect returns a binary image that includes only those objects from the input image that contain one of the specified pixels. 10-41 10 Morphological Operations You can specify the pixels either noninteractively or with a mouse. For example, suppose you want to select objects in the image displayed in the current axes. You type BW2 = bwselect; The cursor changes to crosshairs when it is over the image. Click the objects you want to select; bwselect displays a small star over each pixel you click. When you are done, press Return. bwselect returns a binary image consisting of the objects you selected, and removes the stars. See the reference page for bwselect for more information. Finding the Area of the Foreground of a Binary Image The bwarea function returns the area of a binary image. The area is a measure of the size of the foreground of the image. Roughly speaking, the area is the number of on pixels in the image. bwarea does not simply count the number of pixels set to on, however. Rather, bwarea weights different pixel patterns unequally when computing the area. This weighting compensates for the distortion that is inherent in representing a continuous image with discrete pixels. For example, a diagonal line of 50 pixels is longer than a horizontal line of 50 pixels. As a result of the weighting bwarea uses, the horizontal line has area of 50, but the diagonal line has area of 62.5. This example uses bwarea to determine the percentage area increase in circbw.tif that results from a dilation operation. BW = imread('circbw.tif'); SE = ones(5); BW2 = imdilate(BW,SE); increase = (bwarea(BW2) - bwarea(BW))/bwarea(BW) increase = 0.3456 10-42 Labeling and Measuring Objects in a Binary Image See the reference page for bwarea for more information about the weighting pattern. Finding the Euler Number of a Binary Image The bweuler function returns the Euler number for a binary image. The Euler number is a measure of the topology of an image. It is defined as the total number of objects in the image minus the number of holes in those objects. You can use either 4- or 8-connected neighborhoods. This example computes the Euler number for the circuit image, using 8-connected neighborhoods. BW1 = imread('circbw.tif'); eul = bweuler(BW1,8) eul = -85 In this example, the Euler number is negative, indicating that the number of holes is greater than the number of objects. 10-43 10 Morphological Operations Lookup Table Operations In this section... “Creating a Lookup Table” on page 10-44 “Using a Lookup Table” on page 10-44 Creating a Lookup Table Certain binary image operations can be implemented most easily through lookup tables. A lookup table is a column vector in which each element represents the value to return for one possible combination of pixels in a neighborhood. To create lookup tables for various operations, use the makelut function. makelut creates lookup tables for 2-by-2 and 3-by-3 neighborhoods. The following figure illustrates these types of neighborhoods. Each neighborhood pixel is indicated by an x, and the center pixel is the one with a circle. For a 2-by-2 neighborhood, there are 16 possible permutations of the pixels in the neighborhood. Therefore, the lookup table for this operation is a 16-element vector. For a 3-by-3 neighborhood, there are 512 permutations, so the lookup table is a 512-element vector. Note makelut and applylut support only 2-by-2 and 3-by-3 neighborhoods. Lookup tables larger than 3-by-3 neighborhoods are not practical. For example, a lookup table for a 4-by-4 neighborhood would have 65,536 entries. Using a Lookup Table Once you create a lookup table, you can use it to perform the desired operation by using the applylut function. 10-44 Lookup Table Operations The example below illustrates using lookup table operations to modify an image containing text. The example creates an anonymous function that returns 1 if three or more pixels in the 3-by-3 neighborhood are 1; otherwise, it returns 0. The example then calls makelut, passing in this function as the first argument, and using the second argument to specify a 3-by-3 lookup table. f = @(x) sum(x(:)) >= 3; lut = makelut(f,3); lut is returned as a 512-element vector of 1’s and 0’s. Each value is the output from the function for one of the 512 possible permutations. You then perform the operation using applylut. BW1 = imread('text.png'); BW2 = applylut(BW1,lut); imshow(BW1) figure, imshow(BW2) Image Before and After Applying Lookup Table Operation For information about how applylut maps pixel combinations in the image to entries in the lookup table, see the reference page for applylut. 10-45 10 10-46 Morphological Operations 11 Analyzing and Enhancing Images This chapter describes functions that support a range of standard image processing operations for analyzing and enhancing images. • “Getting Information about Image Pixel Values and Image Statistics” on page 11-2 • “Analyzing Images” on page 11-11 • “Analyzing the Texture of an Image” on page 11-27 • “Adjusting Pixel Intensity Values” on page 11-37 • “Removing Noise from Images” on page 11-50 11 Analyzing and Enhancing Images Getting Information about Image Pixel Values and Image Statistics In this section... “Getting Image Pixel Values Using impixel” on page 11-2 “Creating an Intensity Profile of an Image Using improfile” on page 11-3 “Displaying a Contour Plot of Image Data” on page 11-7 “Creating an Image Histogram Using imhist” on page 11-9 “Getting Summary Statistics About an Image” on page 11-10 “Computing Properties for Image Regions” on page 11-10 Getting Image Pixel Values Using impixel To determine the values of one or more pixels in an image and return the values in a variable, use the impixel function. You can specify the pixels by passing their coordinates as input arguments or you can select the pixels interactively using a mouse. impixel returns the value of specified pixels in a variable in the MATLAB workspace. Note You can also get pixel value information interactively using the Image Tool -- see “Getting Information about the Pixels in an Image” on page 4-30. This example illustrates how to use impixel to get pixel values. 1 Display an image. imshow canoe.tif 2 Call impixel. When called with no input arguments, impixel associates itself with the image in the current axes. vals = impixel 3 Select the points you want to examine in the image by clicking the mouse. impixel places a star at each point you select. 11-2 Getting Information about Image Pixel Values and Image Statistics 4 When you are finished selecting points, press Return. impixel returns the pixel values in an n-by-3 array, where n is the number of points you selected. The stars used to indicate selected points disappear from the image. pixel_values = 0.1294 0.5176 0.7765 0.1294 0 0.6118 0.1294 0 0.4196 Creating an Intensity Profile of an Image Using improfile The intensity profile of an image is the set of intensity values taken from regularly spaced points along a line segment or multiline path in an image. For points that do not fall on the center of a pixel, the intensity values are interpolated. To create an intensity profile, use the improfile function. This function calculates and plots the intensity values along a line segment or a multiline path in an image. You define the line segment (or segments) by specifying 11-3 11 Analyzing and Enhancing Images their coordinates as input arguments. You can define the line segments using a mouse. (By default, improfile uses nearest-neighbor interpolation, but you can specify a different method. For more information, see “Specifying the Interpolation Method” on page 6-3.) improfile works best with grayscale and truecolor images. For a single line segment, improfile plots the intensity values in a two-dimensional view. For a multiline path, improfile plots the intensity values in a three-dimensional view. If you call improfile with no arguments, the cursor changes to crosshairs when it is over the image. You can then specify line segments by clicking the endpoints; improfile draws a line between each two consecutive points you select. When you finish specifying the path, press Return. improfile displays the plot in a new figure. In this example, you call improfile and specify a single line with the mouse. In this figure, the line is shown in red, and is drawn from top to bottom. I = fitsread('solarspectra.fts'); imshow(I,[]); improfile improfile displays a plot of the data along the line. Notice the peaks and valleys and how they correspond to the light and dark bands in the image. 11-4 Getting Information about Image Pixel Values and Image Statistics Plot Produced by improfile The example below shows how improfile works with an RGB image. Use imshow to display the image in a figure window. Call improfile without any arguments and trace a line segment in the image interactively. In the figure, the black line indicates a line segment drawn from top to bottom. Double-click to end the line segment. imshow peppers.png improfile 11-5 11 Analyzing and Enhancing Images RGB Image with Line Segment Drawn with improfile The improfile function displays a plot of the intensity values along the line segment. The plot includes separate lines for the red, green, and blue intensities. In the plot, notice how low the blue values are at the beginning of the plot where the line traverses the orange pepper. 11-6 Getting Information about Image Pixel Values and Image Statistics Plot of Intensity Values Along a Line Segment in an RGB Image Displaying a Contour Plot of Image Data You can use the toolbox function imcontour to display a contour plot of the data in a grayscale image. A contour is a path in an image along which the image intensity values are equal to a constant. This function is similar to the contour function in MATLAB, but it automatically sets up the axes so their orientation and aspect ratio match the image. This example displays a grayscale image of grains of rice and a contour plot of the image data: 11-7 11 Analyzing and Enhancing Images 1 Read a grayscale image and display it. I = imread('rice.png'); imshow(I) 2 Display a contour plot of the grayscale image. figure, imcontour(I,3) You can use the clabel function to label the levels of the contours. See the description of clabel in the MATLAB Function Reference for details. 11-8 Getting Information about Image Pixel Values and Image Statistics Creating an Image Histogram Using imhist An image histogram is a chart that shows the distribution of intensities in an indexed or grayscale image. You can use the information in a histogram to choose an appropriate enhancement operation. For example, if an image histogram shows that the range of intensity values is small, you can use an intensity adjustment function to spread the values across a wider range. To create an image histogram, use the imhist function. This function creates a histogram plot by making n equally spaced bins, each representing a range of data values. It then calculates the number of pixels within each range. The following example displays an image of grains of rice and a histogram based on 64 bins. The histogram shows a peak at around 100, corresponding to the dark gray background in the image. For information about how to modify an image by changing the distribution of its histogram, see “Adjusting Intensity Values to a Specified Range” on page 11-38. 1 Read image and display it. I = imread('rice.png'); imshow(I) 2 Display histogram of image. figure, imhist(I) 11-9 11 Analyzing and Enhancing Images Getting Summary Statistics About an Image You can compute standard statistics of an image using the mean2, std2, and corr2 functions. mean2 and std2 compute the mean and standard deviation of the elements of a matrix. corr2 computes the correlation coefficient between two matrices of the same size. These functions are two-dimensional versions of the mean, std, and corrcoef functions described in the MATLAB Function Reference. Computing Properties for Image Regions You can use the regionprops function to compute properties for image regions. For example, regionprops can measure such properties as the area, center of mass, and bounding box for a region you specify. See the reference page for regionprops for more information. 11-10 Analyzing Images Analyzing Images In this section... “Detecting Edges Using the edge Function” on page 11-11 “Detecting Corners Using the corner Function” on page 11-13 “Tracing Object Boundaries in an Image” on page 11-15 “Detecting Lines Using the Hough Transform” on page 11-20 “Analyzing Image Homogeneity Using Quadtree Decomposition” on page 11-24 The toolbox also includes functions that return information about the texture of an image. See “Analyzing the Texture of an Image” on page 11-27 for more information. Detecting Edges Using the edge Function In an image, an edge is a curve that follows a path of rapid change in image intensity. Edges are often associated with the boundaries of objects in a scene. Edge detection is used to identify the edges in an image. To find edges, you can use the edge function. This function looks for places in the image where the intensity changes rapidly, using one of these two criteria: • Places where the first derivative of the intensity is larger in magnitude than some threshold • Places where the second derivative of the intensity has a zero crossing edge provides a number of derivative estimators, each of which implements one of the definitions above. For some of these estimators, you can specify whether the operation should be sensitive to horizontal edges, vertical edges, or both. edge returns a binary image containing 1’s where edges are found and 0’s elsewhere. The most powerful edge-detection method that edge provides is the Canny method. The Canny method differs from the other edge-detection methods in that it uses two different thresholds (to detect strong and weak edges), and 11-11 11 Analyzing and Enhancing Images includes the weak edges in the output only if they are connected to strong edges. This method is therefore less likely than the others to be fooled by noise, and more likely to detect true weak edges. The following example illustrates the power of the Canny edge detector by showing the results of applying the Sobel and Canny edge detectors to the same image: 1 Read image and display it. I = imread('coins.png'); imshow(I) 2 Apply the Sobel and Canny edge detectors to the image and display them. BW1 = edge(I,'sobel'); BW2 = edge(I,'canny'); imshow(BW1) figure, imshow(BW2) 11-12 Analyzing Images Detecting Corners Using the corner Function Corners are the most reliable feature you can use to find the correspondence between images. The following diagram shows three pixels—one inside the object, one on the edge of the object, and one on the corner. If a pixel is inside an object, its surroundings (solid square) correspond to the surroundings of its neighbor (dotted square). This is true for neighboring pixels in all directions. If a pixel is on the edge of an object, its surroundings differ from the surroundings of its neighbors in one direction, but correspond to the surroundings of its neighbors in the other (perpendicular) direction. A corner pixel has surroundings different from all of its neighbors in all directions. The corner function identifies corners in an image. Two methods are available—the Harris corner detection method (the default) and Shi and Tomasi’s minimum eigenvalue method. Both methods use algorithms that depend on the eigenvalues of the summation of the squared difference matrix 11-13 11 Analyzing and Enhancing Images (SSD). The eigenvalues of an SSD matrix represent the differences between the surroundings of a pixel and the surroundings of its neighbors. The larger the difference between the surroundings of a pixel and those of its neighbors, the larger the eigenvalues. The larger the eigenvalues, the more likely that a pixel appears at a corner. The following example demonstrates how to locate corners with the corner function and adjust your results by refining the maximum number of desired corners. 1 Create a checkerboard image, and find the corners. I = checkerboard(40,2,2); C = corner(I); 2 Display the corners when the maximum number of desired corners is the default setting of 200. subplot(1,2,1); imshow(I); hold on plot(C(:,1), C(:,2), '.', 'Color', 'g') title('Maximum Corners = 200') hold off 3 Display the corners when the maximum number of desired corners is 3. corners_max_specified = corner(I,3); subplot(1,2,2); imshow(I); hold on plot(corners_max_specified(:,1), corners_max_specified(:,2), ... '.', 'Color', 'g') title('Maximum Corners = 3') hold off 11-14 Analyzing Images Tracing Object Boundaries in an Image The toolbox includes two functions you can use to find the boundaries of objects in a binary image: • bwtraceboundary • bwboundaries The bwtraceboundary function returns the row and column coordinates of all the pixels on the border of an object in an image. You must specify the location of a border pixel on the object as the starting point for the trace. The bwboundaries function returns the row and column coordinates of border pixels of all the objects in an image. For both functions, the nonzero pixels in the binary image belong to an object, and pixels with the value 0 (zero) constitute the background. The following example uses bwtraceboundary to trace the border of an object in a binary image. Then, using bwboundaries, the example traces the borders of all the objects in the image: 1 Read image and display it. I = imread('coins.png'); imshow(I) 11-15 11 Analyzing and Enhancing Images 2 Convert the image to a binary image. bwtraceboundary and bwboundaries only work with binary images. BW = im2bw(I); imshow(BW) 3 Determine the row and column coordinates of a pixel on the border of the object you want to trace. bwboundary uses this point as the starting location for the boundary tracing. dim = size(BW) col = round(dim(2)/2)-90; row = min(find(BW(:,col))) 4 Call bwtraceboundary to trace the boundary from the specified point. As required arguments, you must specify a binary image, the row and column coordinates of the starting point, and the direction of the first step. The example specifies north ('N'). For information about this parameter, see 11-16 Analyzing Images “Choosing the First Step and Direction for Boundary Tracing” on page 11-18. boundary = bwtraceboundary(BW,[row, col],'N'); 5 Display the original grayscale image and use the coordinates returned by bwtraceboundary to plot the border on the image. imshow(I) hold on; plot(boundary(:,2),boundary(:,1),'g','LineWidth',3); 6 To trace the boundaries of all the coins in the image, use the bwboundaries function. By default, bwboundaries finds the boundaries of all objects in an image, including objects inside other objects. In the binary image used in this example, some of the coins contain black areas that bwboundaries interprets as separate objects. To ensure that bwboundaries only traces the coins, use imfill to fill the area inside each coin. BW_filled = imfill(BW,'holes'); boundaries = bwboundaries(BW_filled); bwboundaries returns a cell array, where each cell contains the row/column coordinates for an object in the image. 7 Plot the borders of all the coins on the original grayscale image using the coordinates returned by bwboundaries. for k=1:10 11-17 11 Analyzing and Enhancing Images b = boundaries{k}; plot(b(:,2),b(:,1),'g','LineWidth',3); end Choosing the First Step and Direction for Boundary Tracing For certain objects, you must take care when selecting the border pixel you choose as the starting point and the direction you choose for the first step parameter (north, south, etc.). For example, if an object contains a hole and you select a pixel on a thin part of the object as the starting pixel, you can trace the outside border of the object or the inside border of the hole, depending on the direction you choose for the first step. For filled objects, the direction you select for the first step parameter is not as important. To illustrate, this figure shows the pixels traced when the starting pixel is on a thin part of the object and the first step is set to north and south. The connectivity is set to 8 (the default). 11-18 Analyzing Images Impact of First Step and Direction Parameters on Boundary Tracing 11-19 11 Analyzing and Enhancing Images Detecting Lines Using the Hough Transform This section describes how to use the Hough transform functions to detect lines in an image. The following table lists the Hough transform functions in the order you use them to perform this task. Function Description hough The hough function implements the Standard Hough Transform (SHT). The Hough transform is designed to detect lines, using the parametric representation of a line: rho = x*cos(theta) + y*sin(theta) The variable rho is the distance from the origin to the line along a vector perpendicular to the line. theta is the angle between the x-axis and this vector. The hough function generates a parameter space matrix whose rows and columns correspond to these rho and theta values, respectively. houghpeaks After you compute the Hough transform, you can use the houghpeaks function to find peak values in the parameter space. These peaks represent potential lines in the input image. houghlines After you identify the peaks in the Hough transform, you can use the houghlines function to find the endpoints of the line segments corresponding to peaks in the Hough transform. This function automatically fills in small gaps in the line segments. The following example shows how to use these functions to detect lines in an image. 1 Read an image into the MATLAB workspace. I = imread('circuit.tif'); 2 For this example, rotate and crop the image using the imrotate function. rotI = imrotate(I,33,'crop'); fig1 = imshow(rotI); 11-20 Analyzing Images 3 Find the edges in the image using the edge function. BW = edge(rotI,'canny'); figure, imshow(BW); 4 Compute the Hough transform of the image using the hough function. [H,theta,rho] = hough(BW); 5 Display the transform using the imshow function. figure, imshow(imadjust(mat2gray(H)),[],'XData',theta,'YData',rho,... 'InitialMagnification','fit'); xlabel('\theta (degrees)'), ylabel('\rho'); axis on, axis normal, hold on; colormap(hot) 11-21 11 Analyzing and Enhancing Images −300 −200 ρ −100 0 100 200 300 −80 −60 −40 −20 0 20 θ (degrees) 40 60 80 6 Find the peaks in the Hough transform matrix, H, using the houghpeaks function. P = houghpeaks(H,5,'threshold',ceil(0.3*max(H(:)))); 7 Superimpose a plot on the image of the transform that identifies the peaks. x = theta(P(:,2)); y = rho(P(:,1)); plot(x,y,'s','color','black'); 11-22 Analyzing Images −300 −200 ρ −100 0 100 200 300 −80 −60 −40 −20 0 20 θ (degrees) 40 60 80 8 Find lines in the image using the houghlines function. lines = houghlines(BW,theta,rho,P,'FillGap',5,'MinLength',7); 9 Create a plot that superimposes the lines on the original image. figure, imshow(rotI), hold on max_len = 0; for k = 1:length(lines) xy = [lines(k).point1; lines(k).point2]; plot(xy(:,1),xy(:,2),'LineWidth',2,'Color','green'); % Plot beginnings and ends of lines plot(xy(1,1),xy(1,2),'x','LineWidth',2,'Color','yellow'); plot(xy(2,1),xy(2,2),'x','LineWidth',2,'Color','red'); % Determine the endpoints of the longest line segment len = norm(lines(k).point1 - lines(k).point2); if ( len > max_len) 11-23 11 Analyzing and Enhancing Images max_len = len; xy_long = xy; end end % highlight the longest line segment plot(xy_long(:,1),xy_long(:,2),'LineWidth',2,'Color','red'); Analyzing Image Homogeneity Using Quadtree Decomposition Quadtree decomposition is an analysis technique that involves subdividing an image into blocks that are more homogeneous than the image itself. This technique reveals information about the structure of the image. It is also useful as the first step in adaptive compression algorithms. You can perform quadtree decomposition using the qtdecomp function. This function works by dividing a square image into four equal-sized square blocks, and then testing each block to see if it meets some criterion of homogeneity (e.g., if all the pixels in the block are within a specific dynamic range). If a block meets the criterion, it is not divided any further. If it does not meet the criterion, it is subdivided again into four blocks, and the test criterion is applied to those blocks. This process is repeated iteratively until each block meets the criterion. The result might have blocks of several different sizes. 