DEVELOPMENT AND IMPLEMENTATION OF IMAGE FUSION ALGORITHMS BASED ON WAVELETS

DEVELOPMENT AND IMPLEMENTATION OF IMAGE FUSION ALGORITHMS BASED ON WAVELETS
DEVELOPMENT AND IMPLEMENTATION OF
IMAGE FUSION ALGORITHMS BASED ON
WAVELETS
A Thesis Submitted in Partial Fulfilment
of the Requirements for the Award of the Degree of
Master of Technology
in
Electronics and Instrumentation Engineering
by
PRIYA RANJAN MUDULI
Roll No: 211EC3315
Department of Electronics & Communication Engineering
National Institute of Technology, Rourkela
Odisha- 769008, India
May 2013
DEVELOPMENT AND IMPLEMENTATION OF
IMAGE FUSION ALGORITHMS BASED ON
WAVELETS
A Thesis Submitted in Partial Fulfilment
of the Requirements for the Award of the Degree of
Master of Technology
in
Electronics and Instrumentation Engineering
by
PRIYA RANJAN MUDULI
Roll No: 211EC3315
Under the Supervision of
Prof. Umesh Chandra Pati
Department of Electronics & Communication Engineering
National Institute of Technology, Rourkela
Odisha- 769008, India
May 2013
Department of Electronics & Communication Engineering
National Institute of Technology, Rourkela
CERTIFICATE
This
is
to
certify
that
the
thesis
report
entitled
“DEVELOPMENT
AND
IMPLEMENTATION OF IMAGE FUSION ALGORITHMS BASED ON WAVELETS
”Submitted by Mr PRIYA RANJAN MUDULI bearing roll no. 211EC3315 in partial
fulfilment of the requirements for the award of Master of Technology in Electronics and
Communication Engineering with specialization in “Electronics and Instrumentation
Engineering” during session 2011-2013 at National Institute of Technology, Rourkela is an
authentic work carried out by him under my supervision and guidance.
To the best of my knowledge, the matter embodied in the thesis has not been submitted to
any other University / Institute for the award of any Degree or Diploma.
Prof. Umesh Chandra Pati
Place:
Associate Professor
Date:
Dept. of Electronics and Comm. Engineering
National Institute of Technology
Rourkela-769008
Dedicated
to
My Family & Teachers
ACKNOWLEDGEMENTS
First of all, I would like to express my deep sense of respect and gratitude towards my
advisor and guide Prof. U.C. Pati, who has been the guiding force behind this work. I am
greatly indebted to him for his constant encouragement, invaluable advice and for propelling
me further in every aspect of my academic life. His presence and optimism have provided an
invaluable influence on my career and outlook for the future. I consider it my good fortune to
have an opportunity to work with such a wonderful person.
Next, I want to express my respects to Prof. T. K. Dan, Prof. S. K. Patra, Prof. K. K.
Mahapatra, Prof. S. Meher, Prof. A. Swain, Prof. Poonam Singh and Prof. L. P. Roy for
teaching me and helping me how to learn. They have been great sources of inspiration to me
and I thank them from the bottom of my heart.
I also extend my thanks to all faculty members and staff of the Department of Electronics
and Communication Engineering, National Institute of Technology, Rourkela who have
encouraged me throughout the course of Master’s Degree.
I would like to thank all my friends and especially my classmates for all the thoughtful
and mind stimulating discussions we had, which prompted us to think beyond the obvious. I
have enjoyed their companionship so much during my stay at NIT, Rourkela.
I am especially indebted to my parents for their love, sacrifice, and support. They are my
first teachers after I came to this world and have set great examples for me about how to live,
study, and work.
Date:
Roll No: 211EC3315
Place:
Dept. of ECE
NIT, Rourkela
i
ABSTRACT
Image fusion is a process of blending the complementary as well as the common features
of a set of images, to generate a resultant image with superior information content in terms of
subjective as well as objective analysis point of view. The objective of this research work is
to develop some novel image fusion algorithms and their applications in various fields such
as crack detection, multi spectra sensor image fusion, medical image fusion and edge
detection of multi-focus images etc.
The first part of this research work deals with a novel crack detection technique based
on Non-Destructive Testing (NDT) for cracks in walls suppressing the diversity and
complexity of wall images. It follows different edge tracking algorithms such as Hyperbolic
Tangent (HBT) filtering and canny edge detection algorithm. The fusion of detector
responses are performed using Haar Discrete Wavelet Transform (HDWT) and maximumapproximation with mean-detail image fusion algorithm to get more prominent detection of
crack edges. The proposed system gives improved edge detection in images with superior
edge localization and higher PSNR. .
The second part of this research work deals with a novel edge detection approach for
multi-focused images by means of complex wavelets based image fusion. An illumination
invariant hyperbolic tangent filter (HBT) is applied followed by an adaptive thresholding to
get the real edges. The shift invariance and directionally selective diagonal filtering as well as
the ease of implementation of Dual-Tree Complex Wavelet Transform (DT-CWT) ensure
robust sub band fusion. It helps in avoiding the ringing artefacts that are more pronounced in
Discrete Wavelet Transform (DWT). The fusion using DT-CWT also solves the problem of
low contrast and blocking effects. To fulfil the symmetry of sub-sampling structure and biorthogonal property, a Q-shift dual tree CWT is implemented here. The adaptive thresholding
varies the threshold value smartly over the image. This helps to combat with a potent
illumination gradient, shadowing and multi focus blurring of an image.
In the third part, an improved DT-CWT based image fusion technique has been
developed to compose a resultant image with better perceptual as well as quantitative image
quality indices. A bilateral sharpness based weighting scheme has been implemented for the
high frequency coefficients taking both gradient and its phase coherence in account. A
normalized maximum gradient weighting scheme is implemented for low frequency wavelet
components. The proposed technique shows superior result as compared to DWT and
traditional DT-CWT based image fusion algorithms.
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TABLE OF CONTENTS
Page No.
ACKNOWLEDGEMENTS ...………………………………………………………………i
ABSTRACT …………………………………………………………………………….… ii
TABLE OF CONTENT ……………………………………………………………….….. iii
LIST OF FIGURES
……………………………………………………………………. .v
LIST OF ABBREVIATIONS ……………………………………………………………...vii
Chapter 1 INTRODUCTION TO IMAGE FUSION …………………………………1
1.1 Overview ……………………………………………………………….....2
1.2 Single Sensor Image Fusion System……………………………………....5
1.3 Multi Sensor Image Fusion System……………………………….....…....5
1.4 Image Pre-processing………………………………………………….…..7
1.5 Image Fusion Techniques ………………………………………….….….7
1.6 Motivation…………………………… ……………………………...…...8
1.7 Objectives.…………………………………………………………….......9
1.8 Thesis Organisation.……………………………………………….…..….9
Chapter 2
LITERATURE REVIEW………………..…………………………….......12
2.1 Multiresolution Pyramidal Image Fusion....……………………………..14
2.2 Wavelet Transform based Image Fusion Algorithms…….……………...20
2.2.1 Discrete wavelet transform...……………………….………….…..23
Chapter 3
IMAGE FUSION AND EDGE DETECTION…..……………………….. 29
3.1 Crack Detection using Image Fusion ………..……………………....….30
3.1.1 Proposed crack detection technique………………………………..31
3.1.2 Wavelet decomposition and fusion...……………………….……...35
3.1.3 Result and Discussion……………………………………..….........37
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3.1.4 Summary ………………………………………………………...........42
3.2 Edge Detection for Multi-focus Images using Image Fusion …………....43
3.2.1 Proposed technique ………………………………………….…….44
3.2.2 DT-CWT based image fusion ………………………………..........44
3.2.3 Edge detection using HBT filter……………………………….......46
3.2.4 Results and Discussion…………………………………………….49
3.2.5 Summary............................................................................................53
Chapter 4
IMAGE FUSION BASED ON BILATERAL SHARPNESS
CRITERION IN DT-CWT DOMAIN…………………………………....54
4.1 Dual-Tree Complex Wavelet Transform.……………………………......56
4. 2 Proposed Image Fusion using DT-CWT..………………….…….…......58
4.2.1 Fusion rules for low frequency coefficients..……………………...58
4.2.2 Gradient based sharpness criterion…………………………...........58
4.2.3 Fusion rules for high frequency coefficients………….……...........60
4.3 Simulation Results and Discussions.……………………………............61
4.3.1 Quantitative evaluation ……………………………….…….........64
4.4 Summary …………………………………………………………...….....67
Chapter 5
CONCLUSIONS……………………………………………………….........68
5.1 Conclusions ………………………………………………………..........69
5.2 Future Work ……………………….………………………………........70
BIBLIOGRAPHY…………………………………………………….………………........72
DISSEMINATION OF THIS RESEARCH WORK ……………………………….…...77
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LIST OF FIGURES
Figure No.
Page No.
Fig.1.1: Fundamental information fusion system block diagram……………………............4
Fig.1.2: The level classification of the various popular image fusion methods…………......4
Fig.1.3: Single sensor image fusion system …………………………………………….......5
Fig.1.4: Multi sensor image fusion system ……………………………………….…………6
Fig.2.1: Pyramid transform description with an example ………………………….....…...15
Fig.2.2: Wavelet families representation …………………………………………….….....24
Fig.2.3: Two channel wavelet filter bank ………………………………………….……....25
Fig.2.4: Filter bank structure of the DWT analysis. …………………………………….....26
Fig.2.5: Filter bank structure of the reverse DWT synthesis…..……………………….......27
Fig.2.6: Image decomposition with natural orientation of sub bands ……………….…......27
Fig.3.1: Proposed crack detection algorithm ……………………………………..……..…32
Fig.3.2: Discrete Wavelet Transform filter banks ……………………………..………..…36
Fig.3.3: Original wall image showing a hairline cracks………………..…………………..38
Fig.3.4: Canny edge detector response ……………………………………..…………...…38
Fig.3.5: HBT filter response with sigma = 0.48, Totalminerror = 0.168,
gamma = 0.0208, Threshold = 0.83 ………………………………………….…39
Fig.3.6: Second largest PCA Eigen values in spatial domain for wall image ……….........39
Fig.3.7: Third largest PCA Eigen values in spatial domain for wall image ………..….…..39
Fig.3.8: Total minimum error Vs.  w plot ……………………………..…………...….…..40
Fig.3.9: GUI for DWT based Image Fusion ……………………………..……...……..…..40
Fig.3.10: Fusion with 3 level Haar DWT decomposition using GUI …………..….....…....41
Fig.3.11: Image fusion response using GUI …………………………..…………………...41
Fig.3.12: Flow chart for proposed edge detection technique …………………….…….….44
Fig.3.13: Dual tree Q-shift CWT………………………………………………………..….45
Fig.3.14: Edge detection result of multi-focus clock images ……………………….……..49
Fig.3.15: Edge detection result of multi-focus Pepsi-Can images………………………....50
Fig.3.16: Total min-error Vs sigma plot for Clock image showing total min-error
of 0.1627 at
  0.55
…………………………………………….…………..…51
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Figure No.
Page No.
Fig.3.17: Total min-error Vs sigma plot for Pepsi Can image showing total min-error
of 0.3626 at
  0.68 …………………………………………………………...51
Fig.3.18: PCA Eigen value e2 and e3 for fused Clock Image.…………………………….52
Fig.3.19: PCA Eigen value e2 and e3 for fused Pepsi Can Image..……………………..... 52
Fig.4.1: Dual tree of real filters for the Q-shift wavelet transform...………………….…...57
Fig.4.2: Dual Tree Complex Wavelet Transform (DT-CWT) fusion ……………………..58
Fig.4.3: LLTV and FLIR sensor image fusion responses using proposed method ………. 61
Fig.4.4: Multispectral sensor image fusion responses using proposed method …………...62
Fig.4.5: CT and MRI image fusion responses using proposed method.…………………...63
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LIST OF ABBREVIATIONS
CT: Computerized Tomography
HR: High Resolution
LR: Low Resolution
MR/MRI: Magnetic Resonance (Imaging)
PSNR: Peak Signal to Noise Ratio
NDE: Non-Destructive Evaluation
DWT: Discrete Wavelet Transform
DT-CWT: Dual Tree Complex Wavelet Transform
HBT: Hyperbolic Tangent Filter
GUI: Graphical User Interface
HSV: Hue Saturation Value color representation
IHS: Intensity Hue Saturation color space
MRA: Multi Resolution Approach
PCA: Principal Component Analysis
SAR: Synthetic Aperture Radar
GUI: Graphical User Interface
LLTV: Low Light Television
FLIR: Forward-Looking-Infrared
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CHAPTER 1
Introduction to Image Fusion
Overview
Single Sensor Image Fusion System
Multi-Sensor Image Fusion System
Image Fusion Techniques
Motivation for Image Fusion Research
Objectives
Thesis Organisation
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Introduction
1. INTRODUCTION
1.1 Overview
Image fusion is the technique of merging several images from multi-modal sources with
respective complementary information to form a new image, which carries all the common as
well as complementary features of individual images. With the recent rapid developments in
the domain of imaging technologies, multisensory systems have become a reality in wide
fields such as remote sensing, medical imaging, machine vision and the military applications.
Image fusion provides an effective way of reducing thisincreasing volume of information by
extracting all the usefulinformation from the source images. Image fusion provides an
effective method to enable comparison andanalysis of Multi-sensor data having
complementary information about the concerned region. Image fusion creates new images
that are more suitable for the purposes of human/machine perception, and for further imageprocessing tasks such assegmentation, object detection or target recognition in applications
such as remotesensing and medical imaging.