11-24 Analyzing Images Example: Performing Quadtree Decomposition To illustrate, this example performs quadtree decomposition on a 512-by-512 grayscale image. 1 Read in the grayscale image. I = imread('liftingbody.png'); 2 Specify the test criteria used to determine the homogeneity of each block in the decomposition. For example, the criterion might be this threshold calculation. max(block(:)) - min(block(:)) <= 0.27 You can also supply qtdecomp with a function (rather than a threshold value) for deciding whether to split blocks; for example, you might base the decision on the variance of the block. See the reference page for qtdecomp for more information. 3 Perform this quadtree decomposition by calling the qtdecomp function, specifying the image and the threshold value as arguments. S = qtdecomp(I,0.27) You specify the threshold as a value between 0 and 1, regardless of the class of I. If I is uint8, qtdecomp multiplies the threshold value by 255 to determine the actual threshold to use. If I is uint16, qtdecomp multiplies the threshold value by 65535. qtdecomp first divides the image into four 256-by-256 blocks and applies the test criterion to each block. If a block does not meet the criterion, qtdecomp subdivides it and applies the test criterion to each block. qtdecomp continues to subdivide blocks until all blocks meet the criterion. Blocks can be as small as 1-by-1, unless you specify otherwise. qtdecomp returns S as a sparse matrix, the same size as I. The nonzero elements of S represent the upper left corners of the blocks; the value of each nonzero element indicates the block size. The following figure shows the original image and a representation of its quadtree decomposition. (To see how this representation was created, see the 11-25 11 Analyzing and Enhancing Images example on the qtdecomp reference page.) Each black square represents a homogeneous block, and the white lines represent the boundaries between blocks. Notice how the blocks are smaller in areas corresponding to large changes in intensity in the image. Image and a Representation of Its Quadtree Decomposition 11-26 Analyzing the Texture of an Image Analyzing the Texture of an Image In this section... “Understanding Texture Analysis” on page 11-27 “Using Texture Filter Functions” on page 11-27 “Gray-Level Co-Occurrence Matrix (GLCM)” on page 11-31 Understanding Texture Analysis The toolbox supports a set of functions that you can use for texture analysis. Texture analysis refers to the characterization of regions in an image by their texture content. Texture analysis attempts to quantify intuitive qualities described by terms such as rough, smooth, silky, or bumpy as a function of the spatial variation in pixel intensities. In this sense, the roughness or bumpiness refers to variations in the intensity values, or gray levels. Texture analysis is used in a variety of applications, including remote sensing, automated inspection, and medical image processing. Texture analysis can be used to find the texture boundaries, called texture segmentation. Texture analysis can be helpful when objects in an image are more characterized by their texture than by intensity, and traditional thresholding techniques cannot be used effectively. Using Texture Filter Functions The toolbox includes several texture analysis functions that filter an image using standard statistical measures, listed in the following table. Function Description rangefilt Calculates the local range of an image. stdfilt Calculates the local standard deviation of an image. entropyfilt Calculates the local entropy of a grayscale image. Entropy is a statistical measure of randomness. These statistics can characterize the texture of an image because they provide information about the local variability of the intensity values of pixels in an 11-27 11 Analyzing and Enhancing Images image. For example, in areas with smooth texture, the range of values in the neighborhood around a pixel will be a small value; in areas of rough texture, the range will be larger. Similarly, calculating the standard deviation of pixels in a neighborhood can indicate the degree of variability of pixel values in that region. The following sections provide additional information about the texture functions: • “Understanding the Texture Filter Functions” on page 11-28 • “Example: Using the Texture Functions” on page 11-29 Understanding the Texture Filter Functions The functions all operate in a similar way: they define a neighborhood around the pixel of interest, calculate the statistic for that neighborhood, and use that value as the value of the pixel of interest in the output image. This example shows how the rangefilt function operates on a simple array. A = [ 1 2 3 4 5; 6 7 8 9 10; 11 12 13 14 15; 16 17 18 19 20 ] A = 1 6 11 16 2 7 12 17 3 8 13 18 4 9 14 19 5 10 15 20 7 12 12 7 7 12 12 7 6 11 11 6 B = rangefilt(A) B = 6 11 11 6 11-28 7 12 12 7 Analyzing the Texture of an Image The following figure shows how the value of element B(2,4) was calculated from A(2,4). By default, the rangefilt function uses a 3-by-3 neighborhood but you can specify neighborhoods of different shapes and sizes. Determining Pixel Values in Range Filtered Output Image The stdfilt and entropyfilt functions operate similarly, defining a neighborhood around the pixel of interest and calculating the statistic for the neighborhood to determine the pixel value in the output image. The stdfilt function calculates the standard deviation of all the values in the neighborhood. The entropyfilt function calculates the entropy of the neighborhood and assigns that value to the output pixel. Note that, by default, the entropyfilt function defines a 9-by-9 neighborhood around the pixel of interest. To calculate the entropy of an entire image, use the entropy function. Example: Using the Texture Functions The following example illustrates how the texture filter functions can detect regions of texture in an image. In the figure, the background is smooth; there is very little variation in the gray-level values. In the foreground, the surface contours of the coins exhibit more texture. In this image, foreground pixels have more variability and thus higher range values. Range filtering makes the edges and contours of the coins more visible. To see an example of using filtering functions, view the Texture Segmentation Using Texture Filters example. 11-29 11 Analyzing and Enhancing Images 1 Read in the image and display it. I = imread('eight.tif'); imshow(I) 2 Filter the image with the rangefilt function and display the results. Note how range filtering highlights the edges and surface contours of the coins. K = rangefilt(I); figure, imshow(K) 11-30 Analyzing the Texture of an Image Gray-Level Co-Occurrence Matrix (GLCM) A statistical method of examining texture that considers the spatial relationship of pixels is the gray-level co-occurrence matrix (GLCM), also known as the gray-level spatial dependence matrix. The GLCM functions characterize the texture of an image by calculating how often pairs of pixel with specific values and in a specified spatial relationship occur in an image, creating a GLCM, and then extracting statistical measures from this matrix. (The texture filter functions, described in “Using Texture Filter Functions” on page 11-27, cannot provide information about shape, i.e., the spatial relationships of pixels in an image.) After you create the GLCMs, you can derive several statistics from them using the graycoprops function. These statistics provide information about the texture of an image. The following table lists the statistics. Statistic Description Contrast Measures the local variations in the gray-level co-occurrence matrix. Correlation Measures the joint probability occurrence of the specified pixel pairs. Energy Provides the sum of squared elements in the GLCM. Also known as uniformity or the angular second moment. Homogeneity Measures the closeness of the distribution of elements in the GLCM to the GLCM diagonal. Create a Gray-Level Co-Occurrence Matrix To create a GLCM, use the graycomatrix function. The graycomatrix function creates a gray-level co-occurrence matrix (GLCM) by calculating how often a pixel with the intensity (gray-level) value i occurs in a specific spatial relationship to a pixel with the value j. By default, the spatial relationship is defined as the pixel of interest and the pixel to its immediate right (horizontally adjacent), but you can specify other spatial relationships between the two pixels. Each element (i,j) in the resultant glcm is simply the sum of the number of times that the pixel with value i occurred in the specified spatial relationship to a pixel with value j in the input image. 11-31 11 Analyzing and Enhancing Images The number of gray levels in the image determines the size of the GLCM. By default, graycomatrix uses scaling to reduce the number of intensity values in an image to eight, but you can use the NumLevels and the GrayLimits parameters to control this scaling of gray levels. See the graycomatrix reference page for more information. The gray-level co-occurrence matrix can reveal certain properties about the spatial distribution of the gray levels in the texture image. For example, if most of the entries in the GLCM are concentrated along the diagonal, the texture is coarse with respect to the specified offset. You can also derive several statistical measures from the GLCM. See for more information. To illustrate, the following figure shows how graycomatrix calculates the first three values in a GLCM. In the output GLCM, element (1,1) contains the value 1 because there is only one instance in the input image where two horizontally adjacent pixels have the values 1 and 1, respectively. glcm(1,2) contains the value 2 because there are two instances where two horizontally adjacent pixels have the values 1 and 2. Element (1,3) in the GLCM has the value 0 because there are no instances of two horizontally adjacent pixels with the values 1 and 3. graycomatrix continues processing the input image, scanning the image for other pixel pairs (i,j) and recording the sums in the corresponding elements of the GLCM. Process Used to Create the GLCM 11-32 Analyzing the Texture of an Image Specifying the Offsets By default, the graycomatrix function creates a single GLCM, with the spatial relationship, or offset, defined as two horizontally adjacent pixels. However, a single GLCM might not be enough to describe the textural features of the input image. For example, a single horizontal offset might not be sensitive to texture with a vertical orientation. For this reason, graycomatrix can create multiple GLCMs for a single input image. To create multiple GLCMs, specify an array of offsets to the graycomatrix function. These offsets define pixel relationships of varying direction and distance. For example, you can define an array of offsets that specify four directions (horizontal, vertical, and two diagonals) and four distances. In this case, the input image is represented by 16 GLCMs. When you calculate statistics from these GLCMs, you can take the average. You specify these offsets as a p-by-2 array of integers. Each row in the array is a two-element vector, [row_offset, col_offset], that specifies one offset. row_offset is the number of rows between the pixel of interest and its neighbor. col_offset is the number of columns between the pixel of interest and its neighbor. This example creates an offset that specifies four directions and 4 distances for each direction. For more information about specifying offsets, see the graycomatrix reference page. offsets = [ 0 -1 -1 -1 1; 0 2; 0 3; 0 4;... 1; -2 2; -3 3; -4 4;... 0; -2 0; -3 0; -4 0;... -1; -2 -2; -3 -3; -4 -4]; The figure illustrates the spatial relationships of pixels that are defined by this array of offsets, where D represents the distance from the pixel of interest. 11-33 11 Analyzing and Enhancing Images Derive Statistics from a GLCM and Plot Correlation This example shows how to create a set of GLCMs and derive statistics from them and illustrates how the statistics returned by graycoprops have a direct relationship to the original input image. 1 Read in a grayscale image and display it. The example converts the truecolor image to a grayscale image and then rotates it 90° for this example. circuitBoard = rot90(rgb2gray(imread('board.tif'))); imshow(circuitBoard) 11-34 Analyzing the Texture of an Image 2 Define offsets of varying direction and distance. Because the image contains objects of a variety of shapes and sizes that are arranged in horizontal and vertical directions, the example specifies a set of horizontal offsets that only vary in distance. offsets0 = [zeros(40,1) (1:40)']; 3 Create the GLCMs. Call the graycomatrix function specifying the offsets. glcms = graycomatrix(circuitBoard,'Offset',offsets0) 4 Derive statistics from the GLCMs using the graycoprops function. The example calculates the contrast and correlation. stats = graycoprops(glcms,'Contrast Correlation'); 5 Plot correlation as a function of offset. figure, plot([stats.Correlation]); title('Texture Correlation as a function of offset'); xlabel('Horizontal Offset') ylabel('Correlation') 11-35 11 Analyzing and Enhancing Images The plot contains peaks at offsets 7, 15, 23, and 30. If you examine the input image closely, you can see that certain vertical elements in the image have a periodic pattern that repeats every seven pixels. The following figure shows the upper left corner of the image and points out where this pattern occurs. 11-36 Adjusting Pixel Intensity Values Adjusting Pixel Intensity Values In this section... “Understanding Intensity Adjustment” on page 11-37 “Adjusting Intensity Values to a Specified Range” on page 11-38 “Adjusting Intensity Values Using Histogram Equalization” on page 11-42 “Adjusting Intensity Values Using Contrast-Limited Adaptive Histogram Equalization” on page 11-44 “Enhancing Color Separation Using Decorrelation Stretching” on page 11-45 Understanding Intensity Adjustment Image enhancement techniques are used to improve an image, where “improve” is sometimes defined objectively (e.g., increase the signal-to-noise ratio), and sometimes subjectively (e.g., make certain features easier to see by modifying the colors or intensities). Intensity adjustment is an image enhancement technique that maps an image’s intensity values to a new range. To illustrate, this figure shows a low-contrast image with its histogram. Notice in the histogram of the image how all the values gather in the center of the range. I = imread('pout.tif'); imshow(I) figure, imhist(I,64) 11-37 11 Analyzing and Enhancing Images If you remap the data values to fill the entire intensity range [0, 255], you can increase the contrast of the image. The functions described in this section apply primarily to grayscale images. However, some of these functions can be applied to color images as well. For information about how these functions work with color images, see the reference pages for the individual functions. Adjusting Intensity Values to a Specified Range You can adjust the intensity values in an image using the imadjust function, where you specify the range of intensity values in the output image. For example, this code increases the contrast in a low-contrast grayscale image by remapping the data values to fill the entire intensity range [0, 255]. I = imread('pout.tif'); J = imadjust(I); imshow(J) figure, imhist(J,64) This figure displays the adjusted image and its histogram. Notice the increased contrast in the image, and that the histogram now fills the entire range. 11-38 Adjusting Pixel Intensity Values Adjusted Image and Its Histogram Specifying the Adjustment Limits You can optionally specify the range of the input values and the output values using imadjust. You specify these ranges in two vectors that you pass to imadjust as arguments. The first vector specifies the low- and high-intensity values that you want to map. The second vector specifies the scale over which you want to map them. Note Note that you must specify the intensities as values between 0 and 1 regardless of the class of I. If I is uint8, the values you supply are multiplied by 255 to determine the actual values to use; if I is uint16, the values are multiplied by 65535. To learn about an alternative way to set these limits automatically, see “Setting the Adjustment Limits Automatically” on page 11-40. For example, you can decrease the contrast of an image by narrowing the range of the data. In the example below, the man’s coat is too dark to reveal 11-39 11 Analyzing and Enhancing Images any detail. imadjust maps the range [0,51] in the uint8 input image to [128,255] in the output image. This brightens the image considerably, and also widens the dynamic range of the dark portions of the original image, making it much easier to see the details in the coat. Note, however, that because all values above 51 in the original image are mapped to 255 (white) in the adjusted image, the adjusted image appears washed out. I = imread('cameraman.tif'); J = imadjust(I,[0 0.2],[0.5 1]); imshow(I) figure, imshow(J) Image After Remapping and Widening the Dynamic Range Setting the Adjustment Limits Automatically To use imadjust, you must typically perform two steps: 1 View the histogram of the image to determine the intensity value limits. 2 Specify these limits as a fraction between 0.0 and 1.0 so that you can pass them to imadjust in the [low_in high_in] vector. For a more convenient way to specify these limits, use the stretchlim function. (The imadjust function uses stretchlim for its simplest syntax, imadjust(I).) This function calculates the histogram of the image and determines the adjustment limits automatically. The stretchlim function returns these 11-40 Adjusting Pixel Intensity Values values as fractions in a vector that you can pass as the [low_in high_in] argument to imadjust; for example: I = imread('rice.png'); J = imadjust(I,stretchlim(I),[0 1]); By default, stretchlim uses the intensity values that represent the bottom 1% (0.01) and the top 1% (0.99) of the range as the adjustment limits. By trimming the extremes at both ends of the intensity range, stretchlim makes more room in the adjusted dynamic range for the remaining intensities. But you can specify other range limits as an argument to stretchlim. See the stretchlim reference page for more information. Gamma Correction imadjust maps low to bottom, and high to top. By default, the values between low and high are mapped linearly to values between bottom and top. For example, the value halfway between low and high corresponds to the value halfway between bottom and top. imadjust can accept an additional argument that specifies the gamma correction factor. Depending on the value of gamma, the mapping between values in the input and output images might be nonlinear. For example, the value halfway between low and high might map to a value either greater than or less than the value halfway between bottom and top. Gamma can be any value between 0 and infinity. If gamma is 1 (the default), the mapping is linear. If gamma is less than 1, the mapping is weighted toward higher (brighter) output values. If gamma is greater than 1, the mapping is weighted toward lower (darker) output values. The figure below illustrates this relationship. The three transformation curves show how values are mapped when gamma is less than, equal to, and greater than 1. (In each graph, the x-axis represents the intensity values in the input image, and the y-axis represents the intensity values in the output image.) 11-41 11 Analyzing and Enhancing Images Plots Showing Three Different Gamma Correction Settings The example below illustrates gamma correction. Notice that in the call to imadjust, the data ranges of the input and output images are specified as empty matrices. When you specify an empty matrix, imadjust uses the default range of [0,1]. In the example, both ranges are left empty; this means that gamma correction is applied without any other adjustment of the data. [X,map] = imread('forest.tif'); I = ind2gray(X,map); J = imadjust(I,[],[],0.5); imshow(I) figure, imshow(J) Image Before and After Applying Gamma Correction Adjusting Intensity Values Using Histogram Equalization The process of adjusting intensity values can be done automatically by the histeq function. histeq performs histogram equalization, which involves 11-42 Adjusting Pixel Intensity Values transforming the intensity values so that the histogram of the output image approximately matches a specified histogram. (By default, histeq tries to match a flat histogram with 64 bins, but you can specify a different histogram instead; see the reference page for histeq.) This example illustrates using histeq to adjust a grayscale image. The original image has low contrast, with most values in the middle of the intensity range. histeq produces an output image having values evenly distributed throughout the range. I = imread('pout.tif'); J = histeq(I); imshow(J) figure, imhist(J,64) Image After Histogram Equalization with Its Histogram histeq can return a 1-by-256 vector that shows, for each possible input value, the resulting output value. (The values in this vector are in the range [0,1], regardless of the class of the input image.) You can plot this data to get the transformation curve. For example: I = imread('pout.tif'); [J,T] = histeq(I); figure,plot((0:255)/255,T); 11-43 11 Analyzing and Enhancing Images Notice how this curve reflects the histograms in the previous figure, with the input values mostly between 0.3 and 0.6, while the output values are distributed evenly between 0 and 1. Adjusting Intensity Values Using Contrast-Limited Adaptive Histogram Equalization As an alternative to using histeq, you can perform contrast-limited adaptive histogram equalization (CLAHE) using the adapthisteq function. While histeq works on the entire image, adapthisteq operates on small regions in the image, called tiles. Each tile’s contrast is enhanced, so that the histogram of the output region approximately matches a specified histogram. After performing the equalization, adapthisteq combines neighboring tiles using bilinear interpolation to eliminate artificially induced boundaries. 11-44 Adjusting Pixel Intensity Values To avoid amplifying any noise that might be present in the image, you can use adapthisteq optional parameters to limit the contrast, especially in homogeneous areas. To illustrate, this example uses adapthisteq to adjust the contrast in a grayscale image. The original image has low contrast, with most values in the middle of the intensity range. adapthisteq produces an output image having values evenly distributed throughout the range. I = imread('pout.tif'); J = adapthisteq(I); imshow(J) figure, imhist(J,64) Image After CLAHE Equalization with Its Histogram Enhancing Color Separation Using Decorrelation Stretching Decorrelation stretching enhances the color separation of an image with significant band-to-band correlation. The exaggerated colors improve visual interpretation and make feature discrimination easier. You apply decorrelation stretching with the decorrstretch function. See “Adding a Linear Contrast Stretch” on page 11-48 on how to add an optional linear contrast stretch to the decorrelation stretch. 