Images from multiple sensors usually have different geometric representations, which
have to be transformed to a common representation for fusion. This representation should
retain the best resolution of either sensor. The alignment of multi-sensor images is also one of
the most important preprocessing steps in image fusion. Multi-sensor registration is also
affected by the differences in the sensor images. However, image fusion does not necessarily
imply multi-sensor sources. There can be single-sensor or multi-sensor image fusion,
whichhas been vividly described in this report.
Analogous to other forms of information fusion, image fusion is usually performed at one
of the three different processing levels: signal, feature and decision. Signal level image
fusion, also known as pixel-level image fusion, represents fusion at the lowest level, where a
number of raw input image signals are combined to produce a single fused image signal.
Object level image fusion, also called feature level image fusion, fuses feature and object
labels and property descriptor information that have already been extracted from individual
input images. Finally, the highest level, decision or symbol level image fusion represents
fusion of probabilistic decision information obtained by local decisionmakers operating on
the results of feature level processing on image data produced from individual sensors.
Figure 1.1 instances a system using image fusion at all three levels of processing. This
general structure could be used as a basis for any image processing system, for example an
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Introduction
automatic target detection/recognition system using two imaging sensors such as visible and
infrared cameras. The main objective is to detect and correctly classify objects in a presented
scene. The two sensors (1 and 2) survey the scene and register their observations in the form
of image signals. Two images are then fused atpixel-level to produce a third fused image and
are also passed independently to local feature extraction processes. The fused imagecan be
directly displayed for a human operator to aid better scene understanding or used in a further
local feature extractor. Feature extractors act as simple automatic target detection systems,
including processing elements such as segmentation, region characterization, morphological
processing and even neural networks to locate regions of interest in the scene. The product of
this process is a list of vectors describing the main characteristics of identified regions of
interest. Feature level fusion is then implemented on the feature sets produced from the
individual sensor outputs and the fused image. This process increases the robustness of the
feature extraction process and forms a more accurate feature set by reducing the amount of
redundant information and combining the complimentary information available in different
individual feature sets. Feature level fusion may also produce an increase in the
dimensionality of the feature property vectors.
The final processing stage in an ATD system is the classification stage. Individual sensor
and fused feature property vectors are input to local decision makers which represent object
classifiers, assigning each detected object to a particular class with proper decision. Decision
level fusion is performed on the decisions reached by the local classifiers, on the basis of the
relative reliability of individual sensor outputs and the fused feature set. Fusion is achieved
using statistical methods such as Bayesian inference and the Dempster-Schafer [1], [2], [3]
method with the aim of maximizing the probability of correct classification for each object of
interest. The output of the whole system is a set of classification decisions associated to the
objects found in the observed scene. The classification of some of the most popular image
fusion algorithms based on the computation source is illustrated in Figure.1.2.
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Introduction
Fig. 1.1 An information fusion system at all three processing
Fig. 1.2 Level classification of the various popular image fusion methods based on the computation source.
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Introduction
1.2 Single Sensor Image Fusion System
The basic single sensor image fusionscheme has beenpresented in Figure 1.3. The sensor
shown could be visible-band sensors or some matching band sensors. This sensor captures the
real world as a sequence of images. The sequence of images are then fused together to
generate anew image with optimum information content. For example in illumination variant
and noisy environment, a human operator may not be able to detect objects of his interest
which can be highlighted in the resultant fused image.
Fig. 1.3
Single Sensor Image Fusion System
The shortcoming of this type of systems lies behind the limitations of the imaging sensor
that is being used. The conditions under which the system can operate, the dynamic range,
resolution, etc. are all restricted by the competency of the sensor. For example, a visible-band
sensor such as the digital camera is appropriate for a brightly illuminated environment such
as daylight scenes but is not suitable for poorly illuminated situations found during night, or
under adverse conditions such as in fog or rain.
1.3 Multi-Sensor Image Fusion System
A multi-sensor image fusion scheme overcomes the limitations of a single sensor image
fusion by merging the images from several sensors to form a composite image. Figure
1.4illustrates a multi-sensor image fusion system. Here, an infrared camera is accompanying
the digital camera and their individual images are merged to obtain a fused image. This
approach overcomes the issues referred to before. The digital camera is suitable for daylight
scenes; the infrared camera is appropriate in poorly illuminated environments.
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Introduction
Fig.1.4 Multisensory Image Fusion System
The benefits of multi-sensor image fusion include [4]:
i.
Improved reliability – The fusion of multiple measurements can reduce noise and
therefore improve the reliability of the measured quantity.
ii.
Robust system performance – Redundancy in multiple measurements can help in
systems robustness. In case one or more sensors fail or the performance of a
particular sensor deteriorates, the system can depend on the other sensors
iii.
Compact representation of information – Fusion leads to compact representations.
For example, in remote sensing, instead of storing imagery from several spectral
bands, it is comparatively more efficient to store the fused information.
iv.
Extended range of operation – Multiple sensors that operate under different
operating conditions can be deployed to extend the effective range of operation.
For example, different sensors can be used for day/night operation.
v.
Extended spatial and temporal coverage – Joint information from sensors that
differ in spatial resolution can increase the spatial coverage. The same is true for
the temporal dimension.
vi.
Reduced uncertainty – Joint information from multiple sensors can reduce the
uncertainty associated with the sensing or decision process.
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Introduction
1.4 Image Preprocessing
Analogous to signal processing, there are very often some concerns that have to be
normalized before the final image fusion. Most of the time the images are geometrically
misaligned. Registration is the techniqueto establish a spatial correspondence between the
sensor images and to determine a spatial geometric transformation. The misalignment of
image features is induced by various factors including the geometries of the sensors, different
spatial positionsand temporal capture rates of the sensors and the inherent misalignment of
the sensing elements. Registration techniques align the images by exploiting the similarities
between sensor images. The mismatch of image features in multisensor images reduces the
similarities between the images and makes it difficult to establish the correspondence
between the images.
The second issue is the difference in spatial resolution between the images developed by
different sensors. There are several techniques to overcome this issue such as the
Superresolution techniques [5],[6]. Another methodology is to use multi-resolution image
representations so that the lower resolution imagery does not adversely affect the higher
resolution imagery.
1.5 Image Fusion Techniques
The most essential dispute concerning image fusion is to decide how to merge the sensor
images. In recent years, a number of image fusion methods have been projected [7]. One of
the primitive fusion schemes is pixel-by-pixel gray level average of the source images. This
simplistic method often has severe side effects such as dropping the contrast. Some more
refined approaches began to develop with the launching of pyramid transform in mid-80s.