11-45 11 Analyzing and Enhancing Images The number of color bands, NBANDS, in the image is usually three. But you can apply decorrelation stretching regardless of the number of color bands. The original color values of the image are mapped to a new set of color values with a wider range. The color intensities of each pixel are transformed into the color eigenspace of the NBANDS-by-NBANDS covariance or correlation matrix, stretched to equalize the band variances, then transformed back to the original color bands. To define the bandwise statistics, you can use the entire original image or, with the subset option, any selected subset of it. See the decorrstretch reference page. Simple Decorrelation Stretching You can apply decorrelation and stretching operations on the library of images available in the imdemos directory. The library includes a LANDSAT image of the Little Colorado River. In this example, you perform a simple decorrelation stretch on this image: 1 The image has seven bands, but just read in the three visible colors: A = multibandread('littlecoriver.lan', [512, 512, 7], ... 'uint8=>uint8', 128, 'bil', 'ieee-le', ... {'Band','Direct',[3 2 1]}); 2 Then perform the decorrelation stretch: B = decorrstretch(A); 3 Now view the results: imshow(A) figure, imshow(B) Compare the two images. The original has a strong violet (red-bluish) tint, while the transformed image has a somewhat expanded color range. 11-46 Adjusting Pixel Intensity Values Little Colorado River Before (left) and After (right) Decorrelation Stretch A color band scatterplot of the images shows how the bands are decorrelated and equalized: rA = A(:,:,1); gA = A(:,:,2); bA = A(:,:,3); figure, plot3(rA(:),gA(:),bA(:),'.') grid on xlabel('Red (Band 3)') ylabel('Green (Band 2)') zlabel('Blue (Band 1)') rB = B(:,:,1); gB = B(:,:,2); bB = B(:,:,3); figure, plot3(rB(:),gB(:),bB(:),'.') grid on xlabel('Red (Band 3)') ylabel('Green (Band 2)') zlabel('Blue (Band 1)') 11-47 11 Analyzing and Enhancing Images Color Scatterplot Before (left) and After (right) Decorrelation Stretch Adding a Linear Contrast Stretch Now try the same transformation, but with a linear contrast stretch applied after the decorrelation stretch: imshow(A) C = decorrstretch(A,'Tol',0.01); figure, imshow(C) Compare the transformed image to the original. 11-48 Adjusting Pixel Intensity Values Little Colorado River After Decorrelation Stretch Followed by Linear Contrast Stretch Adding the linear contrast stretch enhances the resulting image by further expanding the color range. In this case, the transformed color range is mapped within each band to a normalized interval between 0.01 and 0.99, saturating 2%. See the stretchlim function reference page for more about Tol. Without the Tol option, decorrstretch applies no linear contrast stretch. Note You can apply a linear contrast stretch as a separate operation after performing a decorrelation stretch, using stretchlim and imadjust. This alternative, however, often gives inferior results for uint8 and uint16 images, because the pixel values must be clamped to [0 255] (or [0 65535]). The Tol option in decorrstretch circumvents this limitation. 11-49 11 Analyzing and Enhancing Images Removing Noise from Images In this section... “Understanding Sources of Noise in Digital Images” on page 11-50 “Removing Noise By Linear Filtering” on page 11-50 “Removing Noise By Median Filtering” on page 11-51 “Removing Noise By Adaptive Filtering” on page 11-54 Understanding Sources of Noise in Digital Images Digital images are prone to a variety of types of noise. Noise is the result of errors in the image acquisition process that result in pixel values that do not reflect the true intensities of the real scene. There are several ways that noise can be introduced into an image, depending on how the image is created. For example: • If the image is scanned from a photograph made on film, the film grain is a source of noise. Noise can also be the result of damage to the film, or be introduced by the scanner itself. • If the image is acquired directly in a digital format, the mechanism for gathering the data (such as a CCD detector) can introduce noise. • Electronic transmission of image data can introduce noise. To simulate the effects of some of the problems listed above, the toolbox provides the imnoise function, which you can use to add various types of noise to an image. The examples in this section use this function. Removing Noise By Linear Filtering You can use linear filtering to remove certain types of noise. Certain filters, such as averaging or Gaussian filters, are appropriate for this purpose. For example, an averaging filter is useful for removing grain noise from a photograph. Because each pixel gets set to the average of the pixels in its neighborhood, local variations caused by grain are reduced. 11-50 Removing Noise from Images See “Designing and Implementing Linear Filters in the Spatial Domain” on page 8-2 for more information about linear filtering using imfilter. Removing Noise By Median Filtering Median filtering is similar to using an averaging filter, in that each output pixel is set to an average of the pixel values in the neighborhood of the corresponding input pixel. However, with median filtering, the value of an output pixel is determined by the median of the neighborhood pixels, rather than the mean. The median is much less sensitive than the mean to extreme values (called outliers). Median filtering is therefore better able to remove these outliers without reducing the sharpness of the image. The medfilt2 function implements median filtering. Note Median filtering is a specific case of order-statistic filtering, also known as rank filtering. For information about order-statistic filtering, see the reference page for the ordfilt2 function. The following example compares using an averaging filter and medfilt2 to remove salt and pepper noise. This type of noise consists of random pixels’ being set to black or white (the extremes of the data range). In both cases the size of the neighborhood used for filtering is 3-by-3. 1 Read in the image and display it. I = imread('eight.tif'); imshow(I) 11-51 11 Analyzing and Enhancing Images 2 Add noise to it. J = imnoise(I,'salt & pepper',0.02); figure, imshow(J) 3 Filter the noisy image with an averaging filter and display the results. K = filter2(fspecial('average',3),J)/255; 11-52 Removing Noise from Images figure, imshow(K) 4 Now use a median filter to filter the noisy image and display the results. Notice that medfilt2 does a better job of removing noise, with less blurring of edges. L = medfilt2(J,[3 3]); figure, imshow(L) 11-53 11 Analyzing and Enhancing Images Removing Noise By Adaptive Filtering The wiener2 function applies a Wiener filter (a type of linear filter) to an image adaptively, tailoring itself to the local image variance. Where the variance is large, wiener2 performs little smoothing. Where the variance is small, wiener2 performs more smoothing. This approach often produces better results than linear filtering. The adaptive filter is more selective than a comparable linear filter, preserving edges and other high-frequency parts of an image. In addition, there are no design tasks; the wiener2 function handles all preliminary computations and implements the filter for an input image. wiener2, however, does require more computation time than linear filtering. wiener2 works best when the noise is constant-power (“white”) additive noise, such as Gaussian noise. The example below applies wiener2 to an image of Saturn that has had Gaussian noise added. 1 Read in an image. Because the image is a truecolor image, the example converts it to grayscale. RGB = imread('saturn.png'); I = rgb2gray(RGB); 2 The example then add Gaussian noise to the image and then displays the image. Because the image is quite large, the figure only shows a portion of the image. J = imnoise(I,'gaussian',0,0.025); imshow(J) 11-54 Removing Noise from Images Portion of the Image with Added Gaussian Noise 3 Remove the noise, using the wiener2 function. Again, the figure only shows a portion of the image K = wiener2(J,[5 5]); figure, imshow(K) Portion of the Image with Noise Removed by Wiener Filter 11-55 11 11-56 Analyzing and Enhancing Images 12 ROI-Based Processing This chapter describes how to define a region of interest (ROI) and perform processing on the ROI you define. • “Specifying a Region of Interest (ROI)” on page 12-2 • “Filtering an ROI” on page 12-5 • “Filling an ROI” on page 12-8 12 ROI-Based Processing Specifying a Region of Interest (ROI) In this section... “Overview of ROI Processing” on page 12-2 “Creating a Binary Mask” on page 12-2 “Creating an ROI Without an Associated Image” on page 12-3 “Creating an ROI Based on Color Values” on page 12-4 Overview of ROI Processing A region of interest (ROI) is a portion of an image that you want to filter or perform some other operation on. You define an ROI by creating a binary mask, which is a binary image that is the same size as the image you want to process with pixels that define the ROI set to 1 and all other pixels set to 0. You can define more than one ROI in an image. The regions can be geographic in nature, such as polygons that encompass contiguous pixels, or they can be defined by a range of intensities. In the latter case, the pixels are not necessarily contiguous. Using Binary Images as a Mask This section describes how to create binary masks to define ROIs. However, any binary image can be used as a mask, provided that the binary image is the same size as the image being filtered. For example, suppose you want to filter the grayscale image I, filtering only those pixels whose values are greater than 0.5. You can create the appropriate mask with this command: BW = (I > 0.5). Creating a Binary Mask You can use the createMask method of the imroi base class to create a binary mask for any type of ROI object — impoint, imline, imrect, imellipse, impoly, or imfreehand. The createMask method returns a binary image the same size as the input image, containing 1s inside the ROI and 0s everywhere else. The example below illustrates how to use the createMask method: 12-2 Specifying a Region of Interest (ROI) img = imread('pout.tif'); h_im = imshow(img); e = imellipse(gca,[55 10 120 120]); BW = createMask(e,h_im); You can reposition the mask by dragging it with the mouse. Right click, select copy position, and call createMask again. BW = createMask(e,h_im); The mask behaves like a cookie cutter and can be repositioned repeatedly to select new ROIs. Creating an ROI Without an Associated Image Using the createMask method of ROI objects you can create a binary mask that defines an ROI associated with a particular image. To create a binary mask without having an associated image, use the poly2mask function. Unlike the createMask method, poly2mask does not require an input image. You specify the vertices of the ROI in two vectors and specify the size of the 12-3 12 ROI-Based Processing binary mask returned. For example, the following creates a binary mask that can be used to filter an ROI in the pout.tif image. c = [123 123 170 170]; r = [160 210 210 160]; m = 291; % height of pout image n = 240; % width of pout image BW = poly2mask(c,r,m,n); figure, imshow(BW) Creating an ROI Based on Color Values You can use the roicolor function to define an ROI based on color or intensity range. For more information, see the reference page for roicolor. 12-4 Filtering an ROI Filtering an ROI In this section... “Overview of ROI Filtering” on page 12-5 “Filtering a Region in an Image” on page 12-5 “Specifying the Filtering Operation” on page 12-6 Overview of ROI Filtering Filtering a region of interest (ROI) is the process of applying a filter to a region in an image, where a binary mask defines the region. For example, you can apply an intensity adjustment filter to certain regions of an image. To filter an ROI in an image, use the roifilt2 function. When you call roifilt2, you specify: • Input grayscale image to be filtered • Binary mask image that defines the ROI • Filter (either a 2-D filter or function) roifilt2 filters the input image and returns an image that consists of filtered values for pixels where the binary mask contains 1s and unfiltered values for pixels where the binary mask contains 0s. This type of operation is called masked filtering. roifilt2 is best suited for operations that return data in the same range as in the original image, because the output image takes some of its data directly from the input image. Certain filtering operations can result in values outside the normal image data range (i.e., [0,1] for images of class double, [0,255] for images of class uint8, and [0,65535] for images of class uint16). For more information, see the reference page for roifilt2. Filtering a Region in an Image This example uses masked filtering to increase the contrast of a specific region of an image: 12-5 12 ROI-Based Processing 1 Read in the image. I = imread('pout.tif'); 2 Create the mask. This example uses the mask BW created by the createMask method in the section “Creating a Binary Mask” on page 12-2. The region of interest specified is the child’s face. 3 Use fspecial to create the filter: h = fspecial('unsharp'); 4 Call roifilt2, specifying the filter, the image to be filtered, and the mask: I2 = roifilt2(h,I,BW); imshow(I) figure, imshow(I2) Image Before and After Using an Unsharp Filter on the Region of Interest Specifying the Filtering Operation roifilt2 also enables you to specify your own function to operate on the ROI. This example uses the imadjust function to lighten parts of an image: 1 Read in the image. I = imread('cameraman.tif'); 12-6 Filtering an ROI 2 Create the mask. In this example, the mask is a binary image containing text. The mask image must be cropped to be the same size as the image to be filtered: BW = imread('text.png'); mask = BW(1:256,1:256); 3 Create the function you want to use as a filter: f = @(x) imadjust(x,[],[],0.3); 4 Call roifilt2, specifying the image to be filtered, the mask, and the filter. The resulting image, I2, has the text imprinted on it: I2 = roifilt2(I,mask,f); imshow(I2) Image Brightened Using a Binary Mask Containing Text 12-7 12 ROI-Based Processing Filling an ROI Filling is a process that fills a region of interest (ROI) by interpolating the pixel values from the borders of the region. This process can be used to make objects in an image seem to disappear as they are replaced with values that blend in with the background area. To fill an ROI, you can use the roifill function. This function is useful for image editing, including removal of extraneous details or artifacts. roifill performs the fill operation using an interpolation method based on Laplace’s equation. This method results in the smoothest possible fill, given the values on the boundary of the region. Select the region of interest with the mouse. When you complete the selection, roifill returns an image with the selected ROI filled in. This example shows how to use roifill to fill an ROI in an image. 1 Read an image into the MATLAB workspace and display it. Because the image is an indexed image, the example uses ind2gray to convert it to a grayscale image: load trees I = ind2gray(X,map); imshow(I) 2 Call roifill to specify the ROI you want to fill. When you move the pointer . Define the ROI over the image, the pointer shape changes to cross hairs by clicking the mouse to specify the vertices of a polygon. You can use the mouse to adjust the size and position of the ROI: I2 = roifill; 12-8 Filling an ROI 3 Perform the fill operation. Double-click inside the ROI or right-click and select Fill Area. roifill returns the modified image in I2. View the output image to see how roifill filled in the area defined by the ROI: imshow(I2) 12-9 12 12-10 ROI-Based Processing 13 Image Deblurring This chapter describes how to deblur an image using the toolbox deblurring functions. • “Understanding Deblurring” on page 13-2 • “Deblurring with the Wiener Filter” on page 13-6 • “Deblurring with a Regularized Filter” on page 13-7 • “Deblurring with the Lucy-Richardson Algorithm” on page 13-10 • “Deblurring with the Blind Deconvolution Algorithm” on page 13-16 • “Creating Your Own Deblurring Functions” on page 13-23 • “Avoiding Ringing in Deblurred Images” on page 13-24 13 Image Deblurring Understanding Deblurring In this section... “Causes of Blurring” on page 13-2 “Deblurring Model” on page 13-2 “Deblurring Functions” on page 13-4 Causes of Blurring The blurring, or degradation, of an image can be caused by many factors: • Movement during the image capture process, by the camera or, when long exposure times are used, by the subject • Out-of-focus optics, use of a wide-angle lens, atmospheric turbulence, or a short exposure time, which reduces the number of photons captured • Scattered light distortion in confocal microscopy Deblurring Model A blurred or degraded image can be approximately described by this equation g = Hf + n, where 13-2 g The blurred image H The distortion operator, also called the point spread function (PSF). In the spatial domain, the PSF describes the degree to which an optical system blurs (spreads) a point of light. The PSF is the inverse Fourier transform of the optical transfer function (OTF). In the frequency domain, the OTF describes the response of a linear, position-invariant system to an impulse. The OTF is the Fourier transform of the point spread function (PSF). The distortion operator, when convolved with the image, creates the distortion. Distortion caused by a point spread function is just one type of distortion. f The original true image n Additive noise, introduced during image acquisition, that corrupts the image Understanding Deblurring Note The image f really doesn’t exist. This image represents what you would have if you had perfect image acquisition conditions. Importance of the PSF Based on this model, the fundamental task of deblurring is to deconvolve the blurred image with the PSF that exactly describes the distortion. Deconvolution is the process of reversing the effect of convolution. Note The quality of the deblurred image is mainly determined by knowledge of the PSF. To illustrate, this example takes a clear image and deliberately blurs it by convolving it with a PSF. The example uses the fspecial function to create a PSF that simulates a motion blur, specifying the length of the blur in pixels, (LEN=31), and the angle of the blur in degrees (THETA=11). Once the PSF is created, the example uses the imfilter function to convolve the PSF with the original image, I, to create the blurred image, Blurred. (To see how deblurring is the reverse of this process, using the same images, see “Deblurring with the Wiener Filter” on page 13-6.) I = imread('peppers.png'); I = I(60+[1:256],222+[1:256],:); % crop the image figure; imshow(I); title('Original Image'); 13-3 13 Image Deblurring LEN = 31; THETA = 11; PSF = fspecial('motion',LEN,THETA); % create PSF Blurred = imfilter(I,PSF,'circular','conv'); figure; imshow(Blurred); title('Blurred Image'); Deblurring Functions The toolbox includes four deblurring functions, listed here in order of complexity. All the functions accept a PSF and the blurred image as their primary arguments. 13-4 deconvwnr Implements a least squares solution. You should provide some information about the noise to reduce possible noise amplification during deblurring. See “Deblurring with the Wiener Filter” on page 13-6 for more information. deconvreg Implements a constrained least squares solution, where you can place constraints on the output image (the smoothness requirement is the default). You should provide some information about the noise to reduce possible noise amplification during deblurring. See “Deblurring with a Regularized Filter” on page 13-7 for more information. Understanding Deblurring deconvlucy Implements an accelerated, damped Lucy-Richardson algorithm. This function performs multiple iterations, using optimization techniques and Poisson statistics. You do not need to provide information about the additive noise in the corrupted image. See “Deblurring with the Lucy-Richardson Algorithm” on page 13-10 for more information. deconvblind Implements the blind deconvolution algorithm, which performs deblurring without knowledge of the PSF. You pass as an argument your initial guess at the PSF. The deconvblind function returns a restored PSF in addition to the restored image. The implementation uses the same damping and iterative model as the deconvlucy function. See “Deblurring with the Blind Deconvolution Algorithm” on page 13-16 for more information. When using the deblurring functions, note the following: • Deblurring is an iterative process. You might need to repeat the deblurring process multiple times, varying the parameters you specify to the deblurring functions with each iteration, until you achieve an image that, based on the limits of your information, is the best approximation of the original scene. Along the way, you must make numerous judgments about whether newly uncovered features in the image are features of the original scene or simply artifacts of the deblurring process. • To avoid "ringing" in a deblurred image, you can use the edgetaper function to preprocess your image before passing it to the deblurring functions. See “Avoiding Ringing in Deblurred Images” on page 13-24 for more information. • For information about creating your own deblurring functions, see “Creating Your Own Deblurring Functions” on page 13-23. 13-5 13 Image Deblurring Deblurring with the Wiener Filter Use the deconvwnr function to deblur an image using the Wiener filter. Wiener deconvolution can be used effectively when the frequency characteristics of the image and additive noise are known, to at least some degree. In the absence of noise, the Wiener filter reduces to the ideal inverse filter. See the deconvwnr reference page for an example of deblurring an image with the Wiener filter. Refining the Result You can affect the deconvolution results by providing values for the optional arguments supported by the deconvwnr function. Using these arguments you can specify the noise-to-signal power value and/or provide autocorrelation functions to help refine the result of deblurring. To see the impact of these optional arguments, view the Image Processing Toolbox deblurring examples. 13-6 Deblurring with a Regularized Filter Deblurring with a Regularized Filter Use the deconvreg function to deblur an image using a regularized filter. A regularized filter can be used effectively when limited information is known about the additive noise. To illustrate, this example simulates a blurred image by convolving a Gaussian filter PSF with an image (using imfilter). Additive noise in the image is simulated by adding Gaussian noise of variance V to the blurred image (using imnoise): 1 Read an image into the MATLAB workspace. The example uses cropping to reduce the size of the image to be deblurred. This is not a required step in deblurring operations. I = imread('tissue.png'); I = I(125+[1:256],1:256,:); figure, imshow(I) title('Original Image') Image Courtesy Alan W. Partin 2 Create the PSF. PSF = fspecial('gaussian',11,5); 3 Create a simulated blur in the image and add noise. Blurred = imfilter(I,PSF,'conv'); 13-7 13 Image Deblurring V = .02; BlurredNoisy = imnoise(Blurred,'gaussian',0,V); figure, imshow(BlurredNoisy) title('Blurred and Noisy Image') 4 Use deconvreg to deblur the image, specifying the PSF used to create the blur and the noise power, NP. NP = V*prod(size(I)); [reg1 LAGRA] = deconvreg(BlurredNoisy,PSF,NP); figure,imshow(reg1) title('Restored Image') Refining the Result You can affect the deconvolution results by providing values for the optional arguments supported by the deconvreg function. Using these arguments you can specify the noise power value, the range over which deconvreg should 13-8 Deblurring with a Regularized Filter iterate as it converges on the optimal solution, and the regularization operator to constrain the deconvolution. To see the impact of these optional arguments, view the Image Processing Toolbox deblurring examples. 13-9 13 Image Deblurring Deblurring with the Lucy-Richardson Algorithm In this section... “Overview” on page 13-10 “Reducing the Effect of Noise Amplification” on page 13-10 “Accounting for Nonuniform Image Quality” on page 13-11 “Handling Camera Read-Out Noise” on page 13-11 “Handling Undersampled Images” on page 13-12 “Example: Using the deconvlucy Function to Deblur an Image” on page 13-12 “Refining the Result” on page 13-15 Overview Use the deconvlucy function to deblur an image using the accelerated, damped, Lucy-Richardson algorithm. The algorithm maximizes the likelihood that the resulting image, when convolved with the PSF, is an instance of the blurred image, assuming Poisson noise statistics. This function can be effective when you know the PSF but know little about the additive noise in the image. The deconvlucy function implements several adaptations to the original Lucy-Richardson maximum likelihood algorithm that address complex image restoration tasks. Reducing the Effect of Noise Amplification Noise amplification is a common problem of maximum likelihood methods that attempt to fit data as closely as possible. After many iterations, the restored image can have a speckled appearance, especially for a smooth object observed at low signal-to-noise ratios. These speckles do not represent any real structure in the image, but are artifacts of fitting the noise in the image too closely. To control noise amplification, the deconvlucy function uses a damping parameter, DAMPAR. This parameter specifies the threshold level for the 13-10 Deblurring with the Lucy-Richardson Algorithm deviation of the resulting image from the original image, below which damping occurs. For pixels that deviate in the vicinity of their original values, iterations are suppressed. Damping is also used to reduce ringing, the appearance of high-frequency structures in a restored image. Ringing is not necessarily the result of noise amplification. See “Avoiding Ringing in Deblurred Images” on page 13-24 for more information. Accounting for Nonuniform Image Quality Another complication of real-life image restoration is that the data might include bad pixels, or that the quality of the receiving pixels might vary with time and position. By specifying the WEIGHT array parameter with the deconvlucy function, you can specify that certain pixels in the image be ignored. To ignore a pixel, assign a weight of zero to the element in the WEIGHT array that corresponds to the pixel in the image. The algorithm converges on predicted values for the bad pixels based on the information from neighborhood pixels. The variation in the detector response from pixel to pixel (the so-called flat-field correction) can also be accommodated by the WEIGHT array. Instead of assigning a weight of 1.0 to the good pixels, you can specify fractional values and weight the pixels according to the amount of the flat-field correction. Handling Camera Read-Out Noise Noise in charge coupled device (CCD) detectors has two primary components: • Photon counting noise with a Poisson distribution • Read-out noise with a Gaussian distribution The Lucy-Richardson iterations intrinsically account for the first type of noise. You must account for the second type of noise; otherwise, it can cause pixels with low levels of incident photons to have negative values. The deconvlucy function uses the READOUT input parameter to handle camera read-out noise. The value of this parameter is typically the sum of the read-out noise variance and the background noise (e.g., number of counts 13-11 13 Image Deblurring from the background radiation). The value of the READOUT parameter specifies an offset that ensures that all values are positive. Handling Undersampled Images The restoration of undersampled data can be improved significantly if it is done on a finer grid. The deconvlucy function uses the SUBSMPL parameter to specify the subsampling rate, if the PSF is known to have a higher resolution. If the undersampled data is the result of camera pixel binning during image acquisition, the PSF observed at each pixel rate can serve as a finer grid PSF. Otherwise, the PSF can be obtained via observations taken at subpixel offsets or via optical modeling techniques. This method is especially effective for images of stars (high signal-to-noise ratio), because the stars are effectively forced to be in the center of a pixel. If a star is centered between pixels, it is restored as a combination of the neighboring pixels. A finer grid redirects the consequent spreading of the star flux back to the center of the star’s image. Example: Using the deconvlucy Function to Deblur an Image To illustrate a simple use of deconvlucy, this example simulates a blurred, noisy image by convolving a Gaussian filter PSF with an image (using imfilter) and then adding Gaussian noise of variance V to the blurred image (using imnoise): 1 Read an image into the MATLAB workspace. (The example uses cropping to reduce the size of the image to be deblurred. This is not a required step in deblurring operations.) I = imread('board.tif'); I = I(50+[1:256],2+[1:256],:); figure, imshow(I) title('Original Image') 13-12 Deblurring with the Lucy-Richardson Algorithm 2 Create the PSF. PSF = fspecial('gaussian',5,5); 3 Create a simulated blur in the image and add noise. Blurred = imfilter(I,PSF,'symmetric','conv'); V = .002; BlurredNoisy = imnoise(Blurred,'gaussian',0,V); figure, imshow(BlurredNoisy) title('Blurred and Noisy Image') 13-13 13 Image Deblurring 4 Use deconvlucy to restore the blurred and noisy image, specifying the PSF used to create the blur, and limiting the number of iterations to 5 (the default is 10). Note The deconvlucy function can return values in the output image that are beyond the range of the input image. luc1 = deconvlucy(BlurredNoisy,PSF,5); figure, imshow(luc1) title('Restored Image') 13-14 Deblurring with the Lucy-Richardson Algorithm Refining the Result The deconvlucy function, by default, performs multiple iterations of the deblurring process. You can stop the processing after a certain number of iterations to check the result, and then restart the iterations from the point where processing stopped. To do this, pass in the input image as a cell array, for example, {BlurredNoisy}. The deconvlucy function returns the output image as a cell array that you can then pass as an input argument to deconvlucy to restart the deconvolution. The output cell array contains these four elements: Element Description output{1} Original input image output{2} Image produced by the last iteration output{3} Image produced by the next to last iteration output{4} Internal information used by deconvlucy to know where to restart the process The deconvlucy function supports several other optional arguments you can use to achieve the best possible result, such as specifying a damping parameter to handle additive noise in the blurred image. To see the impact of these optional arguments, view the Image Processing Toolbox deblurring examples. 13-15 13 Image Deblurring Deblurring with the Blind Deconvolution Algorithm Use the deconvblind function to deblur an image using the blind deconvolution algorithm. The algorithm maximizes the likelihood that the resulting image, when convolved with the resulting PSF, is an instance of the blurred image, assuming Poisson noise statistics. The blind deconvolution algorithm can be used effectively when no information about the distortion (blurring and noise) is known. The deconvblind function restores the image and the PSF simultaneously, using an iterative process similar to the accelerated, damped Lucy-Richardson algorithm. The deconvblind function, just like the deconvlucy function, implements several adaptations to the original Lucy-Richardson maximum likelihood algorithm that address complex image restoration tasks. Using these adaptations, you can • Reduce the effect of noise on the restoration • Account for nonuniform image quality (e.g., bad pixels) • Handle camera read-out noise For more information about these adaptations, see “Deblurring with the Lucy-Richardson Algorithm” on page 13-10. In addition, the deconvblind function supports PSF constraints that can be passed in through a user-specified function. Example: Using the deconvblind Function to Deblur an Image To illustrate blind deconvolution, this example creates a simulated blurred image and then uses deconvblind to deblur it. The example makes two passes at deblurring the image to show the effect of certain optional parameters on the deblurring operation: 13-16 Deblurring with the Blind Deconvolution Algorithm 1 Read an image into the MATLAB workspace. I = imread('cameraman.tif'); figure, imshow(I) title('Original Image') 2 Create the PSF. PSF = fspecial('motion',13,45); figure, imshow(PSF,[],'InitialMagnification','fit') title('Original PSF') 3 Create a simulated blur in the image. Blurred = imfilter(I,PSF,'circ','conv'); figure, imshow(Blurred) 13-17 13 Image Deblurring title('Blurred Image') 4 Deblur the image, making an initial guess at the size of the PSF. To determine the size of the PSF, examine the blurred image and measure the width of a blur (in pixels) around an obviously sharp object. In the sample blurred image, you can measure the blur near the contour of the man’s sleeve. Because the size of the PSF is more important than the values it contains, you can typically specify an array of 1’s as the initial PSF. The following figure shows a restoration where the initial guess at the PSF is the same size as the PSF that caused the blur. In a real application, you might need to rerun deconvblind, experimenting with PSFs of different sizes, until you achieve a satisfactory result. The restored PSF returned by each deconvolution can also provide valuable hints at the optimal PSF size. See the Image Processing Toolbox deblurring example. INITPSF = ones(size(PSF)); [J P]= deconvblind(Blurred,INITPSF,30); figure, imshow(J) title('Restored Image') figure, imshow(P,[],'InitialMagnification','fit') title('Restored PSF') 13-18 Deblurring with the Blind Deconvolution Algorithm Although deconvblind was able to deblur the image to a great extent, the ringing around the sharp intensity contrast areas in the restored image is unsatisfactory. (The example eliminated edge-related ringing by using the 'circular' option with imfilter when creating the simulated blurred image in step 3.) The next steps in the example repeat the deblurring process, attempting to achieve a better result by • Eliminating high-contrast areas from the processing • Specifying a better PSF 5 Create a WEIGHT array to exclude areas of high contrast from the deblurring operation. This can reduce contrast-related ringing in the result. To exclude a pixel from processing, you create an array of the same size as the original image, and assign the value 0 to the pixels in the array that correspond to pixels in the original image that you want to exclude from processing. (See “Accounting for Nonuniform Image Quality” on page 13-11 for information about WEIGHT arrays.) To create a WEIGHT array, the example uses a combination of edge detection and morphological processing to detect high-contrast areas in the image. Because the blur in the image is linear, the example dilates the image twice. (For more information about using these functions, see“Morphological Filtering” .) To exclude the image boundary pixels (a high-contrast area) 13-19 13 Image Deblurring from processing, the example uses padarray to assign the value 0 to all border pixels. WEIGHT = edge(I,'sobel',.28); se1 = strel('disk',1); se2 = strel('line',13,45); WEIGHT = ~imdilate(WEIGHT,[se1 se2]); WEIGHT = padarray(WEIGHT(2:end-1,2:end-1),[2 2]); figure, imshow(WEIGHT) title('Weight Array') 6 Refine the guess at the PSF. The reconstructed PSF P returned by the first pass at deconvolution shows a clear linearity, as shown in the figure in step 4. For the second pass, the example uses a new PSF, P1, which is the same as the restored PSF but with the small amplitude pixels set to 0. P1 = P; P1(find(P1 < 0.01))=0; 7 Rerun the deconvolution, specifying the WEIGHT array and the modified PSF. Note how the restored image has much less ringing around the sharp intensity contrast areas than the result of the first pass (step 4). [J2 P2] = deconvblind(Blurred,P1,50,[],WEIGHT); figure, imshow(J2) title('Newly Deblurred Image'); figure, imshow(P2,[],'InitialMagnification','fit') title('Newly Reconstructed PSF') 13-20 Deblurring with the Blind Deconvolution Algorithm Refining the Result The deconvblind function, by default, performs multiple iterations of the deblurring process. You can stop the processing after a certain number of iterations to check the result, and then restart the iterations from the point where processing stopped. To use this feature, you must pass in both the blurred image and the PSF as cell arrays, for example, {Blurred} and {INITPSF}. The deconvblind function returns the output image and the restored PSF as cell arrays. The output image cell array contains these four elements: Element Description output{1} Original input image output{2} Image produced by the last iteration output{3} Image produced by the next to last iteration output{4} Internal information used by deconvlucy to know where to restart the process 13-21 13 Image Deblurring The PSF output cell array contains similar elements. The deconvblind function supports several other optional arguments you can use to achieve the best possible result, such as specifying a damping parameter to handle additive noise in the blurred image. To see the impact of these optional arguments, as well as the functional option that allows you to place additional constraints on the PSF reconstruction, see the Image Processing Toolbox deblurring examples. 13-22 Creating Your Own Deblurring Functions Creating Your Own Deblurring Functions All the toolbox deblurring functions perform deconvolution in the frequency domain, where the process becomes a simple matrix multiplication. To work in the frequency domain, the deblurring functions must convert the PSF you provide into an optical transfer function (OTF), using the psf2otf function. The toolbox also provides a function to convert an OTF into a PSF, otf2psf. The toolbox makes these functions available in case you want to create your own deblurring functions. (In addition, to aid this conversion between PSFs and OTFs, the toolbox also makes the padding function padarray available.) 13-23 13 Image Deblurring Avoiding Ringing in Deblurred Images The discrete Fourier transform (DFT), used by the deblurring functions, assumes that the frequency pattern of an image is periodic. This assumption creates a high-frequency drop-off at the edges of images. In the figure, the shaded area represents the actual extent of the image; the unshaded area represents the assumed periodicity. This high-frequency drop-off can create an effect called boundary related ringing in deblurred images. In this figure, note the horizontal and vertical patterns in the image. To avoid ringing, use the edgetaper function to preprocess your images before passing them to the deblurring functions. The edgetaper function removes the high-frequency drop-off at the edge of an image by blurring the entire image and then replacing the center pixels of the blurred image with the original image. In this way, the edges of the image taper off to a lower frequency. 13-24 14 Color This chapter describes the toolbox functions that help you work with color image data. Note that “color“ includes shades of gray; therefore much of the discussion in this chapter applies to grayscale images as well as color images. • “Displaying Colors” on page 14-2 • “Reducing the Number of Colors in an Image” on page 14-4 • “Converting Color Data Between Color Spaces” on page 14-13 14 Color Displaying Colors The number of bits per screen pixel determines the display’s screen bit depth. The screen bit depth determines the screen color resolution, which is how many distinct colors the display can produce. Most computer displays use 8, 16, or 24 bits per screen pixel. Depending on your system, you might be able to choose the screen bit depth you want to use. In general, 24-bit display mode produces the best results. If you need to use a lower screen bit depth, 16-bit is generally preferable to 8-bit. However, keep in mind that a 16-bit display has certain limitations, such as • An image might have finer gradations of color than a 16-bit display can represent. If a color is unavailable, MATLAB uses the closest approximation. • There are only 32 shades of gray available. If you are working primarily with grayscale images, you might get better display results using 8-bit display mode, which provides up to 256 shades of gray. To determine the bit depth of your system’s screen, enter this command at the MATLAB prompt. get(0,'ScreenDepth') ans = 32 14-2 Displaying Colors The integer MATLAB returns represents the number of bits per screen pixel: Value Screen Bit Depth 8 8-bit displays support 256 colors. An 8-bit display can produce any of the colors available on a 24-bit display, but only 256 distinct colors can appear at one time. (There are 256 shades of gray available, but if all 256 shades of gray are used, they take up all the available color slots.) 16 16-bit displays usually use 5 bits for each color component, resulting in 32 (i.e., 25) levels each of red, green, and blue. This supports 32,768 (i.e., 215) distinct colors (of which 32 are shades of gray). Some systems use the extra bit to increase the number of levels of green that can be displayed. In this case, the number of different colors supported by a 16-bit display is actually 64,536 (i.e. 216). 24 24-bit displays use 8 bits for each of the three color components, resulting in 256 (i.e., 28) levels each of red, green, and blue. This supports 16,777,216 (i.e., 224) different colors. (Of these colors, 256 are shades of gray. Shades of gray occur where R=G=B.) The 16 million possible colors supported by 24-bit display can render a lifelike image. 32 32-bit displays use 24 bits to store color information and use the remaining 8 bits to store transparency data (alpha channel). For information about how MATLAB supports the alpha channel, see the section “Mapping Data to Transparency — Alpha Data” in the MATLAB 3-D Visualization documentation. Regardless of the number of colors your system can display, MATLAB can store and process images with very high bit depths: 224 colors for uint8 RGB images, 248 colors for uint16 RGB images, and 2159 for double RGB images. These images are displayed best on systems with 24-bit color, but usually look fine on 16-bit systems as well. (For additional information about how MATLAB handles color, see the graphics documentation.) For information about reducing the number of colors used by an image, see “Reducing the Number of Colors in an Image” on page 14-4. 14-3 14 Color Reducing the Number of Colors in an Image In this section... “Reducing Colors Using Color Approximation” on page 14-4 “Reducing Colors Using imapprox” on page 14-10 “Dithering” on page 14-11 Reducing Colors Using Color Approximation On systems with 24-bit color displays, truecolor images can display up to 16,777,216 (i.e., 224) colors. On systems with lower screen bit depths, truecolor images are still displayed reasonably well, because MATLAB automatically uses color approximation and dithering if needed. Color approximation is the process by which the software chooses replacement colors in the event that direct matches cannot be found. Indexed images, however, might cause problems if they have a large number of colors. In general, you should limit indexed images to 256 colors for the following reasons: • On systems with 8-bit display, indexed images with more than 256 colors will need to be dithered or mapped and, therefore, might not display well. • On some platforms, colormaps cannot exceed 256 entries. • If an indexed image has more than 256 colors, MATLAB cannot store the image data in a uint8 array, but generally uses an array of class double instead, making the storage size of the image much larger (each pixel uses 64 bits). • Most image file formats limit indexed images to 256 colors. If you write an indexed image with more than 256 colors (using imwrite) to a format that does not support more than 256 colors, you will receive an error. To reduce the number of colors in an image, use the rgb2ind function. This function converts a truecolor image to an indexed image, reducing the number of colors in the process. rgb2ind provides the following methods for approximating the colors in the original image: 14-4 Reducing the Number of Colors in an Image • Quantization (described in “Quantization” on page 14-5) - Uniform quantization Minimum variance quantization • Colormap mapping (described in “Colormap Mapping” on page 14-9) The quality of the resulting image depends on the approximation method you use, the range of colors in the input image, and whether or not you use dithering. Note that different methods work better for different images. See “Dithering” on page 14-11 for a description of dithering and how to enable or disable it. Quantization Reducing the number of colors in an image involves quantization. The function rgb2ind uses quantization as part of its color reduction algorithm. rgb2ind supports two quantization methods: uniform quantization and minimum variance quantization. An important term in discussions of image quantization is RGB color cube, which is used frequently throughout this section. The RGB color cube is a three-dimensional array of all of the colors that are defined for a particular data type. Since RGB images in MATLAB can be of type uint8, uint16, or double, three possible color cube definitions exist. For example, if an RGB image is of class uint8, 256 values are defined for each color plane (red, blue, and green), and, in total, there will be 224 (or 16,777,216) colors defined by the color cube. This color cube is the same for all uint8 RGB images, regardless of which colors they actually use. The uint8, uint16, and double color cubes all have the same range of colors. In other words, the brightest red in a uint8 RGB image appears the same as the brightest red in a double RGB image. The difference is that the double RGB color cube has many more shades of red (and many more shades of all colors). The following figure shows an RGB color cube for a uint8 image. 14-5 14 Color RGB Color Cube for uint8 Images Quantization involves dividing the RGB color cube into a number of smaller boxes, and then mapping all colors that fall within each box to the color value at the center of that box. Uniform quantization and minimum variance quantization differ in the approach used to divide up the RGB color cube. With uniform quantization, the color cube is cut up into equal-sized boxes (smaller cubes). With minimum variance quantization, the color cube is cut up into boxes (not necessarily cubes) of different sizes; the sizes of the boxes depend on how the colors are distributed in the image. Uniform Quantization. To perform uniform quantization, call rgb2ind and specify a tolerance. The tolerance determines the size of the cube-shaped boxes into which the RGB color cube is divided. The allowable range for a tolerance setting is [0,1]. For example, if you specify a tolerance of 0.1, the edges of the boxes are one-tenth the length of the RGB color cube and the maximum total number of boxes is n = (floor(1/tol)+1)^3 The commands below perform uniform quantization with a tolerance of 0.1. RGB = imread('peppers.png'); [x,map] = rgb2ind(RGB, 0.1); 14-6 Reducing the Number of Colors in an Image The following figure illustrates uniform quantization of a uint8 image. For clarity, the figure shows a two-dimensional slice (or color plane) from the color cube where red=0 and green and blue range from 0 to 255. The actual pixel values are denoted by the centers of the x’s. Uniform Quantization on a Slice of the RGB Color Cube After the color cube has been divided, all empty boxes are thrown out. Therefore, only one of the boxes is used to produce a color for the colormap. As shown earlier, the maximum length of a colormap created by uniform quantization can be predicted, but the colormap can be smaller than the prediction because rgb2ind removes any colors that do not appear in the input image. Minimum Variance Quantization. To perform minimum variance quantization, call rgb2ind and specify the maximum number of colors in the output image’s colormap. The number you specify determines the number of boxes into which the RGB color cube is divided. These commands use minimum variance quantization to create an indexed image with 185 colors. RGB = imread('peppers.png'); [X,map] = rgb2ind(RGB,185); 14-7 14 Color Minimum variance quantization works by associating pixels into groups based on the variance between their pixel values. For example, a set of blue pixels might be grouped together because they have a small variance from the center pixel of the group. In minimum variance quantization, the boxes that divide the color cube vary in size, and do not necessarily fill the color cube. If some areas of the color cube do not have pixels, there are no boxes in these areas. While you set the number of boxes, n, to be used by rgb2ind, the placement is determined by the algorithm as it analyzes the color data in your image. Once the image is divided into n optimally located boxes, the pixels within each box are mapped to the pixel value at the center of the box, as in uniform quantization. The resulting colormap usually has the number of entries you specify. This is because the color cube is divided so that each region contains at least one color that appears in the input image. If the input image uses fewer colors than the number you specify, the output colormap will have fewer than n colors, and the output image will contain all of the colors of the input image. The following figure shows the same two-dimensional slice of the color cube as shown in the preceding figure (demonstrating uniform quantization). Eleven boxes have been created using minimum variance quantization. 