Improved results were obtained with image fusion, performed in the transform domain. The
pyramid transform solves this purpose in the transformed domain. The basic idea is to
perform a multiresolution decomposition on each source image, then integrate all these
decompositions to develop a composite depiction and finally reconstruct the fused image by
performing an inverse multi-resolution transform. A number of pyramidal decomposition
techniques have beendeveloped for image fusion, such as, Laplacian Pyramid, Ratio-of-lowpass Pyramid, Morphological Pyramid, and Gradient Pyramid. Most recently, with the
evolutionof wavelet based multi resolution analysis concepts, the multi-scale wavelet
decomposition has begun to take the place of pyramid decomposition for image fusion.
Actually, the wavelet transform can be considered one special type of pyramid
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Introduction
decompositions. It retains most of the advantages for image fusion but has much more
complete theoretical support.The real Discrete Wavelet Transform (DWT) has the property of
good compression of signal energy. Perfect reconstruction is possible using short support
filters. The unique feature of DWT is the absence of redundancy and very low computation.
Therefore, DWT has been used extensively for Multi Resolution Analysis (MRA) based
image fusion. The Discrete Wavelet Transform primarily suffers from the various problems
(Ivan, W. Selesnick, Richard G. Baraniuk, and Kingsbury, N., 2005) such as oscillations,
aliasing, shift variance and lack of directionality. The ringing artefacts introduced by DWT
are also completely eliminated by the implementation of Dual Tree Complex Wavelet (DTCWT) based image fusion methods.
The research work proposed in this thesis deals with the development and implementation
of some novel Discrete Wavelet Transform based image fusion techniques. A novel image
fusion approach based on bilateral sharpness measure by the help of Dual-Tree Complex
Wavelet Transform has been proposed in the later part of the thesis.For all the image fusion
work demonstrated in this thesis, it has been assumed that the input images must be of the
same scene, i.e. the fields of view of the sensors must contain a spatial overlap. Again, the
input images are assumed to be spatially registered and of equal size as well as equal spatial
resolution.
1.6 Motivation
The motivation for image fusion research is mainly due to the contemporary
developments in the fields of multi-spectral, high resolution, robust and cost effective image
sensor design technology. Since last few decades, with the introduction of these multisensory imaging techniques, image fusion has been an emerging field of research in remote
sensing, medical imaging, night vision, military and civilian avionics, autonomous vehicle
navigation, remote sensing, concealed weapons detection, various security and surveillance
systems applications.There has been a lot of improvement in dedicated real time imaging
systems with the high spatial, spectral resolution as well as faster sensor technology. The
solution for information overloading can be met by a corresponding increase in the number of
processing units, using faster Digital Signal Processing (DSP) and larger memory devices.
This solution however, can be quite expensive. Pixel-level image fusion algorithms represent
an efficient solution to this problem of operator related information overload. Pixel Level
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Introduction
fusion effectively reduces the amount of data that needs to be processed without any
significant loss of useful information and also integrates information from multi-spectral
sensors. Explicit inspiration for the research work has come from the necessity to develop
some competent image fusion techniques along with the enhancement of existing fusion
technologies. Furthermore, aNon-Destructive Testing (NDT) has been a popular analysis
technique used in industrial product evaluation and for troubleshooting in research work
without causing damage which can also save both money and time. There has always been
the requirement of some novel edge detection techniques based on NDT for detection of
faults in industrial products suppressing the diversity and complexity of measuring
environment.Using the wavelet based Multiresolution analysis techniques and some efficient
edge detection technique, it is possible to accomplish distortion less fusion which results in a
reduced loss of input information. The proposed novel fusion methods in this research work
also exhibit improvement with respect to objective as well as subjective evaluation point of
view as compared to some of the existing image fusion techniques.
1.7 Objectives
The objectives of the thesis are as follows.
i. Development of a novel crack detection technique using discrete wavelet transform
based image fusion suppressing the diversity and complexity of imaging environment.
ii. Development of an effective edge detection technique for multi-focus images using
Dual-Tree Complex Wavelet Transform (DT-CWT) based image fusion technique.
iii. Development and implementation of an improved image fusion technique based on
Bilateral Sharpness Criterion in DT-CWT Domain.
1.8 Thesis Organisation
Including the introductory chapter, the thesis is divided into 5 chapters. The organization
of the thesis is presented below.
Chapter-2 Literature Review
This chapter illustrates the chronological evolution of some competitive image fusion
algorithms from various publications both in the fields of pixel-level fusion and performance
evaluation.
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Introduction
Chapters-3 Image Fusion and Edge Detection
This chapter is devoted to the first and second objectives. In the first part of this chapter,
the complete methodology and illustration of crack detection technique for non-destructive
evaluation in civil structures has been performed using Discrete Wavelet Transform (DWT)
based image fusion. It also reveals the detail exploration of two competitive edge detectors,
i.e. Canny edge detector and Hyperbolic Tangent (HBT) based edge detector. The second part
of this chapter proposes a novel edge detection technique for multi-focus images using
complex wavelet based image fusion algorithm.
Chapter – 4 Image Fusion based on Bilateral Sharpness Criterion in DT-CWT Domain
In this chapter, an improved DT-CWT based image fusion technique has been developed
to generate a resultant image with better perceptual as well as quantitative image quality
indices. The competency of the proposed technique is properly justified by comparing its
response with traditional DWT as well as Complex Wavelet based image fusion.
Chapter – 5 Conclusions
The overall conclusion of the thesis is presented in this chapter. It also contains some
future
research
areas,
which
need
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attention
and
further
investigation.
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Literature Review
CHAPTER 2
Literature Review
Multiresolution Pyramidal Image Fusion
Wavelet Transform based Image Fusion Algorithms
Discrete Wavelet Transform
Classification of Wavelets
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Literature Review
2 LITERATURE REVIEW
Since last few decades, an extensive number of approaches to fuse visual image
information. These techniques vary in their complexity, robustness and sophistication.
Remote sensing is perhaps one of the leading image fusion applications with a large number
of dedicated publications. The main principle of some of the popular image fusion algorithms
have been discussed below.
 Fusion using Principle Component Analysis (PCA): The PCA image fusion method [8]
basically uses the pixel values of all source images at each pixel location, adds a weight
factor to each pixel value, and takes an average of the weighted pixel values to produce
the result for the fused image at the same pixel location. The optimal weighted factors are
determined by the PCA technique. The PCA image fusion method reduces the
redundancy of the image data.
 Super-resolution image reconstruction: Super-resolution (SR) reconstruction [9] is a
branch of image fusion for bandwidth extrapolation beyond the limits of a traditional
electronic image system. Katartzis and Petrou describe the main principles of SR
reconstruction and provide an overview of the most representative methodologies in the
domain. The general strategy that characterizes super-resolution comprises three major
processing steps which are low resolution image acquisition, image registration/motion
compensation, and high resolution image reconstruction. Katartzis and Petrou presented a
promising new approach based on Normalized Convolution and a robust Bayesian
estimation, and perform quantitative and qualitative comparisons using real video
sequences..
 Image fusion schemes using ICA bases: Mitianoudis and Stathaki demonstrate the
efficiency of a transform constructed using Independent Component Analysis (ICA) and
Topographic Independent Component Analysis based for image fusion in this study [10].
The bases are trained offline using images of similar context to the observed scene. The
images are fused in the transform domain using novel pixel-based or region-based rules.
An unsupervised adaption ICA-based fusion scheme is also introduced. The proposed
schemes feature improved performance when compared to approaches based on the
wavelet transform and a slightly increased computational complexity. The authors
introduced the use of ICA and topographical ICA based for image fusion applications.
These bases seem to construct very efficient tools, which can complement common
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Literature Review
techniques used in image fusion, such as the Dual-Tree Wavelet Transform. The proposed
method can outperform the wavelet approaches. The Topographical ICA based method
offers a more accurate directional selectivity, thus capturing the salient features of the
image more accurately.
 Region-based multi-focus image fusion: Li and Yang first describe the principle of
region-based image fusion in the spatial domain [11]. Then two region-based fusion
methods are introduced. They proposed a spatial domain region-based fusion method
using fixed-size blocks. Experimental results from the proposed methods are encouraging.
More specifically, in spite of the crudeness of the segmentation methods used, the results
obtained from the proposed fusionprocesses, which consider specific feature information
regarding the source images, are excellentin terms of visual perception. The presented
algorithm, spatial domain region-based fusion method using fixed-size blocks, is
computationally simple and can be applied in real time. It is also valuable in practical
applications. Although the results obtained from a number of experiments are promising,
there are more parameters to be considered as compared to an MR-based type of method,
such as the wavelet method. Adaptive methods for choosing those parameters should be
researched further. In addition, further investigations are necessary for selecting more
effective clarity measures.
 Image fusion techniques for non-destructive testing and remote sensing application:
Theauthors present several algorithms of fusion based on multi-scale Kalman filtering
and computational intelligence methodologies [12]. The proposed algorithms areapplied
to two kinds of problems: a remote sensing segmentation, classification, and object
detection application performed on real data available from experiments and a nondestructive testing/evaluation problem of flaw detection using electro-magnetic and
ultrasound recordings. In both problems, the fusion techniques are shown to achieve a
modest superior performance with respect to the single-sensor image modality. The joint
use of the eddy current and ultrasonic measurements is suggested because of the poor
results that are obtained by processing each single recorded type of signal alone.
Therefore, both measurements are jointly processed, and the information used to perform
the classification has been extracted at three different levels: pixel, feature, and symbol.
The numerical performance of these techniques has been compared by using the
probability of detection and probability of false alarm. Experiments performed on real
data confirmed the effectiveness of the proposed SL based approach, by maximizing the
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probability of detection and achieving an acceptable probability of false alarm with
respect to the PL and FL fusion techniques.
2.1 Multi-resolution Pyramidal Image Fusion
Hierarchical multiscale and multiresolution image processing techniques, as mentioned
previously, are the basis for the majority of sophisticated image fusion algorithms. The
usefulness of such approaches to image processing was initially established by Burt and
Adelson [13, 14]. Multiresolution processing methods enable an image fusion system to fuse
image information in a suitable pyramid format. Image pyramids are made up of a series of
Sub-band signals, organized into pyramid levels, of decreasing resolution each representing a
portion of the original image spectrum. Information contained within the individual sub-band
signals corresponds to a particular scale range, i.e. each sub-band contains features of a
certain size. Coarse resolution pyramid levels contain large scale information while those of
higher resolution contain finer detail from the original image signal. Fusing images in their
pyramid representation therefore, enables the fusion system to consider image features of
different scales separately even when they overlap in the original image. By fusing
information in the pyramid domain, superposition of features from different input images is
achieved with a much smaller loss of information than in the case of single resolution
processing where cut and paste or arithmetic combination methods are used. Furthermore,
this scale reparability also limits damage of sub-optimal fusion decisions, made during the
feature selection process, to a small portion of the spectrum. These properties make
multiresolution fusion algorithms potentially more robust than other fusion approaches.
Multiresolution image processing was first applied to pixel-level image fusion using
derivatives of the Gaussian pyramid representation [13] in which the information from the
original image signal is represented through a series of (coarser) low-pass approximations of
decreasing resolution. The pyramid is formed by iterative applicationof low-pass filtering,
usually with a 5x5 pixel Gaussian template, followed by subsampling with a factor 2, a
process also known as reduction. All multiresolution image fusion systems based on this
general approach exhibit a very similar structure which is shown in the block diagram of
Figure 2.1. Input images obtained from different sensors are first decomposed into their
Gaussian pyramid representations. Gaussian pyramids are then used as a basis for another
type of high pass pyramids, such as the Laplacian, which contain, at each level, only
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information exclusive to the corresponding level of the Gaussian pyramid. HP pyramids
represent a suitable representation for image fusion. Important features from the input images
are identified as significant coefficients in the high pass pyramids and they are transferred
(fused) into the fused image by producing a new, fused, high pass pyramid from the
coefficients of the input pyramids. The process of selecting significant information from the
input pyramids is usually referred to as feature selectionand the whole process of forming a
new composite pyramid is known as pyramid fusion. The fused pyramid is transformed into
the fused image using a multiresolution reconstruction process. This process is dual to the
decomposition andinvolves iterative expansion (up-sampling) of the successive levels of the
fused Gaussian pyramid and combination (addition in the case of Laplacian pyramids) with
the corresponding levels of the fused high pass pyramid, known as expandoperation.
Fig. 2.1 Pyramid Transform description with an example
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The first multiresolution image fusion research work done using derivatives of the
Gaussian pyramid was at the TNO Institute for perception in the Netherlands. Toet et. al.
presented an algorithm based on the contrast or Ratio of Low Pass (RoLP) pyramid [15]. In
this representation each level of the RoLP pyramid is formed as the ratio of the corresponding
level of the Gaussian pyramid and the expanded version of its low-pass approximation (the
next level). The coefficients of the RoLP pyramid, reduced by unity, represent an
approximation of the local luminance contrast, C, as defined by Weber:
C
L
1
Lb
(2.1)
Where,L is the local luminance given by the signal value at the current level and Lb is the
background luminance approximated by its low-pass approximation. RoLP pyramid fusion is
achieved as the maximization of the local luminance contrast at each position and scale, by
choosing and transferring the input pyramid coefficient corresponding to the greatest local
contrast into the fused pyramid. Finally, the fused image is obtained from the fused RoLP
pyramid by recursively expanding the lowest level of the Gaussian pyramid and multiplying
by the corresponding levels of the fused RoLP pyramid until all the levels of the fused
pyramid are used up. Further to this fusion system, the same author presented a multiscale
contrast enhancement technique that increases the performance of the RoLP fusion process
[16]. Contrast enhancement results in fusion performance that is independent of changes in
lighting and gray-level gradients, and is achieved through non-linear multiplication of
successive layers of the RoLP pyramid. The usefulness of this technique was demonstrated
on fusion of degraded visual and infrared images.