14-8 Reducing the Number of Colors in an Image Minimum Variance Quantization on a Slice of the RGB Color Cube For a given number of colors, minimum variance quantization produces better results than uniform quantization, because it takes into account the actual data. Minimum variance quantization allocates more of the colormap entries to colors that appear frequently in the input image. It allocates fewer entries to colors that appear infrequently. As a result, the accuracy of the colors is higher than with uniform quantization. For example, if the input image has many shades of green and few shades of red, there will be more greens than reds in the output colormap. Note that the computation for minimum variance quantization takes longer than that for uniform quantization. Colormap Mapping If you specify an actual colormap to use, rgb2ind uses colormap mapping (instead of quantization) to find the colors in the specified colormap that best match the colors in the RGB image. This method is useful if you need to create images that use a fixed colormap. For example, if you want to display multiple indexed images on an 8-bit display, you can avoid color problems by mapping them all to the same colormap. Colormap mapping produces a good approximation if the specified colormap has similar colors to those in the RGB image. If the colormap does not have similar colors to those in the RGB image, this method produces poor results. 14-9 14 Color This example illustrates mapping two images to the same colormap. The colormap used for the two images is created on the fly using the MATLAB function colorcube, which creates an RGB colormap containing the number of colors that you specify. (colorcube always creates the same colormap for a given number of colors.) Because the colormap includes colors all throughout the RGB color cube, the output images can reasonably approximate the input images. RGB1 RGB2 X1 = X2 = = imread('autumn.tif'); = imread('peppers.png'); rgb2ind(RGB1,colorcube(128)); rgb2ind(RGB2,colorcube(128)); Note The function subimage is also helpful for displaying multiple indexed images. For more information, see “Displaying Multiple Images in the Same Figure” on page 4-8 or the reference page for subimage. Reducing Colors Using imapprox Use imapprox when you need to reduce the number of colors in an indexed image. imapprox is based on rgb2ind and uses the same approximation methods. Essentially, imapprox first calls ind2rgb to convert the image to RGB format, and then calls rgb2ind to return a new indexed image with fewer colors. For example, these commands create a version of the trees image with 64 colors, rather than the original 128. load trees [Y,newmap] = imapprox(X,map,64); imshow(Y, newmap); The quality of the resulting image depends on the approximation method you use, the range of colors in the input image, and whether or not you use dithering. Note that different methods work better for different images. See “Dithering” on page 14-11 for a description of dithering and how to enable or disable it. 14-10 Reducing the Number of Colors in an Image Dithering When you use rgb2ind or imapprox to reduce the number of colors in an image, the resulting image might look inferior to the original, because some of the colors are lost. rgb2ind and imapprox both perform dithering to increase the apparent number of colors in the output image. Dithering changes the colors of pixels in a neighborhood so that the average color in each neighborhood approximates the original RGB color. For an example of how dithering works, consider an image that contains a number of dark orange pixels for which there is no exact match in the colormap. To create the appearance of this shade of orange, dithering selects a combination of colors from the colormap, that, taken together as a six-pixel group, approximate the desired shade of orange. From a distance, the pixels appear to be the correct shade, but if you look up close at the image, you can see a blend of other shades. To illustrate dithering, the following example loads a 24-bit truecolor image, and then uses rgb2ind to create an indexed image with just eight colors. The first example does not use dithering, the second does use dithering. 1 Read image and display it. rgb=imread('onion.png'); imshow(rgb); 2 Create an indexed image with eight colors and without dithering. [X_no_dither,map]= rgb2ind(rgb,8,'nodither'); figure, imshow(X_no_dither,map); 14-11 14 Color 3 Create an indexed image using eight colors with dithering. Notice that the dithered image has a larger number of apparent colors but is somewhat fuzzy-looking. The image produced without dithering has fewer apparent colors, but an improved spatial resolution when compared to the dithered image. One risk in doing color reduction without dithering is that the new image can contain false contours. [X_dither,map]=rgb2ind(rgb,8,'dither'); figure, imshow(X_dither,map); 14-12 Converting Color Data Between Color Spaces Converting Color Data Between Color Spaces In this section... “Understanding Color Spaces and Color Space Conversion” on page 14-13 “Converting Between Device-Independent Color Spaces” on page 14-13 “Performing Profile-Based Color Space Conversions” on page 14-17 “Converting Between Device-Dependent Color Spaces” on page 14-21 Understanding Color Spaces and Color Space Conversion The Image Processing Toolbox software represents colors as RGB values, either directly (in an RGB image) or indirectly (in an indexed image, where the colormap is stored in RGB format). However, there are other models besides RGB for representing colors numerically. The various models are referred to as color spaces because most of them can be mapped into a 2-D, 3-D, or 4-D coordinate system; thus, a color specification is made up of coordinates in a 2-D, 3-D, or 4-D space. The various color spaces exist because they present color information in ways that make certain calculations more convenient or because they provide a way to identify colors that is more intuitive. For example, the RGB color space defines a color as the percentages of red, green, and blue hues mixed together. Other color models describe colors by their hue (green), saturation (dark green), and luminance, or intensity. The toolbox supports these color spaces by providing a means for converting color data from one color space to another through a mathematical transformation. Converting Between Device-Independent Color Spaces The standard terms used to describe colors, such as hue, brightness, and intensity, are subjective and make comparisons difficult. 14-13 14 Color In 1931, the International Commission on Illumination, known by the acronym CIE, for Commission Internationale de l’Éclairage, studied human color perception and developed a standard, called the CIE XYZ. This standard defined a three-dimensional space where three values, called tristimulus values, define a color. This standard is still widely used today. In the decades since that initial specification, the CIE has developed several additional color space specifications that attempt to provide alternative color representations that are better suited to some purposes than XYZ. For example, in 1976, in an effort to get a perceptually uniform color space that could be correlated with the visual appearance of colors, the CIE created the L*a*b* color space. The toolbox supports conversions between members of the CIE family of device-independent color spaces. In addition, the toolbox also supports conversions between these CIE color spaces and the sRGB color space. This color space was defined by an industry group to describe the characteristics of a typical PC monitor. This section • Lists the supported device-independent color spaces • Provides an example of how to perform a conversion • Provides guidelines about data type support of the various conversions Supported Conversions This table lists all the device-independent color spaces that the toolbox supports. 14-14 Color Space Description Supported Conversions XYZ The original, 1931 CIE color space specification. xyY, uvl, u′v′L, and L*a*b* xyY CIE specification that provides normalized chromaticity values. The capital Y value represents luminance and is the same as in XYZ. XYZ Converting Color Data Between Color Spaces Color Space Description Supported Conversions uvL CIE specification that attempts to make the chromaticity plane more visually uniform. L is luminance and is the same as Y in XYZ. XYZ u′v′L CIE specification in which u and v are rescaled to improve uniformity. XYZ L*a*b* CIE specification that attempts to make the luminance scale more perceptually uniform. L* is a nonlinear scaling of L, normalized to a reference white point. XYZ L*ch CIE specification where c is chroma and h is hue. These values are a polar coordinate conversion of a* and b* in L*a*b*. L*a*b* sRGB Standard adopted by major manufacturers that characterizes the average PC monitor. XYZ and L*a*b* Example: Performing a Color Space Conversion To illustrate a conversion between two device-independent color spaces, this example reads an RGB color image into the MATLAB workspace and converts the color data to the XYZ color space: 1 Import color space data. This example reads an RGB color image into the MATLAB workspace. I_rgb = imread('peppers.png'); 2 Create a color transformation structure. A color transformation structure defines the conversion between two color spaces. You use the makecform function to create the structure, specifying a transformation type string as an argument. This example creates a color transformation structure that defines a conversion from RGB color data to XYZ color data. C = makecform('srgb2xyz'); 14-15 14 Color 3 Perform the conversion. You use the applycform function to perform the conversion, specifying as arguments the color data you want to convert and the color transformation structure that defines the conversion. The applycform function returns the converted data. I_xyz = applycform(I_rgb,C); View a list of the workspace variables for the original and converted images. whos Name C I_rgb I_xyz Size 1x1 384x512x3 384x512x3 Bytes 7744 589824 1179648 Class Attributes struct uint8 uint16 Color Space Data Encodings When you convert between two device-independent color spaces, the data type used to encode the color data can sometimes change, depending on what encodings the color spaces support. In the preceding example, the original image is uint8 data. The XYZ conversion is uint16 data. The XYZ color space does not define a uint8 encoding. The following table lists the data types that can be used to represent values in all the device-independent color spaces. Color Space Encodings XYZ uint16 or double xyY double uvL double u'v'L double L*a*b* uint8, uint16, or double L*ch double sRGB double As the table indicates, certain color spaces have data type limitations. For example, the XYZ color space does not define a uint8 encoding. If you convert 14-16 Converting Color Data Between Color Spaces 8-bit CIE LAB data into the XYZ color space, the data is returned in uint16 format. If you want the returned XYZ data to be in the same format as the input LAB data, you can use one of the following toolbox color space format conversion functions. • lab2double • lab2uint8 • lab2uint16 • xyz2double • xyz2uint16 Performing Profile-Based Color Space Conversions The Image Processing Toolbox software can perform color space conversions based on device profiles. This section includes the following topics: • “Understanding Device Profiles” on page 14-17 • “Reading ICC Profiles” on page 14-18 • “Writing Profile Information to a File” on page 14-18 • “Example: Performing a Profile-Based Conversion” on page 14-19 • “Specifying the Rendering Intent” on page 14-21 Understanding Device Profiles If two colors have the same CIE colorimetry, they will match if viewed under the same conditions. However, because color images are typically produced for a wide variety of viewing environments, it is necessary to go beyond simple application of the CIE system. For this reason, the International Color Consortium (ICC) has defined a Color Management System (CMS) that provides a means for communicating color information among input, output, and display devices. The CMS uses device profiles that contain color information specific to a particular device. Vendors that support CMS provide profiles that characterize the color reproduction of their devices, and methods, called Color Management Modules (CMM), that interpret the contents of each profile and perform the necessary image processing. 14-17 14 Color Device profiles contain the information that color management systems need to translate color data between devices. Any conversion between color spaces is a mathematical transformation from some domain space to a range space. With profile-based conversions, the domain space is often called the source space and the range space is called the destination space. In the ICC color management model, profiles are used to represent the source and destination spaces. For more information about color management systems, go to the International Color Consortium Web site, www.color.org. Reading ICC Profiles To read an ICC profile into the MATLAB workspace, use the iccread function. In this example, the function reads in the profile for the color space that describes color monitors. P = iccread('sRGB.icm'); You can use the iccfind function to find ICC color profiles on your system, or to find a particular ICC color profile whose description contains a certain text string. To get the name of the directory that is the default system repository for ICC profiles, use iccroot. iccread returns the contents of the profile in the structure P. All profiles contain a header, a tag table, and a series of tagged elements. The header contains general information about the profile, such as the device class, the device color space, and the file size. The tagged elements, or tags, are the data constructs that contain the information used by the CMM. For more information about the contents of this structure, see the iccread function reference page. Using iccread, you can read both Version 2 (ICC.1:2001-04) or Version 4 (ICC.1:2001-12) ICC profile formats. For detailed information about these specifications and their differences, visit the ICC web site, www.color.org. Writing Profile Information to a File To export ICC profile information from the MATLAB workspace to a file, use the iccwrite function. This example reads a profile into the MATLAB workspace and then writes the profile information out to a new file. 14-18 Converting Color Data Between Color Spaces P = iccread('sRGB.icm'); P_new = iccwrite(P,'my_profile.icm'); iccwrite returns the profile it writes to the file in P_new because it can be different than the input profile P. For example, iccwrite updates the Filename field in P to match the name of the file specified as the second argument. iccwrite checks the validity of the input profile structure. If any required fields are missing, iccwrite returns an error message. For more information about the writing ICC profile data to a file, see the iccwrite function reference page. To determine if a structure is a valid ICC profile, use the isicc function. Using iccwrite, you can export profile information in both Version 2 (ICC.1:2001-04) or Version 4 (ICC.1:2001-12) ICC profile formats. The value of the Version field in the file profile header determines the format version. For detailed information about these specifications and their differences, visit the ICC web site, www.color.org. Example: Performing a Profile-Based Conversion To illustrate a profile-based color space conversion, this section presents an example that converts color data from the RGB space of a monitor to the CMYK space of a printer. This conversion requires two profiles: a monitor profile and a printer profile. The source color space in this example is monitor RGB and the destination color space is printer CMYK: 1 Import RGB color space data. This example imports an RGB color image into the MATLAB workspace. I_rgb = imread('peppers.png'); 2 Read ICC profiles. Read the source and destination profiles into the MATLAB workspace. This example uses the sRGB profile as the source profile. The sRGB profile is an industry-standard color space that describes a color monitor. inprof = iccread('sRGB.icm'); 14-19 14 Color For the destination profile, the example uses a profile that describes a particular color printer. The printer vendor supplies this profile. (The following profile and several other useful profiles can be obtained as downloads from www.adobe.com.) outprof = iccread('USSheetfedCoated.icc'); 3 Create a color transformation structure. You must create a color transformation structure to define the conversion between the color spaces in the profiles. You use the makecform function to create the structure, specifying a transformation type string as an argument. Note The color space conversion might involve an intermediate conversion into a device-independent color space, called the Profile Connection Space (PCS), but this is transparent to the user. This example creates a color transformation structure that defines a conversion from RGB color data to CMYK color data. C = makecform('icc',inprof,outprof); 4 Perform the conversion. You use the applycform function to perform the conversion, specifying as arguments the color data you want to convert and the color transformation structure that defines the conversion. The function returns the converted data. I_cmyk = applycform(I_rgb,C); 5 Write the converted data to a file. To export the CMYK data, use the imwrite function, specifying the format as TIFF. If the format is TIFF and the data is an m-by-n-by-4 array, imwrite writes CMYK data to the file. imwrite(I_cmyk,'pep_cmyk.tif','tif') To verify that the CMYK data was written to the file, use imfinfo to get information about the file and look at the PhotometricInterpretation field. info = imfinfo('pep_cmyk.tif'); info.PhotometricInterpretation ans = 14-20 Converting Color Data Between Color Spaces 'CMYK' Specifying the Rendering Intent For most devices, the range of reproducible colors is much smaller than the range of colors represented by the PCS. It is for this reason that four rendering intents (or gamut mapping techniques) are defined in the profile format. Each one has distinct aesthetic and color-accuracy tradeoffs. When you create a profile-based color transformation structure, you can specify the rendering intent for the source as well as the destination profiles. For more information, see the makecform reference information. Converting Between Device-Dependent Color Spaces The toolbox includes functions that you can use to convert RGB data to several common device-dependent color spaces, and vice versa: • YIQ • YCbCr • Hue, saturation, value (HSV) YIQ Color Space The National Television Systems Committee (NTSC) defines a color space known as YIQ. This color space is used in televisions in the United States. One of the main advantages of this format is that grayscale information is separated from color data, so the same signal can be used for both color and black and white sets. In the NTSC color space, image data consists of three components: luminance (Y), hue (I), and saturation (Q). The first component, luminance, represents grayscale information, while the last two components make up chrominance (color information). The function rgb2ntsc converts colormaps or RGB images to the NTSC color space. ntsc2rgb performs the reverse operation. For example, these commands convert an RGB image to NTSC format. 14-21 14 Color RGB = imread('peppers.png'); YIQ = rgb2ntsc(RGB); Because luminance is one of the components of the NTSC format, the RGB to NTSC conversion is also useful for isolating the gray level information in an image. In fact, the toolbox functions rgb2gray and ind2gray use the rgb2ntsc function to extract the grayscale information from a color image. For example, these commands are equivalent to calling rgb2gray. YIQ = rgb2ntsc(RGB); I = YIQ(:,:,1); Note In the YIQ color space, I is one of the two color components, not the grayscale component. YCbCr Color Space The YCbCr color space is widely used for digital video. In this format, luminance information is stored as a single component (Y), and chrominance information is stored as two color-difference components (Cb and Cr). Cb represents the difference between the blue component and a reference value. Cr represents the difference between the red component and a reference value. (YUV, another color space widely used for digital video, is very similar to YCbCr but not identical.) YCbCr data can be double precision, but the color space is particularly well suited to uint8 data. For uint8 images, the data range for Y is [16, 235], and the range for Cb and Cr is [16, 240]. YCbCr leaves room at the top and bottom of the full uint8 range so that additional (nonimage) information can be included in a video stream. The function rgb2ycbcr converts colormaps or RGB images to the YCbCr color space. ycbcr2rgb performs the reverse operation. For example, these commands convert an RGB image to YCbCr format. RGB = imread('peppers.png'); YCBCR = rgb2ycbcr(RGB); 14-22 Converting Color Data Between Color Spaces HSV Color Space The HSV color space (Hue, Saturation, Value) is often used by people who are selecting colors (e.g., of paints or inks) from a color wheel or palette, because it corresponds better to how people experience color than the RGB color space does. The functions rgb2hsv and hsv2rgb convert images between the RGB and HSV color spaces. Note MATLAB and the Image Processing Toolbox software do not support the HSI color space (Hue, Saturation, Intensity). However, if you want to work with color data in terms of hue, saturation, and intensity, the HSV color space is very similar. Another option is to use the LCH color space (Luminosity, Chroma, and Hue), which is a polar transformation of the CIE L*a*b* color space — see “Converting Between Device-Independent Color Spaces” on page 14-13. As hue varies from 0 to 1.0, the corresponding colors vary from red through yellow, green, cyan, blue, magenta, and back to red, so that there are actually red values both at 0 and 1.0. As saturation varies from 0 to 1.0, the corresponding colors (hues) vary from unsaturated (shades of gray) to fully saturated (no white component). As value, or brightness, varies from 0 to 1.0, the corresponding colors become increasingly brighter. The following figure illustrates the HSV color space. 14-23 14 Color Illustration of the HSV Color Space The rgb2hsv function converts colormaps or RGB images to the HSV color space. hsv2rgb performs the reverse operation. These commands convert an RGB image to the HSV color space. RGB = imread('peppers.png'); HSV = rgb2hsv(RGB); For closer inspection of the HSV color space, the next block of code displays the separate color planes (hue, saturation, and value) of an HSV image. RGB=reshape(ones(64,1)*reshape(jet(64),1,192),[64,64,3]); HSV=rgb2hsv(RGB); H=HSV(:,:,1); S=HSV(:,:,2); V=HSV(:,:,3); subplot(2,2,1), imshow(H) subplot(2,2,2), imshow(S) subplot(2,2,3), imshow(V) subplot(2,2,4), imshow(RGB) 14-24 Converting Color Data Between Color Spaces The Separated Color Planes of an HSV Image As the hue plane image in the preceding figure illustrates, hue values make a linear transition from high to low. If you compare the hue plane image against the original image, you can see that shades of deep blue have the highest values, and shades of deep red have the lowest values. (As stated previously, there are values of red on both ends of the hue scale. To avoid confusion, the sample image uses only the red values from the beginning of the hue range.) Saturation can be thought of as the purity of a color. As the saturation plane image shows, the colors with the highest saturation have the highest values and are represented as white. In the center of the saturation image, notice the various shades of gray. These correspond to a mixture of colors; the cyans, greens, and yellow shades are mixtures of true colors. Value is roughly equivalent to brightness, and you will notice that the brightest areas of the value plane correspond to the brightest colors in the original image. 14-25 14 14-26 Color 15 Neighborhood and Block Operations This chapter discusses these generic block processing functions. Topics covered include • “Neighborhood or Block Processing: An Overview” on page 15-2 • “Performing Sliding Neighborhood Operations” on page 15-3 • “Performing Distinct Block Operations” on page 15-8 • “Using Columnwise Processing to Speed Up Sliding Neighborhood or Distinct Block Operations” on page 15-26 15 Neighborhood and Block Operations Neighborhood or Block Processing: An Overview Certain image processing operations involve processing an image in sections, called blocks or neighborhoods, rather than processing the entire image at once. Several functions in the toolbox, such as linear filtering and morphological functions, use this approach. The toolbox includes several functions that you can use to implement image processing algorithms as a block or neighborhood operation. These functions break the input image into blocks or neighborhoods, call the specified function to process each block or neighborhood, and then reassemble the results into an output image. The following table summarizes these functions. 15-2 Function Description nlfilter Implements sliding neighborhood operations that you can use to process an input image in a pixelwise fashion. For each pixel in the input image, the function performs the operation you specify on a block of neighboring pixels to determine the value of the corresponding pixel in the output image. For more information, see “Performing Sliding Neighborhood Operations” on page 15-3 blockproc Implements distinct block operations that you can use to process an input image a block at a time. The function divides the image into rectangular blocks, and performs the operation you specify on each individual block to determine the values of the pixels in the corresponding block of the output image. For more information, see “Performing Distinct Block Operations” on page 15-8 colfilt Implements columnwise processing operations which provide a way of speeding up neighborhood or block operations by rearranging blocks into matrix columns. For more information, see “Using Columnwise Processing to Speed Up Sliding Neighborhood or Distinct Block Operations” on page 15-26. Performing Sliding Neighborhood Operations Performing Sliding Neighborhood Operations In this section... “Understanding Sliding Neighborhood Processing” on page 15-3 “Implementing Linear and Nonlinear Filtering as Sliding Neighborhood Operations” on page 15-5 Understanding Sliding Neighborhood Processing A sliding neighborhood operation is an operation that is performed a pixel at a time, with the value of any given pixel in the output image being determined by the application of an algorithm to the values of the corresponding input pixel’s neighborhood. A pixel’s neighborhood is some set of pixels, defined by their locations relative to that pixel, which is called the center pixel. The neighborhood is a rectangular block, and as you move from one element to the next in an image matrix, the neighborhood block slides in the same direction. (To operate on an image a block at a time, rather than a pixel at a time, use the distinct block processing function. See “Performing Distinct Block Operations” on page 15-8 for more information.) The following figure shows the neighborhood blocks for some of the elements in a 6-by-5 matrix with 2-by-3 sliding blocks. The center pixel for each neighborhood is marked with a dot. For information about how the center pixel is determined, see “Determining the Center Pixel” on page 15-4. Neighborhood Blocks in a 6-by-5 Matrix 15-3 15 Neighborhood and Block Operations Determining the Center Pixel The center pixel is the actual pixel in the input image being processed by the operation. If the neighborhood has an odd number of rows and columns, the center pixel is actually in the center of the neighborhood. If one of the dimensions has even length, the center pixel is just to the left of center or just above center. For example, in a 2-by-2 neighborhood, the center pixel is the upper left one. For any m-by-n neighborhood, the center pixel is floor(([m n]+1)/2) In the 2-by-3 block shown in the preceding figure, the center pixel is (1,2), or the pixel in the second column of the top row of the neighborhood. General Algorithm of Sliding Neighborhood Operations To perform a sliding neighborhood operation, 1 Select a single pixel. 2 Determine the pixel’s neighborhood. 3 Apply a function to the values of the pixels in the neighborhood. This function must return a scalar. 4 Find the pixel in the output image whose position corresponds to that of the center pixel in the input image. Set this output pixel to the value returned by the function. 5 Repeat steps 1 through 4 for each pixel in the input image. For example, the function might be an averaging operation that sums the values of the neighborhood pixels and then divides the result by the number of pixels in the neighborhood. The result of this calculation is the value of the output pixel. Padding Borders in Sliding Neighborhood Operations As the neighborhood block slides over the image, some of the pixels in a neighborhood might be missing, especially if the center pixel is on the border of 15-4 Performing Sliding Neighborhood Operations the image. For example, if the center pixel is the pixel in the upper left corner of the image, the neighborhoods include pixels that are not part of the image. To process these neighborhoods, sliding neighborhood operations pad the borders of the image, usually with 0’s. In other words, these functions process the border pixels by assuming that the image is surrounded by additional rows and columns of 0’s. These rows and columns do not become part of the output image and are used only as parts of the neighborhoods of the actual pixels in the image. Implementing Linear and Nonlinear Filtering as Sliding Neighborhood Operations You can use sliding neighborhood operations to implement many kinds of filtering operations. One example of a sliding neighbor operation is convolution, which is used to implement linear filtering. MATLAB provides the conv and filter2 functions for performing convolution, and the toolbox provides the imfilter function. See “2-D Filtering” for more information about these functions. In addition to convolution, there are many other filtering operations you can implement through sliding neighborhoods. Many of these operations are nonlinear in nature. For example, you can implement a sliding neighborhood operation where the value of an output pixel is equal to the standard deviation of the values of the pixels in the input pixel’s neighborhood. To implement a variety of sliding neighborhood operations, use the nlfilter function. nlfilter takes as input arguments an image, a neighborhood size, and a function that returns a scalar, and returns an image of the same size as the input image. nlfilter calculates the value of each pixel in the output image by passing the corresponding input pixel’s neighborhood to the function. Note Many operations that nlfilter can implement run much faster if the computations are performed on matrix columns rather than rectangular neighborhoods. For information about this approach, see “Using Columnwise Processing to Speed Up Sliding Neighborhood or Distinct Block Operations” on page 15-26. 15-5 15 Neighborhood and Block Operations For example, this code computes each output pixel by taking the standard deviation of the values of the input pixel’s 3-by-3 neighborhood (that is, the pixel itself and its eight contiguous neighbors). I = imread('tire.tif'); I2 = nlfilter(I,[3 3],'std2'); You can also write code to implement a specific function, and then use this function with nlfilter. For example, this command processes the matrix I in 2-by-3 neighborhoods with a function called myfun.m. The syntax @myfun is an example of a function handle. I2 = nlfilter(I,[2 3],@myfun); If you prefer not to write code to implement a specific function, you can use an anonymous function instead. This example converts the image to class double because the square root function is not defined for the uint8 datatype. I = im2double(imread('tire.tif')); f = @(x) sqrt(min(x(:))); I2 = nlfilter(I,[2 2],f); (For more information on function handles and anonymous functions, see function_handle in the MATLAB Function Reference documentation.) The following example uses nlfilter to set each pixel to the maximum value in its 3-by-3 neighborhood. Note This example is only intended to illustrate the use of nlfilter. For a faster way to perform this local maximum operation, use imdilate. I = imread('tire.tif'); f = @(x) max(x(:)); I2 = nlfilter(I,[3 3],f); imshow(I); figure, imshow(I2); 15-6 Performing Sliding Neighborhood Operations Each Output Pixel Set to Maximum Input Neighborhood Value 15-7 15 Neighborhood and Block Operations Performing Distinct Block Operations In this section... “Understanding Distinct Block Processing” on page 15-8 “Implementing Block Processing Using the blockproc Function” on page 15-9 “Applying Padding” on page 15-11 “Block Size and Performance” on page 15-13 “Using Parallel Block Processing on large Image Files” on page 15-15 “Working with Data in Unsupported Formats” on page 15-17 Understanding Distinct Block Processing In distinct block processing, you divide a matrix into m-by-n sections. These sections, or distinct blocks, overlay the image matrix starting in the upper left corner, with no overlap. If the blocks do not fit exactly over the image, you can add padding to the image or work with partial blocks on the right or bottom edges of the image. The following figure shows a 15-by-30 matrix divided into 4-by-8 blocks. The right and bottom edges have partial blocks. You can process partial blocks as is, or you can pad the image so that the resulting size is 16-by-32. For more information, see “Applying Padding” on page 15-11. (To operate on an image a pixel at a time, rather than a block at a time, use the sliding neighborhood processing function. For more information, see “Performing Sliding Neighborhood Operations” on page 15-3.) 15-8 Performing Distinct Block Operations Image Divided into Distinct Blocks Implementing Block Processing Using the blockproc Function To perform distinct block operations, use the blockproc function. The blockproc function extracts each distinct block from an image and passes it to a function you specify for processing. The blockproc function assembles the returned blocks to create an output image. For example, the commands below process image I in 25-by-25 blocks with the function myfun. In this case, the myfun function resizes the blocks to make a thumbnail. (For more information about using function handles and anonymous functions, see function_handle in the MATLAB Function Reference documentation.) myfun = @(block_struct) imresize(block_struct.data,0.15); I = imread('tire.tif'); I2 = blockproc(I,[25 25],myfun); Note Due to block edge effects, resizing an image using blockproc does not produce the same results as resizing the entire image at once. 15-9 15 Neighborhood and Block Operations The example below uses the blockproc function to set every pixel in each 32-by-32 block of an image to the average of the elements in that block. The anonymous function computes the mean of the block, and then multiplies the result by a matrix of ones, so that the output block is the same size as the input block. As a result, the output image is the same size as the input image. The blockproc function does not require that the images be the same size. If this is the result you want, make sure that the function you specify returns blocks of the appropriate size: myfun = @(block_struct) ... uint8(mean2(block_struct.data)*... ones(size(block_struct.data))); I2 = blockproc('moon.tif',[32 32],myfun); figure; imshow('moon.tif'); figure; imshow(I2,[]); Original Image 15-10 Image with Pixels Set to Average Value Performing Distinct Block Operations Note Many operations that blockproc can implement run much faster if the computations are performed on matrix columns rather than rectangular blocks. For information about this approach, see “Using Columnwise Processing to Speed Up Sliding Neighborhood or Distinct Block Operations” on page 15-26. Applying Padding When processing an image in blocks, you may wish to add padding for two reasons: • To address the issue of partial blocks • To create overlapping borders As described in “Understanding Distinct Block Processing” on page 15-8, if blocks do not fit exactly over an image, partial blocks occur along the bottom and right edges of the image. By default, these partial blocks are processed as is, with no additional padding. Set the 'PadPartialBlocks' parameter to true to pad the right or bottom edges of the image and make the blocks full-sized. You can also add borders to each block. Use the 'BorderSize' parameter to specify extra rows and columns of pixels outside the block whose values are taken into account when processing the block. When there is a border, blockproc passes the expanded block, including the border, to the specified function. 15-11 15 Neighborhood and Block Operations Image Divided into Distinct Blocks with Specified Borders To process the blocks in the figure above with the function handle myfun, the call is: B = blockproc(A,[4 8],myfun,'BorderSize',[1 2], ... 'PadPartialBlocks',true) Both padding of partial blocks and block borders add to the overall size of the image, as you can see in the figure. The original 15-by-30 matrix becomes a 16-by-32 matrix due to padding of partial blocks. Also, each block in the image is processed with a 1-by-2 pixel border—one additional pixel on the top and bottom edges and two pixels along the left and right edges. Blocks along the image edges, expanded to include the border, extend beyond the bounds of the original image. The border pixels along the image edges increase the final size of the input matrix to 18-by-36. The outermost rectangle in the figure delineates the new boundaries of the image after all padding has been added. By default, blockproc pads the image with zeros. If you need a different type of padding, use the blockproc function’s 'PadMethod' parameter. 15-12 Performing Distinct Block Operations Block Size and Performance When using the blockproc function to either read or write image files, the number of times the file is accessed can significantly affect performance. In general, selecting larger block sizes reduces the number of times blockproc has to access the disk, at the cost of using more memory to process each block. Knowing the file format layout on disk can help you select block sizes that minimize the number of times the disk is accessed. See the blockproc reference page for more information about file formats. TIFF Image Characteristics TIFF images organize their data on disk in one of two ways: in tiles or in strips. A tiled TIFF image stores rectangular blocks of data contiguously in the file. Each tile is read and written as a single unit. TIFF images with strip layout have data stored in strips; each strip spans the entire width of the image and is one or more rows in height. Like a tile, each strip is stored, read, and written as a single unit. When selecting an appropriate block size for TIFF image processing, understanding the organization of your TIFF image is important. To find out whether your image is organized in tiles or strips, use the imfinfo function. The struct returned by imfinfo for TIFF images contains the fields TileWidth and TileLength. If these fields have valid (nonempty) values, then the image is a tiled TIFF, and these fields define the size of each tile. If these fields contain values of empty ([]), then the TIFF is organized in strips. For TIFFs with strip layout, refer to the struct field RowsPerStrip, which defines the size of each strip of data. When reading TIFF images, the minimum amount of data that can be read is a single tile or a single strip, depending on the type of TIFF. To optimize the performance of blockproc, select block sizes that correspond closely with how your TIFF image is organized on disk. In this way, you can avoid rereading the same pixels multiple times. Choosing Block Size The following three cases demonstrate the influence of block size on the performance of blockproc. In each of these cases, the total number of pixels in each block is approximately the same; only the size of the blocks is different. 15-13 15 Neighborhood and Block Operations First, read in an image file and convert it to a TIFF. imageA = imread('concordorthophoto.png','PNG'); imwrite(imageA,'concordorthophoto.tif','TIFF'); Use imfinfo to determine whether concordorthophoto.tif is organized in strips or tiles. imfinfo concordorthophoto.tif Select fields from the struct appear below: Filename: FileSize: Format: Width: Height: BitDepth: ColorType: BitsPerSample: StripOffsets: SamplesPerPixel: RowsPerStrip: PlanarConfiguration: TileWidth: TileLength: 'concordorthophoto.tif' 6595038 'tif' 2956 2215 8 'grayscale' 8 [1108x1 double] 1 2 'Chunky' [] [] The value 2 in RowsPerStrip indicates that this TIFF image is organized in strips with two rows per strip. Each strip spans the width of the image (2956 pixels) and is two pixels tall. The following three cases illustrate how choosing an appropriate block size can improve performance. Case 1: Typical Case — Square Block. First try a square block of size [500 500]. Each time the blockproc function accesses the disk it reads in an entire strip and discards any part of the strip not included in the current block. With two rows per strip and 500 rows per block, the blockproc function accesses the disk 250 times for each block. The image is 2956 pixels wide and 500 rows wide, or approximately six blocks wide (2956/500 = 5.912). The blockproc function reads the same strip over and over again for each block that includes pixels contained in that strip. Since the image is six blocks wide, blockproc reads every strip of the file six times. 15-14 Performing Distinct Block Operations tic, im = blockproc('concordorthophoto.tif',[500 500],@(s) s.data); toc Elapsed time is 17.806605 seconds. Case 2: Worst Case — Column-Shaped Block. The file layout on the disk is in rows. (Stripped TIFF images are always organized in rows, never in columns.) Try choosing blocks shaped like columns of size [2215 111]. Now the block is shaped exactly opposite the actual file layout on disk. The image is over 26 blocks wide (2956/111 = 26.631). Every strip must be read for every block. The blockproc function reads the entire image from disk 26 times. The amount of time it takes to process the image with the column-shaped blocks is proportional to the number of disk reads. With about four times as many disk reads in Case 2, as compared to Case 1, the elapsed time is about four times as long. tic, im = blockproc('concordorthophoto.tif',[2215 111],@(s) s.data); toc Elapsed time is 60.766139 seconds. Case 3: Best Case — Row-Shaped Block. Finally, choose a block that aligns with the TIFF strips, a block of size [84 2956]. Each block spans the width of the image. Each strip is read exactly one time, and all data for a particular block is stored contiguously on disk. tic, im = blockproc('concordorthophoto.tif',[84 2956],@(s) s.data); toc Elapsed time is 4.610911 seconds. Using Parallel Block Processing on large Image Files If you have a Parallel Computing Toolbox™ license, you can take advantage of multiple processor cores on your machine by specifying the blockproc setting 'UseParallel' as true. Doing so divides the block processing among all available MATLAB sessions to potentially improve the performance of blockproc. 15-15 15 Neighborhood and Block Operations What is Parallel Block Processing? Parallel block processing allows you to process many blocks simultaneously by distributing task computations to a collection of MATLAB sessions, called workers. The MATLAB session with which you interact is called the client. The client reserves a collection of workers, called a MATLAB pool. Then the client MATLAB session divides the input image and sends sections to the worker MATLAB sessions. Each worker processes a subset of blocks and sends the results back to the client. The client MATLAB collects the results into an output variable. When you set 'UseParallel' to true, blockproc uses all available workers in the MATLAB pool to process the input image in parallel. To read more about parallel computing, see Key Problems Addressed by Parallel Computing and Introduction to Parallel Solutions in the Parallel Computing Toolbox User’s Guide. When to Use Parallel Block Processing When processing small images, serial mode is expected to be faster than parallel mode. For larger images, however, you may see significant performance gains from parallel processing. The performance of parallel block processing depends on three factors: • Function used for processing • Image size • Block size In general, using larger blocks while block processing an image results in faster performance than completing the same task using smaller blocks. However, sometimes the task or algorithm you are applying to your image requires a certain block size, and you must use smaller blocks. When block processing using smaller blocks, parallel block processing is typically faster than regular (serial) block processing, often by a large margin. If you are using larger blocks, however, you might need to experiment to determine whether parallel block processing saves computing time. 15-16 Performing Distinct Block Operations How to Use Parallel Block Processing You must meet two conditions to use parallel block processing: • The source image is not specified as an ImageAdapter class. • A Parallel Computing Toolbox license exists in the MATLAB installation. If you meet these conditions, you can enable parallel block processing by opening a MATLAB pool: parpool(4) Here, 4 represents the number of workers in your pool. (See the parpool reference page for more details.) After opening a MATLAB pool, you can invoke parallel processing in blockproc by specifying 'UseParallel' as true. In the following example, compute a discrete cosine transform for each 8 x 8 block of an image in parallel: blockFun = @(block_struct) dct2(block_struct.data); result = blockproc(input_image,[8 8], blockFun, ... 