The contrast pyramid [16] was also used in another interesting fusion approach presented
by Cui et. al. [17]. In their case, the fused pyramid was obtained by multiplying the
corresponding levels of the input contrast pyramids. The main advantage of using this
pyramid approach is that by avoiding the selection process, an efficient implementation can
be obtained. Indeed, the authors reported real time operation at input image resolution level
of 256x256 pixels and quasi real time at 512x512, when implemented on high-speed DSP
devices. Generally however, the RoLP (contrast) pyramid fusion suffers from instability due
to the multiplication/division operations used in the decomposition and reconstruction which
often leads to the introduction of false edges in the fused image and amplification of noise
that might be present in the inputs. The quality of the fused image is clearly good and
reconstruction artifacts are not easily noticeable, however false edges are also obvious, such
as on the roofs in the top right of the image.
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An alternative multiresolution pyramid representation derived from the Gaussian and
used for pixel-level image fusion is the Laplacian pyramid [18, 19]. Similarly to the RoLP
pyramid used by Toet, each level of the Laplacian pyramid is formed as a difference between
the corresponding level of the Gaussian and the expanded version of its low-pass
approximation. Although the coefficients (pixels) of the Laplacian pyramid are not direct
representations of the local contrast like those of the RoLP pyramid, the value of these
coefficients is still proportional to the saliency of the high frequency detail at a given
location. Saliency in the context of information fusion signifies perceptual importance of
visual information in an image.
Pavel et. al. [18] used the Laplacian pyramid approach to fuse simulated passive
millimeter wave (PMMW) images with synthetic images formed from the information
obtained from terrain databases. They use arithmetic pyramid fusion, where the fused
pyramid coefficients take the value of a weighted sum of the input coefficients. The
corresponding equation is
DlF (n, m)  K lA (n, m) DlA (n, m)  K lB (n, m) DlB (n, m)
(2.2)
Where DlF (n, m) , DlA (n, m) and DlB (n, m) represent coefficients of the fused and input
pyramids, at level l and position (n, m), respectively. Weighting coefficients K lA (n, m) ,
K lB (n, m) determine the relative influence of each input on the fused pyramid at thatposition
and scale. In the system by Pavel et. al., the size of the weighting coefficientsdepends on the
local uncertainty of the PMMW image, measured through variance, andthe level of
correlation between the input pyramid coefficients [18].
The pyramid fusion method used by Akerman [19] employs a coefficient selection
approach. It is based on a pixel by pixel selection but the selection rule was left to be flexible
and application dependent. The most common coefficient selection is the pixel-based select
max approach where the fused coefficient takes the value of the input with the largest
absolute value, as expressed by Equation 2.3 as.
DlF (n, m) =
DlA (n, m) if DlA (n, m)  DlB (n, m)
(2.3)
DlB (n, m) Otherwise
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The usefulness of Laplacian pyramid fusion in remote sensing applications was further
demonstrated in the work by Aiazzi et. al. [20]. They used a generalized Laplacian pyramid
(GLP) approach to solve the most common problem in remote sensing image fusion that of
increasing the resolution of multi-spectral (color) images with high resolution panchromatic
(monochrome) images. By replacing the reduce and expand operations of the Gaussian
pyramid multiresolution decomposition reconstructionprocesses with reduce{expand{ }} and
expand{reduce{ }},respectively, using low pass filters with appropriate cut-off frequencies
and corresponding decimationinterpolation factors (p and q), the GLP approach allows a
reduction in resolution by a rational scale factor, p : q. In this way, images whose resolution
ratios are not powers of 2 can be fused without having to be resampled. Fusion resolution
enhancement is then achieved by simple level replacement in the pyramid domain when the
highest resolution level of the panchromatic Laplacian pyramid becomes the missing highest
resolution level for each channel pyramid of the multi-spectral image. This scheme is
significant in its applicability to a wide range of remotely sensed data in addition to slightly
superior performance compared with the wavelet based approach.
The gradient pyramid fusion presented by Burt and Kolczynski is another important
pixel-level image fusion method based on the Gaussian pyramid approach [21]. Their work
represents an extension of the Laplacian pyramid representation in that visual information, in
the gradient pyramid, is separated into sub-bands according to direction as well as scale.
Gradient pyramid is derived from the filter-subtract-decimate (FSD) Laplacian pyramid by
applying four directionally sensitive filters. When applied at all levels of scale, each filter
removes all the information that does not fall within a well-defined orientation range, which
results in four oriented Laplacian pyramids which are then fused independently. That the four
directional filters are complementary means that the original Laplacian pyramid is obtained
by a direct summation of the four oriented pyramids. Indeed, the final fused image is
obtained by conventional Laplacian pyramid reconstruction from the fused pyramid produced
in this way.
More recently, a multi-scale image fusion system for visual display was proposed by Peli
et. al.[22]. Multi-scale image analysis is based on a series of oriented octave band-pass filters
which separate the original input spectra into a series of sub-bands according to scale and
orientation. Sub-band signals of different input images are fused by a simple pixel by pixel
selection using a criterion based on the local contrast evaluation. There is also an
improvement using a different number of orientations in multi-scale from two to four
different orientations.
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There are various types of pyramid transforms. Some of these are as the follows:
 Filter Subtract Decimate Pyramid
 Gradient Pyramid
 Laplacian Pyramid
 Ratio Pyramid
 Morphological Pyramid
The concise multi-resolution analysis based pyramidal image fusion methodology can be
illustrated with the three major phases:
 Decomposition
 Formation of the initial image for decomposition.
 Recomposition
Decomposition is the process where a pyramid is generated successively at each level of
the fusion. The depth of fusion or number of levels of fusion is pre decided. The number of
levels offusion is decided based on the size of the input image. The recomposition process, in
turn, formsthe finally fused image, level wise, by merging the pyramids formed at each level
to the decimated input images. Decomposition phase basically consists of the following steps.
These steps are performed number of times till the levels to which the fusion will be
performed.
 The different pyramidal methods have a predefined filter with which the input
images convolved/filtered.
 Formation of the pyramid for the level from the filtered input images usingBurt’s
method or Li’s Method.
 The input images are decimated to half their size, which would act as the input
imagematrices for the next level of decomposition.
Merging the input images is performed after the decomposition process. This resultant image
Matrix would act as the initial input to the recomposition process. The finally decimated
input pair of images is worked upon the decimated input image by means of suitable fusion
rules. The recomposition is the process wherein, the resultant image is finally developed from
the pyramids formed at each level of decomposition. The various steps involved in the
recomposition phase are discussed below.
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 The input image to the level of recomposition is undecimated
 The undecimated matrix is convolved/filtered with the transpose of the filter
vector used in the decomposition process
 The filtered matrix is then merged, by the process of pixel intensity value
addition, with the pyramid formed at the respective level of decomposition.
 The newly formed image matrix would act as the input to the next level of
recomposition.
 The merged image at the final level of recomposition will be the resultant fused
image. The flow of the pyramid based image fusion can be explained by the
following an example of multi-focus image as depicted in Fig.2.1
2.2 Wavelet Transform based Image Fusion Algorithms
The Discrete Wavelet Transform (DWT) was successfully employed in the field of image
processing with the introduction of Mallat’s algorithm [25]. It enabled the application of twodimensional DWT using one dimensional filter banks. DWT based multiresolution approach
has been implemented successfully in chapter 3. Its general structure, briefly describe here, is
very similar to that of the Gaussian pyramid based approach. Input signals are transformed
using the wavelet decomposition process into the wavelet pyramid representation. Contrary to
Gaussian pyramid based methods, high pass information is also separated into different subband signals according to orientation as well as scale.
The scale structure remains logarithmic, i.e. for every new pyramid level the scale is
reduced by a factor of 2 in both directions. The wavelet pyramid representation has three
different sub-band signals containing information in the horizontal, vertical and diagonal
orientation at each pyramid level. The size of the pyramid coefficients corresponds to
“contrast” at that particular scale in the original signal, and can therefore, beused directly as a
representation of saliency. In addition, wavelet representation is compact, i.e. the overall size
of all sub-band signals in the pyramid is the same as the size of the original image The size
difference, as well as the lack of expansion operations during wavelet decomposition makes
the wavelet approach much more efficient in terms of the processing required to fuse two
images. Advantages of these properties in fusion applications were demonstrated by the
considerable number of publications on the subject of wavelet image fusion in the last five
years.
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One of the first wavelet based fusion systems was presented by Li et. al.[24]. It uses
Mallat's technique to decompose the input images and an area based feature selection for
pyramid fusion. In the proposed system, Li et. al. use a 3x3 or a 5x5 neighborhood to
evaluate a local activity measure associated with the center pixel. It is given as the largest
absolute coefficient size within the neighborhood. In case of coefficients from the two input
pyramids exhibiting dissimilar values, the coefficientwith the largest activity associated with
it is chosen for the fused pyramid. Otherwise, similar coefficients are simply averaged to get
the fused value. Finally, after the selection process, a majority filter is applied to the binary
decision map to remove bad selection decisions caused by noise “hot-spots”. This fusion
technique works well at lower pyramid levels, but for coarser resolution levels, the area
selection and majority filtering, especially with larger neighborhood sizes, can significantly
bias feature selection towards one of the inputs.
Almost contemporarily with the formermethod, wavelets in image fusion were also
considered by Chipman et. al. [25]. The algorithm was basically deals with the general
aspects of wavelet fusion. A comparison was exercised between the conventional isotropic
and more exotic tensor wavelet pyramid representation, in which decomposition is performed
in one direction only. The inference was that isotropic representation produces better fusion
results. For pyramid fusion methods they advised flexibility, suggesting that an “optimal
solution” should be sought for each application independently. More importantly, they
considered problems associated with wavelet image fusion. Miss-registration of the inputs
and the loss of coefficients were deemed as having the worst effects on the fused image
quality. These effects produce what is known as "ringing" artifacts – shadowing and rippling
effects, especially around strong edges. Finally, the authors also considered noise removal
incorporated in the fusion process. They suggested hard thresholding of wavelet coefficients
at lower pyramid levels as a possible solution.
Another significant contribution to the field of wavelet image fusion was given by Yocky
[26]. He investigated wavelet image fusion to increase the resolution of multi-spectral
satellite images with high resolution panchromatic data. The basic principle is that of pyramid
enlargement, i.e. higher detail levels of the panchromatic pyramid are appended to the multispectral pyramids to provide the missing detail information. The number of levels added
depends on the final resolution requirement or the maximum resolution available in the
panchromatic pyramid. Wavelet pyramid extension, to increase resolution of multi-spectral
low resolution satellite images, was also proposed by Garguet-Duport et. al. [27] in a system
very similar to that proposed by Yocky [26]. Concealed weapon detection (CWD) is another
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application which has benefited from the use of multiresolution wavelet based image fusion
techniques.
The CWD system proposed by Ramac et. al. [28] uses the same image fusion method
based on the wavelet decomposition followed by Burt and Kolczynski's feature selection
algorithm. This time however, image fusion is applied to low level processed multisensory
images obtained from infrared and millimeter wave (MMW) cameras. Image fusion is
applied after morphological filtering, but prior to feature extraction. Their results again show
that fusion improves detection and that morphological filtering removes some unwanted
noise artifacts that degrade the fused result.
Wang et. al. [29] also proposed a wavelet based image fusion algorithm for fusion of low
light dual spectrum (visual and infrared) images. The system uses conventional wavelet
decomposition technique and a target contrastmaximization mechanism to fuse input
pyramids. Target contrast is evaluated in according to the ratio of the wavelet coefficient and
local brightness evaluated over a 5x5 template.
Chibani and Houacine [30] examined the effects of multiscale versus multiresolution
wavelet approaches to image fusion. Multiscale wavelet approach corresponds to the
redundant wavelet pyramid representation where all sub-band signals remain at the same
resolution, i.e. there is no sub-sampling. The multiresolution approach is the isotropic
decomposition obtained by applying Mallat's algorithm. The authors report that fusion using
the redundant representation exhibits better results in terms of preserving the consistency of
dominant features and the fidelity of finer details when fusing images with different focus
points. The reason for this is the reduction in the reconstruction error (ringing artifacts)
caused by the reduced sensitivity of the over complete multiscale wavelet fusion to
discontinuities introduced in the pyramid fusion process.
A mechanism for wavelet fusion of image sequences has been also proposed by
Rockinger and Fechner [31]. To achieve temporal stability and consistency in the fused
sequence, the system uses a shift invariant extension of the two dimensional discrete wavelet
transform (SIDWT). SIDWT is a multiscale, redundant wavelet representation that does not
decimate the filtered signals. Instead, analysis filters are interpolated by inserting zeros
between impulse response coefficients to change the pass-band cut-off. Pyramid fusion of
input sequences is implemented through selective fusion of sub-band coefficients and
modified averaging fusion of the low-pass residuals. The SIDWT based fusion is reported to
produce significantly better results in terms of the temporal stability in fused multisensor
sequences compared to conventional multiresolution DWT fusion.
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Finally, Zhang [32] presented a wide-ranging exploration of multiresolution pixel-level
image fusion. A number of different multiresolution and pyramid fusion approaches were
verified. Laplacian and both isotropic and shift invariant wavelet representations were tested
with matching pyramid fusion mechanisms. In terms of pyramid fusion, different vertical and
horizontal integration/grouping methods, area and pixel based selection mechanisms and
selection consistency verification strategies were combined to obtain “optimal” fusion.