'UseParallel',true); Working with Data in Unsupported Formats In addition to reading TIFF or JPEG2000 files and writing TIFF files, the blockproc function can read and write other formats. To work with image data in another file format, you must construct a class that inherits from the class. The ImageAdapter class is an abstract class that is part of the Image Processing Toolbox software. It defines the signature for methods that blockproc uses for file I/O with images on disk. You can associate instances of an Image Adapter class with a file and use them as arguments to blockproc for file-based block processing. This section demonstrates the process of writing an Image Adapter class by discussing an example class (the LanAdapter class). The LanAdapter class is part of the toolbox. Use this simple, read-only class to process arbitrarily large uint8 LAN files with blockproc. 15-17 15 Neighborhood and Block Operations Learning More About the LAN File Format To understand how the LanAdapter class works, you must first know about the LAN file format. Landsat thematic mapper imagery is stored in the Erdas LAN file format. Erdas LAN files contain a 128-byte header followed by one or more spectral bands of data, band-interleaved-by-line (BIL), in order of increasing band number. The data is stored in little-endian byte order. The header contains several pieces of important information about the file, including size, data type, and number of bands of imagery contained in the file. The LAN file format specification defines the first 24 bytes of the file header as shown in the table. File Header Content Bytes Data Type Content 1–6 6-byte character string 'HEADER' or 'HEAD74' 7–8 16-bit integer Pack type of the file (indicating bit depth) 9–10 16-bit integer Number of bands of data 11–16 6 bytes Unused 17–20 32-bit integer Number of columns of data 21–24 32-bit integer Number of rows of data The remaining 104 bytes contain various other properties of the file, which this example does not use. Parsing the Header Typically, when working with LAN files, the first step is to learn more about the file by parsing the header. The following code shows how to parse the header of the rio.lan file: 1 Open the file: file_name = 'rio.lan'; fid = fopen(file_name,'r'); 2 Read the header string: 15-18 Performing Distinct Block Operations header_str = fread(fid,6,'uint8=>char')'; fprintf('Header String: %s\n',header_str); 3 Read the pack type: pack_type = fread(fid,1,'uint16',0,'ieee-le'); fprintf('Pack Type: %d\n',pack_type); 4 Read the number of spectral bands: num_bands = fread(fid,1,'uint16',0,'ieee-le'); fprintf('Number of Bands: %d\n',num_bands); 5 Read the image width and height: unused_bytes = fread(fid,6,'uint8',0,'ieee-le'); width = fread(fid,1,'uint32',0,'ieee-le'); height = fread(fid,1,'uint32',0,'ieee-le'); fprintf('Image Size (w x h): %d x %d\n',width,height); 6 Close the file: fclose(fid); The output appears as follows: Header String: HEAD74 Pack Type: 0 Number of Bands: 7 Image Size (w x h): 512 x 512 The rio.lan file is a 512 x 512, 7-band image. The pack type of 0 indicates that each sample is an 8-bit, unsigned integer (uint8 data type). Reading the File In a typical, in-memory workflow, you would read this LAN file with the multibandread function. The LAN format stores the RGB data from the visible spectrum in bands 3, 2, and 1, respectively. You could create a truecolor image for further processing. truecolor = multibandread('rio.lan', [512, 512, 7],... 15-19 15 Neighborhood and Block Operations 'uint8=>uint8', 128,'bil', 'ieee-le', {'Band','Direct',[3 2 1]}); For very large LAN files, however, reading and processing the entire image in memory using multibandread can be impractical, depending on your system capabilities. To avoid memory limitations, use the blockproc function. With blockproc, you can process images with a file-based workflow. You can read, process, and then write the results, one block at a time. The blockproc function only supports reading and writing certain file formats, but it is extensible via the ImageAdapter class. To write an Image Adapter class for a particular file format, you must be able to: • Query the size of the file on disk • Read a rectangular block of data from the file If you meet these two conditions, you can write an Image Adapter class for LAN files. You can parse the image header to query the file size, and you can modify the call to multibandread to read a particular block of data. You can encapsulate the code for these two objectives in an Image Adapter class structure, and then operate directly on large LAN files with the blockproc function. The LanAdapter class is an Image Adapter class for LAN files, and is part of the Image Processing Toolbox software. Examining the LanAdapter Class This section describes the constructor, properties, and methods of the LanAdapter class. Studying the LanAdapter class helps prepare you for writing your own Image Adapter class. If you are new to object-oriented programming, see Developing Classes—Typical Workflow for general information on writing classes in the MATLAB documentation. Open LanAdapter.m and look at the implementation of the LanAdapter class. Classdef. The LanAdapter class begins with the keyword classdef. The classdef section defines the class name and indicates that LanAdapter inherits from the ImageAdapter superclass. Inheriting from ImageAdapter allows the new class to: • Interact with blockproc 15-20 Performing Distinct Block Operations • Define common ImageAdapter properties • Define the interface that blockproc uses to read and write to LAN files Properties. Following the classdef section, the LanAdapter class contains two blocks of class properties. The first block contains properties that are publicly visible, but not publicly modifiable. The second block contains fully public properties. The LanAdapter class stores some information from the file header as class properties. Other classes that also inherit from ImageAdapter, but that support different file formats, can have different properties. classdef LanAdapter < ImageAdapter properties(GetAccess = public, SetAccess = private) Filename NumBands end properties(Access = public) SelectedBands end In addition to the properties defined in LanAdapter.m, the class inherits the ImageSize property from the ImageAdapter superclass. The new class sets the ImageSize property in the constructor. Methods: Class Constructor. The class constructor initializes the LanAdapter object. The LanAdapter constructor parses the LAN file header information and sets the class properties. Implement the constructor, a class method, inside a methods block. The constructor contains much of the same code used to parse the LAN file header. The LanAdapter class only supports uint8 data type files, so the constructor validates the pack type of the LAN file, as well as the header string. The class properties store the remaining information. The method responsible for reading pixel data uses these properties. The SelectedBands property allows you to read a subset of the bands, with the default set to read all bands. methods function obj = LanAdapter(fname) 15-21 15 Neighborhood and Block Operations % % % % LanAdapter constructor for LanAdapter class. When creating a new LanAdapter object, read the file header to validate the file as well as save some image properties for later use. % Open the file. obj.Filename = fname; fid = fopen(fname,'r'); % Verify that the file begins with the string 'HEADER' or % 'HEAD74', as per the Erdas LAN file specification. header_str = fread(fid,6,'uint8=>char'); if ~(strcmp(header_str','HEADER') || strcmp(header_str',... 'HEAD74')) error('Invalid LAN file header.'); end % Read the data type from the header. pack_type = fread(fid,1,'uint16',0,'ieee-le'); if ~isequal(pack_type,0) error('Unsupported pack type. The LanAdapter example only... supports reading uint8 data.'); end % Provide band information. obj.NumBands = fread(fid,1,'uint16',0,'ieee-le'); % By default, return all bands of data obj.SelectedBands = 1:obj.NumBands; % Specify image width and height. unused_field = fread(fid,6,'uint8',0,'ieee-le'); %#ok<NASGU> width = fread(fid,1,'uint32',0,'ieee-le'); height = fread(fid,1,'uint32',0,'ieee-le'); obj.ImageSize = [height width]; % Close the file handle fclose(fid); end % LanAdapter 15-22 Performing Distinct Block Operations Methods: Required. Adapter classes have two required methods defined in the abstract superclass, ImageAdapter. All Image Adapter classes must implement these methods. The blockproc function uses the first method, readRegion, to read blocks of data from files on disk. The second method, close, performs any necessary cleanup of the Image Adapter object. function data = readRegion(obj, region_start, region_size) % readRegion reads a rectangular block of data from the file. % Prepare various arguments to MULTIBANDREAD. header_size = 128; rows = region_start(1):(region_start(1) + region_size(1) - 1); cols = region_start(2):(region_start(2) + region_size(2) - 1); % Call MULTIBANDREAD to get data. full_size = [obj.ImageSize obj.NumBands]; data = multibandread(obj.Filename, full_size,... 'uint8=>uint8', header_size, 'bil', 'ieee-le',... {'Row', 'Direct', rows},... {'Column','Direct', cols},... {'Band', 'Direct', obj.SelectedBands}); end % readRegion readRegion has two input arguments, region_start and region_size. The region_start argument, a two-element vector in the form [row col], defines the first pixel in the request block of data. The region_size argument, a two-element vector in the form [num_rows num_cols], defines the size of the requested block of data. The readRegion method uses these input arguments to read and return the requested block of data from the image. The readRegion method is implemented differently for different file formats, depending on what tools are available for reading the specific files. The readRegion method for the LanAdapter class uses the input arguments to prepare custom input for multibandread. For LAN files, multibandread provides a convenient way to read specific subsections of an image. The other required method is close. The close method of the LanAdapter class appears as follows: 15-23 15 Neighborhood and Block Operations function close(obj) %#ok<MANU> % Close the LanAdapter object. This method is a part % of the ImageAdapter interface and is required. % Since the readRegion method is "atomic", there are % no open file handles to close, so this method is empty. end end % public methods end % LanAdapter As the comments indicate, the close method for LanAdapter has nothing to do, so close is empty. The multibandread function does not require maintenance of open file handles, so the close method has no handles to clean up. Image Adapter classes for other file formats may have more substantial close methods including closing file handles and performing other class clean-up responsibilities. Methods (Optional). As written, the LanAdapter class can only read LAN files, not write them. If you want to write output to a LAN format file, or another file with a format that blockproc does not support, implement the optional writeRegion method. Then, you can specify your class as a 'Destination' parameter in blockproc and write output to a file of your chosen format. The signature of the writeRegion method is as follows: function [] = writeRegion(obj, region_start, region_data) The first argument, region_start, indicates the first pixel of the block that the writeRegion method writes. The second argument, region_data, contains the new data that the method writes to the file. Classes that implement the writeRegion method can be more complex than LanAdapter. When creating a writable Image Adapter object, classes often have the additional responsibility of creating new files in the class constructor. This file creation requires a more complex syntax in the constructor, where you potentially need to specify the size and data type of a new file you want to create. Constructors that create new files can also encounter other issues, 15-24 Performing Distinct Block Operations such as operating system file permissions or potentially difficult file-creation code. Using the LanAdapter Class with blockproc Now that you understand how the LanAdapter class works, you can use it to enhance the visible bands of a LAN file. Run the Computing Statistics for Large Images (ipexblockprocstats) example to see how the blockproc function works with the LanAdapter class. 15-25 15 Neighborhood and Block Operations Using Columnwise Processing to Speed Up Sliding Neighborhood or Distinct Block Operations In this section... “Understanding Columnwise Processing” on page 15-26 “Using Column Processing with Sliding Neighborhood Operations” on page 15-26 “Using Column Processing with Distinct Block Operations” on page 15-28 Understanding Columnwise Processing Performing sliding neighborhood and distinct block operations columnwise, when possible, can reduce the execution time required to process an image. For example, suppose the operation you are performing involves computing the mean of each block. This computation is much faster if you first rearrange the blocks into columns, because you can compute the mean of every column with a single call to the mean function, rather than calling mean for each block individually. To use column processing, use the colfilt function . This function 1 Reshapes each sliding or distinct block of an image matrix into a column in a temporary matrix 2 Passes the temporary matrix to a function you specify 3 Rearranges the resulting matrix back into the original shape Using Column Processing with Sliding Neighborhood Operations For a sliding neighborhood operation, colfilt creates a temporary matrix that has a separate column for each pixel in the original image. The column corresponding to a given pixel contains the values of that pixel’s neighborhood from the original image. 15-26 Using Columnwise Processing to Speed Up Sliding Neighborhood or Distinct Block Operations The following figure illustrates this process. In this figure, a 6-by-5 image matrix is processed in 2-by-3 neighborhoods. colfilt creates one column for each pixel in the image, so there are a total of 30 columns in the temporary matrix. Each pixel’s column contains the value of the pixels in its neighborhood, so there are six rows. colfilt zero-pads the input image as necessary. For example, the neighborhood of the upper left pixel in the figure has two zero-valued neighbors, due to zero padding. colfilt Creates a Temporary Matrix for Sliding Neighborhood The temporary matrix is passed to a function, which must return a single value for each column. (Many MATLAB functions work this way, for example, mean, median, std, sum, etc.) The resulting values are then assigned to the appropriate pixels in the output image. colfilt can produce the same results as nlfilter with faster execution time; however, it might use more memory. The example below sets each output pixel to the maximum value in the input pixel’s neighborhood, producing the same result as the nlfilter example shown in “Implementing Linear and Nonlinear Filtering as Sliding Neighborhood Operations” on page 15-5. I2 = colfilt(I,[3 3],'sliding',@max); 15-27 15 Neighborhood and Block Operations Using Column Processing with Distinct Block Operations For a distinct block operation, colfilt creates a temporary matrix by rearranging each block in the image into a column. colfilt pads the original image with 0’s, if necessary, before creating the temporary matrix. The following figure illustrates this process. A 6-by-16 image matrix is processed in 4-by-6 blocks. colfilt first zero-pads the image to make the size 8-by-18 (six 4-by-6 blocks), and then rearranges the blocks into six columns of 24 elements each. colfilt Creates a Temporary Matrix for Distinct Block Operation After rearranging the image into a temporary matrix, colfilt passes this matrix to the function. The function must return a matrix of the same size as the temporary matrix. If the block size is m-by-n, and the image is mm-by-nn, 15-28 Using Columnwise Processing to Speed Up Sliding Neighborhood or Distinct Block Operations the size of the temporary matrix is (m*n)-by-(ceil(mm/m)*ceil(nn/n)). After the function processes the temporary matrix, the output is rearranged into the shape of the original image matrix. This example sets all the pixels in each 8-by-8 block of an image to the mean pixel value for the block. I = im2double(imread('tire.tif')); f = @(x) ones(64,1)*mean(x); I2 = colfilt(I,[8 8],'distinct',f); The anonymous function in the example computes the mean of the block and then multiplies the result by a vector of ones, so that the output block is the same size as the input block. As a result, the output image is the same size as the input image. Restrictions You can use colfilt to implement many of the same distinct block operations that blockproc performs. However, colfilt has certain restrictions that blockproc does not: • The output image must be the same size as the input image. • The blocks cannot overlap. For situations that do not satisfy these constraints, use blockproc. 15-29 15 15-30 Neighborhood and Block Operations 16 Code Generation for Image Processing Toolbox Functions 16 Code Generation for Image Processing Toolbox™ Functions Supported Functions You can generate readable, efficient, and compact C/C++ code and MEX functions for a subset of toolbox functions that you call from MATLAB code. In generated code, each supported toolbox function has the same name, arguments, and functionality as its Image Processing Toolbox counterparts. However, to generate code for these functions, you must adhere to certain limitations when calling the functions from your MATLAB source code, as described below. For more information about code generation, see “MATLAB Coder™”. You must have the MATLAB Coder and Image Processing Toolbox software installed to generate C/C++ code from MATLAB for these functions. Function Remarks/Limitations bwlookup For best results, specify an input image of class logical. bwmorph The text string specifying the operation must be a constant and, for best results, specify an input image of class logical. conndef All input arguments must be compile-time constants. fspecial Allinputs must be compile-time constants. Expressions or variables are allowed if their values do not change. imcomplement Does not support int64 and uint64 data types. imfill The optional input connectivity, conn and the string 'holes' must be a compile time constants. Supports only up to 3-D inputs. (No N-D support.) The interactive mode to select points, imfill(BW,0,CONN) is not supported in code generation. locations can be a P-by-1 vector, in which case it contains the linear indices of the starting locations. locations can also be a P-by-ndims(I) matrix, in which case each row contains the array indices of one of the starting locations. Once you select a format at compile-time, you cannot change it at run-time. However, the number of points in locations can be varied at run-time. 16-2 Supported Functions Function Remarks/Limitations Generated code for this function uses a precompiled platform-specific shared library. imhmax The optional third input argument, conn, must be a compile-time constant Generated code for this function uses a precompiled platform-specific shared library. imhmin The optional third input argument, conn, must be a compile-time constant Generated code for this function uses a precompiled platform-specific shared library. imreconstruct The optional third input argument, conn, must be a compile-time constant. Generated code for this function uses a precompiled platform-specific shared library. imregionalmax The optional second input argument, conn, must be a compile-time constant. Generated code for this function uses a precompiled platform-specific shared library. imregionalmin The optional second input argument, conn, must be a compile-time constant. Generated code for this function uses a precompiled platform-specific shared library. iptcheckconn All input arguments must be compile-time constants. 16-3 16 Code Generation for Image Processing Toolbox™ Functions Function Remarks/Limitations label2rgb Referring to the standard syntax: RGB = label2rgb(L, map, zerocolor, order) • Submit at least two input arguments: the label matrix, L, and the colormap matrix, map. • map must be an n-by-3, double, colormap matrix. You cannot use a string containing the name of a MATLAB colormap function or a function handle of a colormap function. • If you set the boundary color zerocolor to the same color as one of the regions, label2rgb will not issue a warning. • If you supply a value for order, it must be 'noshuffle'. padarray Support only up to 3-D inputs. Input arguments, padval and direction are expected to be compile-time constants. 16-4 17 GPU Computing with Image Processing Toolbox Functions • “Image Processing on a GPU” on page 17-2 • “List of Supported Functions with Limitations and Other Notes” on page 17-3 • “Perform Thresholding and Morphological Operations on a GPU” on page 17-5 17 GPU Computing with Image Processing Toolbox™ Functions Image Processing on a GPU To take advantage of the performance benefits offered by a modern Graphics Processing Unit (GPU), certain Image Processing Toolbox functions have been enabled to perform image processing operations on a GPU. To perform an image processing operation on a GPU, follow these steps: • Move the data from the CPU to the GPU. You do this by creating an object of type gpuArray, using the gpuArray function. • Perform the image processing operation on the GPU. Any toolbox function that accepts a gpuArray object as an input can work on a GPU. For example, you can pass a gpuArray to the imfilter function to perform the filtering operation on a GPU. For a list of all the toolbox functions that have been GPU-enabled, see “List of Supported Functions with Limitations and Other Notes” on page 17-3. • Move the data back onto the CPU from the GPU. Applications typically move the data from the GPU back to the CPU after processing, using the gather function. For more information about GPU computing, see “Transfer Arrays Between Workspace and GPU”. To see an example of performing image processing operations on a GPU, see “Perform Thresholding and Morphological Operations on a GPU” on page 17-5. Note To run image processing code on a graphics processing unit (GPU), you must have the Parallel Computing Toolbox software. When working with a GPU, note the following: • Performance improvements can depend on the GPU device. • There may be small differences in the results returned on a GPU from those returned on a CPU. 17-2 List of Supported Functions with Limitations and Other Notes List of Supported Functions with Limitations and Other Notes The following table lists all the Image Processing Toolbox functions that have been enabled to run on a GPU. In most cases, the functions support the same syntaxes and operate the same, but in some cases there are certain differences. This table lists these limitations, if any. Function Remarks/Limitations bwlookup None bwmorph None corr2 None edge Canny method is not supported on the GPU. histeq None im2double None im2int16 None im2single None im2uint8 None im2uint16 None imabsdiff Only single and double are supported imadjust None imbothat gpuArray input must be of type uint8 or logical and the structuring element must be flat and two-dimensional imclose gpuArray input must be of type uint8 or logical and the structuring element must be flat and two-dimensional imdilate gpuArray input must be of type uint8 or logical and the structuring element must be flat and two-dimensional The PACKOPT syntaxes are not supported on the GPU. 17-3 17 GPU Computing with Image Processing Toolbox™ Functions Function Remarks/Limitations imerode gpuArray input must be of type uint8 or logical and the structuring element must be flat and two-dimensional The PACKOPT syntaxes are not supported on the GPU. 17-4 imfilter Input kernel must be 2-D imgradient None imgradientxy None imhist When running on a GPU, imhist does not display the histogram. To display the histogram, use stem(X,counts). imlincomb None imnoise None imopen gpuArray input must be of type uint8 or logical and the structuring element must be flat and two-dimensional imresize Only cubic interpolation is supported on GPU and function always performs antialiasing. imrotate The 'bicubic' interpolation mode used in the GPU implementation of this function differs from the default (CPU) bicubic mode. The GPU and CPU versions of this function are expected to give slightly different results. imshow None imtophat gpuArray input must be of type uint8 or logical and the structuring element must be flat and two-dimensional mat2gray None medfilt2 Padding options are not supported on the GPU padarray None rgb2gray None rgb2ycbcr None std2 None stdfilt None ycbcr2rgb None Perform Thresholding and Morphological Operations on a GPU Perform Thresholding and Morphological Operations on a GPU This example shows how to perform image processing operations on a GPU. The example uses filtering to highlight the watery areas in a large aerial photograph. Read an image into the workspace. imCPU = imread('concordaerial.png'); Move the image to the GPU by creating a gpuArray object. imGPU = gpuArray(imCPU); As a preprocessing step, change the RGB image to a grayscale image. Because you are passing it a gpuArray, rgb2gray performs the conversion operation on a GPU. If you pass a gpuArray as an argument, a function that has been GPU-enabled performs the operation on the GPU. imGPUgray = rgb2gray(imGPU); View the image in the Image Viewer and inspect the pixel values to find the value of watery areas. Note that you must bring the image data back onto the CPU, using the gather function, to use the Image Viewer. As you move the mouse over the image, you can view the value of the pixel under the cursor at the bottom of the Image Viewer. In the image, areas of water have pixel values less than 70. imtool(gather(imGPUgray)); 17-5 17 17-6 GPU Computing with Image Processing Toolbox™ Functions Perform Thresholding and Morphological Operations on a GPU Filter the image on the GPU to get a new image that contains only the pixels with values of 70 or less and view it. imWaterGPU = imGPUgray<70; figure;imshow(imWaterGPU); 17-7 17 17-8 GPU Computing with Image Processing Toolbox™ Functions Perform Thresholding and Morphological Operations on a GPU Using morphological operators that are supported on the GPU, clean up the mask image, removing points that do not represent water. imWaterMask = imopen(imWaterGPU,strel('disk',4)); imWaterMask = bwmorph(imWaterMask,'erode',3); Blur the mask image, using imfilter. blurH = fspecial('gaussian',20,5); imWaterMask = imfilter(single(imWaterMask)*10, blurH); Boost the blue channel to identify the watery areas. blueChannel = imGPU(:,:,3); blueChannel = imlincomb(1, blueChannel,6, uint8(imWaterMask)); imGPU(:,:,3) = blueChannel; View the result. The imshow function can work with images on the GPU. figure;imshow(imGPU); 17-9 17 17-10 GPU Computing with Image Processing Toolbox™ Functions Perform Thresholding and Morphological Operations on a GPU After filtering the image on the GPU, move the data back to the CPU., using the gather function, and write the modified image to a file. outCPU = gather(imGPU); imwrite(outCPU,'concordwater.png'); 17-11 17 17-12 GPU Computing with Image Processing Toolbox™ Functions Index Symbols and Numerics Index 1-bit image files 3-6 16-bit image files creating 3-7 reading 3-3 24-bit image files 2-15 4-bit image files 3-6 8-bit image files creating 3-7 reading 3-3 A adapthisteq increasing contrast 11-45 using 11-44 adaptive filters 11-54 Adjust Contrast tool creating 5-4 overview 4-42 using the dropper button 4-46 aliasing definition 6-4 alpha channel 14-3 antialiasing 6-4 approximation in indexed images 14-10 of an image background 1-13 of colors 14-4 area of binary images 10-42 of image regions 11-10 arrays storing images 2-2 averaging filter example 8-5 B background of an grayscale image 1-13 binary images 2-11 calculating the Euler number 10-43 changing the display colors of 4-70 displaying 4-69 feature measurement 10-39 flood fill operation 10-23 image area 10-42 labeling connected components labeling 10-39 lookup table operations 10-44 morphological operations 10-2 perimeter determination 10-16 selecting objects in 10-41 binary masks creating 12-2 bit depth 1-bit images 3-6 screen bit depth 14-2 blind deconvolution algorithm used for deblurring 13-16 block processing 15-2 and image formats 15-17 applying padding 15-11 block size 15-13 column processing 15-26 distinct blocks 15-8 padding borders in block processing 15-4 sliding neighborhoods 15-3 border padding in block processing 15-4 border replication in image processing 8-10 borders controlling in figure window 4-6 boundary padding. See border padding boundary ringing in image deblurring 13-24 boundary tracing 11-15 bounding box Index-1 Index finding for a region 11-10 brightness adjusting interactively 4-42 adjusting the window/level 4-47 brightness adjustment 11-39 bwarea using 10-42 bwdist using 10-36 bwmorph skeletonization example 10-15 bwtraceboundary using 11-16 C camera read-out noise 13-11 Canny edge detector using the edge function 11-11 center of mass calculating for region 11-10 center pixel calculating 15-4 in sliding neighborhood operations 15-3 Choose Colormap tool creating 5-4 using 4-15 chrominance in CIE color spaces 14-14 in NTSC color space 14-21 in YCbCr color space 14-22 CIE color spaces 14-13 CIELAB color space 14-13 closing morphology 10-12 color approximation 14-5 dithering 14-11 quantization 14-5 reducing number of colors 14-4 Index-2 color cube description of 14-5 quantization of 14-6 color planes of an HSV image 14-24 of an RGB image 2-17 slice of color cube 14-7 color reduction 14-4 color spaces converting among 14-13 data encodings 14-16 device-independent color spaces 14-14 HSV 14-23 NTSC 14-21 YCbCr 14-22 YIQ 14-21 colorbars adding 4-73 colorcube 14-10 colormap mapping 14-9 colormaps choosing in Image Viewer 4-15 creating a colormap using colorcube 14-10 column processing in neighborhood operations 15-26 connected components labeling 10-39 connectivity overview 10-20 specifying custom 10-23 constant component. See zero-frequency component contour plots text labels 11-8 contrast adjusting interactively 4-42 adjusting the window/level 4-47 contrast adjustment decreasing contrast 11-39 increasing contrast 11-38 Index specifying limits automatically 11-40 contrast stretching 11-37 understanding 4-42 with decorrelation stretching 11-48 See also contrast adjustment contrast-limited adaptive histogram equalization (CLAHE) 11-44 Control Point Selection Tool changing view of images 7-15 saving a session 7-30 saving control points 7-30 specifying control points 7-24 starting 7-15 using point prediction 7-26 control points prediction 7-26 saving 7-30 specifying 7-24 conv2 compared to imfilter 8-13 conversions between image types 2-19 convn compared to imfilter 8-13 convolution definition 8-2 Fourier transform and 9-11 two-dimensional 8-2 using sliding neighborhood operations 15-5 with imfilter 8-7 convolution kernel definition 8-2 coordinate systems pixel coordinates 2-3 spatial coordinates 2-4 corner detection 11-13 corr2 calculating summary statistics 11-10 correlation definition 8-4 Fourier transform 9-12 with imfilter 8-7 correlation kernel definition 8-4 cpcorr example 7-32 Crop Image tool creating 5-4 cropping an image 6-6 cross-correlation improving control point selection 7-32 D damping for noise reduction 13-10 data types converting between 3-7 double-precision (double) 3-7 in image filtering 8-6 DC component. See zero-frequency component dct2 equations 9-15 dctmtx using 9-17 deblurring avoiding boundary ringing 13-24 conceptual model 13-2 overview 13-2 overview of functions 13-4 use of frequency domain 13-23 using the blind deconvolution algorithm 13-16 using the Lucy-Richardson algorithm 13-10 with regularized filter 13-7 with the Wiener filter 13-6 decomposition of structuring elements example 10-7 deconvblind example 13-16 deconvlucy Index-3 Index example 13-10 deconvreg example 13-7 deconvwnr example 13-6 decorrelation stretching 11-45 See also contrast adjustment detail rectangle getting position of 4-25 in Control Point Selection Tool 7-15 specifying color in Image Viewer 4-25 DICOM files reading and writing 3-9 DICOM unique identifier generating 3-17 Digital Imaging and Communications in Medicine. See DICOM files dilation 10-2 discrete cosine transform 9-15 image compression 9-17 transform matrix 9-17 discrete Fourier transform 9-7 display depth 14-2 See also screen color resolution display range getting information about 4-35 Display Range tool creating 5-5 in Image Viewer 4-35 displaying images adding a colorbar 4-73 binary 4-69 binary images with different colors 4-70 comparison of functions 4-2 controlling figure window 4-6 grayscale images 4-68 indexed images 4-67 initial size 4-6 multiple images 4-55 multiple images in figure 4-8 Index-4 toolbox preferences for 4-77 truecolor 4-71 unconventional ranges of data 4-68 using imshow 4-4 using the Image Viewer 4-11 distance between pixels 4-37 Euclidean 4-37 Distance tool creating 5-5 distance transform 10-36 distinct block operations 15-8 overlap 15-11 zero padding 15-8 distortion operator 13-2 dithering 14-11 example 14-11 dropper button in Adjust Contrast tool 4-46 E edge example 11-12 edge detection 11-11 Canny method 11-11 example 11-12 Sobel method 11-12 edgetaper avoiding boundary ringing 13-24 enhancing images decorrelation stretching 11-45 intensity adjustment 11-38 noise removal 11-50 erosion 10-2 Euclidean distance 4-37 Euler number calculating 10-43 exploring images using Image Viewer 4-23 Index exporting data in Image Viewer 4-18 eye dropper button in Adjust Contrast tool 4-46 F fan-beam projection data arc geometry 9-37 computing 9-36 line geometry 9-38 reconstructing image from 9-39 fanbeam using 9-36 fast Fourier transform 9-7 zero padding 9-9 See also Fourier transform feature measurement 1-20 area 11-10 binary images 10-39 bounding box 11-10 center of mass 11-10 fft 9-7 fft2 9-7 example 9-8 using 9-10 fftn 9-7 fftshift example 8-17 using 9-10 figure controlling borders 4-6 files displaying images from disk 4-4 filling a region 12-8 filling holes in images 10-25 filter design 8-15 frequency sampling method 8-18 frequency transformation method 8-16 windowing method 8-19 filter2 compared to imfilter 8-13 example 11-52 filtering a region 12-5 masked filtering 12-5 filters adaptive 11-54 binary masks 12-5 computing frequency response 9-10 designing 8-15 finite impulse response (FIR) 8-16 frequency response 8-22 imfilter 8-5 Infinite Impulse Response (IIR) 8-16 linear 8-2 median 11-51 multidimensional 8-12 unsharp masking 8-13 FIR filters 8-16 transforming from one-dimensional to two-dimensional 8-16 fitgeotrans using 7-12 flat-field correction 13-11 flood-fill operation 10-23 Fourier transform 9-2 applications of the Fourier transform 9-10 centering the zero-frequency coefficient 9-10 computing frequency response 9-10 convolution and 9-11 correlation 9-12 DFT coefficients 9-8 examples of transform on simple shapes 9-5 fast convolution with 9-11 for performing correlation 9-12 frequency domain 9-2 increasing resolution 9-9 padding before computation 9-9 two-dimensional 9-2 Index-5 Index zero-frequency component 9-2 freqspace 8-21 example 8-18 frequency domain 9-2 frequency response computing 8-22 desired response matrix 8-21 of linear filters 9-10 frequency sampling method (filter design) 8-18 frequency transformation method (filter design) 8-16 freqz example 8-17 freqz2 computing frequency response of linear filters 9-10 example 8-18 fsamp2 example 8-18 fspecial creating predefined filters 8-13 ftrans2 example 8-17 fwind1 example 8-20 fwind2 example 8-19 G gamma correction 11-41 Gaussian convolution kernel frequency response of 9-10 Gaussian noise 11-54 geometric operations cropping 6-6 resizing 6-2 getimage example 4-5 using with Image Viewer 4-18 Index-6 graphical user interfaces (GUIs) building 5-2 graphics file formats converting from one format to another 3-8 writing data 3-5 grayscale images displaying 4-68 flood-fill operation 10-23 graythresh thresholding image values 1-17 H histeq example 11-43 increase contrast example 11-43 histogram equalization 11-42 histograms 11-9 holes filling 10-23 tracing boundaries 11-15 hough using 11-21 houghpeaks using 11-22 HSV color space 14-23 color planes of 14-24 hsv2rgb 14-23 hue in HSV color space 14-23 in NTSC color space 14-21 I ICC profiles processing 14-17 ifanbeam using 9-39 ifft 9-7 ifft2 9-7 Index ifftn 9-7 IIR filters 8-16 imadjust brightening example 11-40 example 11-38 gamma correction and 11-41 gamma correction example 11-42 increase contrast example 11-38 setting limits automatically 11-41 image analysis contour plots 11-7 corner detection 11-13 edge detection 11-11 histograms 11-9 intensity profiles 11-3 overview 11-11 pixel values 11-2 quadtree decomposition 11-24 summary statistics 11-10 image arithmetic combining functions 2-30 overview 2-29 truncation rules 2-30 image editing 12-8 image filtering data types 8-6 unsharp masking 8-13 with imfilter 8-5 Image Information tool creating 5-6 using 4-40 image metadata viewing 4-40 image properties set by imshow 4-2 image registration fine-tuning point placement 7-32 overview 7-2 procedure 7-2 specifying control point pairs 7-24 types of transformations 7-12 using control point prediction 7-26 image rotation 6-5 specifying interpolation method 6-5 specifying size of output image 6-5 Image Tool compared to imshow 4-2 image transformations supported by fitgeotrans 7-12 image types 2-10 binary 2-11 converting 2-19 grayscale 2-14 indexed 2-12 multiframe images 2-23 supported by the toolbox 2-10 truecolor 2-15 See also binary images, grayscale images, indexed images, multiframe images, truecolor images Image Viewer choosing a colormap 4-15 closing 4-20 controlling initial magnification 4-14 exploring images 4-23 exporting data 4-18 importing data 4-17 opening 4-13 overview 4-11 panning images 4-26 printing 4-20 specifying image magnification 4-27 using the Pixel Region tool 4-30 zoom tools 4-27 ImageAdapter class 15-17 images adjusting contrast 4-42 analyzing 11-2 arithmetic operations 2-29 brightness control 4-42 Index-7 Index causes of blurring 13-2 data types 3-7 displaying large images 4-21 displaying multiple images 4-55 displaying multiple images in figure 4-8 feature measurement 1-20 filling holes in 10-25 finding image minima and maxima 10-26 getting information about 4-40 getting information about display range 4-35 how MATLAB stores 2-2 image types 2-10 improving contrast 1-16 printing 4-75 reducing number of colors 14-4 registering 7-2 restoring blurred images 13-2 returning information about 3-2 using imshow 4-4 viewing as a surface plot 1-14 viewing metadata 4-40 imapprox example 14-10 imclose using 10-12 imcontour example 11-8 imerode closure example 10-13 imextendedmax example 10-29 imfill example 10-25 imfilter compared to other filtering functions 8-13 convolution option 8-7 correlation option 8-7 padding options 8-8 using 8-5 imfinfo 3-2 Index-8 example 3-6 imhist creating a histogram 11-9 imlincomb example 2-30 immovie example 4-66 imnoise example 11-54 salt & pepper example 11-52 imopen using 10-12 impixel example 11-2 importing data in Image Viewer 4-17 improfile example 11-5 grayscale example 11-4 imread 3-3 example for multiframe image 3-4 imreconstruct example 10-20 imresize using 6-2 imrotate specifying interpolation method 6-5 specifying size of output image 6-5 using 6-5 imshow compared to Image Viewer app 4-2 displaying images 4-4 displaying unconventional range data 4-68 example for binary images 4-70 example for grayscale images 4-68 example for truecolor images 4-71 used with indexed images 4-67 imtool compared to imshow 4-2 displaying unconventional range data 4-68 Index example for binary images 4-70 example for grayscale images 4-68 example for truecolor images 4-71 overview 4-11 used with indexed images 4-67 imwrite example 3-6 indexed images 2-12 displaying 4-67 reducing number of colors in 14-10 infinite impulse response (IIR) filter 8-16 intensity adjustment 11-38 gamma correction 11-41 histogram equalization 11-42 specifying limits automatically 11-40 See also contrast adjustment intensity images. See grayscale images intensity profiles 11-3 interpolation intensity profiles 11-3 within a region of interest 12-8 inverse Radon transform 9-29 example 9-34 filtered backprojection algorithm 9-31 iptgetpref using 4-77 iptsetpref using 4-78 iradon 9-29 example 9-29 J JPEG compression discrete cosine transform and 9-17 L label matrix creating 10-39 labeling connected components 10-39 levels of contours 11-8 line detection 9-25 line segment pixel values along 11-3 linear filtering 8-2 convolution 8-2 filter design 8-15 FIR filters 8-16 IIR filters 8-16 noise removal and 11-50 using sliding neighborhood operations 15-5 lookup tables using 10-44 Lucy-Richardson algorithm used for deblurring 13-10 luminance in NTSC color space 14-21 in YCbCr color space 14-22 M magnification specifying in Image Viewer 4-27 specifying initial value in Image Viewer 4-14 Magnification box creating 5-6 magnifying. See resizing images marker image creating 10-33 definition 10-19 mask image definition 10-19 masked filtering 12-5 matrices storing images in 2-2 maxima finding in images 10-27 imposing 10-32 Index-9 Index suppressing 10-30 mean2 11-10 medfilt2 example 11-53 using 11-51 median filtering 11-51 metadata viewing 4-40 minima finding in images 10-27 imposing 10-32 suppressing 10-30 minimum variance quantization 14-7 modular tools connecting 5-28 creating your own 5-33 embedding in existing figures 5-15 navigation aids 5-22 overview 5-2 positioning in a GUI 5-18 specifying parent of 5-15 using 5-28 utility functions 5-33 moire patterns 6-4 montage example 4-64 morphological operations 10-2 dilation 10-2 erosion 10-2 opening 10-12 overview 10-1 predefined operations 10-14 skeletonization 10-15 morphological reconstruction finding peaks and valleys 10-26 overview 10-17 morphology 10-17 See also morphological reconstruction movies creating from images 4-66 Index-10 playing 4-66 multidimensional filters 8-12 multiframe images about 2-23 N navigational aids creating 5-22 neighborhoods neighborhood operations 15-2 noise amplification reducing 13-10 noise removal 11-50 adaptive filtering (Weiner) and 11-54 Gaussian noise 11-54 grain noise 11-50 linear filtering and 11-50 median filter and 11-51 salt and pepper noise 11-51 nonimage data displaying as image 4-68 nonlinear filtering using sliding neighborhood operations 15-5 normalized cross-correlation 7-32 NTSC color space 14-21 ntsc2rgb 14-21 O objects tracing boundaries 11-15 observed image in image registration 7-13 opening morphology 10-12 optical transfer function (OTF) 13-2 orthonormal matrix 9-17 otf2psf use of 13-23 Index overlap in distinct block operations 15-8 Overview tool creating 5-7 customizing 4-25 getting position of detail rectangle 4-25 printing image in 4-26 starting in Image Viewer 4-25 using 4-23 P padding borders in block processing 15-4 options with imfilter 8-8 panning images using the Image Viewer 4-26 parallel beam projections 9-29 perimeter determination in binary images 10-16 phantom 9-32 Pixel Information tool creating 5-8 Pixel Region tool creating 5-8 customizing 4-33 determining location of cursor 4-34 printing contents 4-35 selecting a region 4-33 using 4-30 using in Image Viewer 4-32 pixel regions viewing 4-32 pixel values along a line segment 11-3 using the Pixel Region tool 4-30 pixels correcting for bad pixels 13-11 defining connectivity 10-20 definition 2-2 Euclidean distance between 4-37 getting pixel value information in Image Viewer 4-31 getting value of using Pixel Information tool 4-30 getting values of 11-2 selecting 11-2 viewing values of pixel regions 4-32 pixval using 11-2 PNG (Portable Network Graphics) files writing as 16-bit 3-6 point mapping for image registration 7-2 point spread function (PSF) 13-2 importance of in deblurring 13-3 predicting control point locations in image registration 7-26 preferences getting value of 4-77 Image Processing Toolbox™ display preferences 4-77 setting value of 4-78 printing contents of Overview tool 4-26 contents of Pixel Region tool 4-35 printing images 4-75 from Image Viewer 4-20 profiles reading ICC color profiles 14-17 projections parallel beam 9-29 psf2otf use of 13-23 Q qtdecomp example 11-25 quadtree decomposition 11-24 Index-11 Index quantization 14-5 minimum variance 14-7 tradeoffs between using minimum variance and uniform quantization methods 14-9 R R-Set 4-21 radon example 9-22 Radon transform center pixel 9-22 description of 9-19 example 9-32 inverse Radon transform 9-29 line detection example 9-25 of the Shepp-Logan Head phantom 9-32 relationship to Hough transform 9-25 rank filtering 11-51 See also order-statistic filtering read-out noise correcting 13-11 real orthonormal matrix 9-17 reconstruction morphological 10-17 reference image in image registration 7-13 region labeling 10-39 region of interest based on color or intensity 12-4 binary masks 12-2 filling 12-8 filtering 12-5 selecting 12-2 region property measurement 11-10 regional maxima definition 10-27 imposing 10-32 suppressing 10-30 regional minima Index-12 definition 10-27 imposing 10-32 suppressing 10-30 regionprops using 1-20 11-10 registering an image 7-2 regularized filter used for deblurring 13-7 replication to avoid border effect 8-10 resizing images 6-2 antialiasing 6-4 resolution screen color resolution 14-2 See also bit depth 14-2 RGB color cube description of 14-5 quantization of 14-6 RGB images 2-15 See also truecolor images rgb2hsv 14-23 converting RGB to HSV color space 14-24 example 14-24 rgb2ind colormap mapping example 14-10 example 14-10 in minimum variance quantization 14-7 minimum variance quantization example 14-7 specifying a colormap to use 14-9 uniform quantization example 14-6 used in dithering 14-11 rgb2ntsc example 14-21 rgb2ycbcr example 14-22 Richardson-Lucy algorithm. See Lucy-Richardson ringing in image deblurring 13-24 Index roicolor 12-4 roifill example 12-8 roifilt2 contrast example 12-6 rotation of images 6-5 S salt and pepper noise 11-51 sampling handling undersampled images 13-12 saturation in HSV color space 14-23 in NTSC color space 14-21 Save Image tool creating 5-9 screen bit depth 14-2 screen color resolution 14-2 ScreenDepth 14-3 Scroll Panel tool creating 5-9 scroll panels understanding 5-23 Shepp-Logan head phantom 9-32 shrinking. See resizing images skeletonization 10-15 sliding neighborhood operations 15-3 center pixel in 15-4 padding in 15-5 spatial coordinates 2-4 std2 11-10 storage classes converting between 2-21 stretchlim adjusting image contrast 1-16 using 11-40 structuring elements 10-5 creating 10-6 decomposition of 10-7 subtraction of one image from another 1-15 surf viewing images 1-14 T target images definition 5-2 displaying 5-10 getting handle to 5-14 specifying 5-11 template matching 9-12 thresholding to create a binary image 1-17 tomography 9-29 tools creating your own 5-33 modular 5-2 tracing boundaries 11-15 transformation matrix 8-16 transforms 9-1 discrete cosine 9-15 discrete Fourier transform 9-7 Fourier 9-2 inverse Radon 9-29 Radon 9-19 two-dimensional Fourier transform 9-2 transparency 14-3 truecolor images displaying 4-71 measuring the intensities of each color plane 11-5 reducing number of colors 14-4 truncation rules for image arithmetic operators 2-30 Index-13 Index U X uint16 storing images in 3-3 X-ray absorption tomography 9-29 XYZ color space 14-13 uint8 storing images in 3-3 undersampling correcting 13-12 uniform quantization. See quantization unsharp masking 8-13 W weight array in deblurring 13-11 Wiener filter deblurring with 13-6 wiener2 adaptive filtering 11-54 using 11-54 window/level adjusting 4-47 windowing method (filter design) 8-19 Index-14 Y YCbCr color space 14-22 ycbcr2rgb using 14-22 YIQ color space 14-21 Z zero padding 9-12 and the fast Fourier transform 9-9 image boundaries 8-9 zero-frequency component 9-2 zooming Control Point Selection Tool 7-20 in Image Viewer 4-27
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