According to the results presented, the shift invariant wavelet representation fusion using a
rank-filter-based activity measurement, evaluated in a window of coefficients as criterion for
a choose-max selection with multiscale selection grouping and followed by region based
consistency verification, produced the best results. Further to the problem of image fusion,
this work also considers a number of other issues connected to image fusion such as
multisensor image registration and fusion performance in the presence of sensor noise.
2.2.1 Discrete wavelet transform
The Wavelet Transform provides a time-frequency representation of the signal. It was
developed to overcome the shortcoming of the Short Time Fourier Transform (STFT), which
can also be used to analyze non-stationary signals. While STFT gives a constant resolution at
all frequencies, the Wavelet Transform uses multi-resolution technique by which different
frequencies are analyzed with different resolutions.
Classification of wavelets
We can classify wavelets into two fundamental classes: (a) orthogonal and (b) biorthogonal.
(a)Features of orthogonal wavelet filter banks
The coefficients of orthogonal filters are real numbers. The filters are of the same length and
are not symmetric. The low pass filter, G and the high pass filter, H are related to each other
0
H 0 ( z )  Z  N G0 (Z 1 )
by
0
(2.4)
The two filters are alternated flip of each other. The alternating flip automatically
gives double-shift orthogonality between the low pass and high pass filters, i.e., the scalar
product of the filters, for a shift by two is zero. i.e., ΣG[k]H[k-2l] = 0, where k,lЄ Z . Perfect
reconstruction is possible with alternating flip. Orthogonal filters offer a high number of
vanishing moments. This property is useful in many signal and image processing
applications. They have regular structure which leads to easy implementation and scalable
architecture.
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(b)Features of biorthogonal wavelet filter banks
In the case of the biorthogonal wavelet filters, the low pass and the high pass filters do
not have the same length. The low pass filter is always symmetric, while the high pass filter
could be either symmetric or anti-symmetric. The coefficients of the filters are either real
numbers or integers. For perfect reconstruction, biorthogonal filter bank has all odd length or
all even length filters. The two analysis filters can be symmetric with odd length or one
symmetric and the other antisymmetric with even length. Also, the two sets of analysis and
synthesis filters must be dual.
Wavelet families
There are a number of basis functions that can be used as the mother wavelet for Wavelet
Transformation. Since the mother wavelet produces all wavelet functions used in the
transformation through translation and scaling, it determines the characteristics of the
resulting Wavelet Transform. Therefore, the details of the particular application should be
taken into account and the appropriate mother wavelet should be chosen in order to use the
Wavelet Transform effectively. Figure 2.2 illustrates some of the commonly used wavelet
functions.
Fig. 2.2 Wavelet families (a) Haar (b) Daubechies4 (c) Coiflet1 (d) Symlet2 (e) Meyer (f) Morlet (g) Mexican
Hat.
Haar wavelet is one of the oldest and simplest wavelet. Daubechies wavelets are the most
popular wavelets. They represent the foundations of wavelet signal processing and are used in
numerous applications. There exists another type of wavelets called Maxflat wavelets. Here,
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the frequency responses have maximum flatness at frequencies 0 and π. This is a very
desirable property in some applications. The Haar, Daubechies, Symlets and Coiflets are
compactly supported orthogonal wavelets. These wavelets along with Meyer wavelets are capable
of perfect reconstruction. The Meyer, Morlet and Mexican Hat wavelets are symmetric in shape.
The wavelets are chosen based on their shape and their ability to analyse the signal in a particular
application.
The wavelet transform provides a multi-resolution decomposition of an image in a biorthogonal basis and results in a non-redundant image representation. This basis is called
wavelets, and they are functions generated from one single function, called mother wavelet,
by dilations and translations. Although this is not a new idea, whatmakes this transformation
more suitable than other transformations such as the Fourier Transform or the Discrete
Cosine Transform, is the ability of representing signal features in both time and frequency
domain. Figure 2.3 shows an implementation of the discrete wavelet transform. In this filter
bank, the input signal goes through two one-dimensional digital filters. One of them, H0,
performs a high pass filtering operation and the other H1 low pass one. Each filtering
operation is followed by subsampling by a factor of 2. Then, the signal is reconstructed by
first up sampling, then filtering and summing the sub bands.
Fig. 2.3 Two channel wavelet filter bank
The synthesis filters F0and F1 must be specially adapted to the analysis filters H0 and H1
to achieve perfect reconstruction. By considering the z-transfer function of the 2-chanel filter
bank shown in Figure 2.3, it is easy to obtain the relationship that those filters need to satisfy.
After analysis, the two subbands are:

1
H 0 ( z 1 / 2 ) X ( z 1 / 2 )  H 0 ( z 1 / 2 ) X ( z 1 / 2 )
2
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
(2.5)
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
1
H 1 ( z 1 / 2 ) X ( z 1 / 2 )  H 1 ( z 1 / 2 ) X ( z 1 / 2 )
2

(2.6)
The combined filter bank in z-domain is given by
^
X ( z) 
1
F0 ( z) H 0 ( z)  F1 ( z) H1 ( z)X ( z)  1 F0 ( z) H 0 ( z)  F1 ( z) H1 ( z)X ( z) (2.7)
2
2
In order to eliminate the problems of aliasing and distortion, the following conditions
must be satisfied:
F0 ( z)  H1 ( z)
F1 ( z )   H 0 ( z )
The final filtering equation with the delay term by Smith and Barnwell is presented as:
^
X ( z) 


1 N
z H 0 ( z ) H 0 ( z 1 )  H 0 ( z ) H 0 ( z 1 ) X ( z )
2
(2.8)
The multiscale pyramid decomposition and reconstruction of an image with high and low
pass filtering is shown below.
Fig. 2.4 Filter bank structure of the DWT Analysis.
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Fig. 2.5 Filter bank structure of the reverse DWT Synthesis
Successive application of this decomposition to the LL sub band gives rise to apyramid
decomposition where the sub images correspond to different resolution levels and
orientations.
Fig. 2.6 Image decomposition. Each subband has a natural orientation.
After one level of decomposition, there will be four frequency bands, namely Low-Low (LL),
Low-High (LH), High-Low (HL) and High-High (HH). The next level decomposition is just
applied to the LL band of the current decomposition stage, which forms a recursive
decomposition procedure. Thus, an N-level decomposition will finally have 3N+1 different
frequency bands, which include 3N high frequency bands and just one LL frequency band.
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Image Fusion & Edge Detection
CHAPTER 3
Image Fusion & Edge Detection
Crack Detection using Image Fusion
Edge Detection Technique for Multi-focus Images using Image Fusion
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Image Fusion & Edge Detection
3. IMAGE FUSION AND EDGE DETECTION
Analysis of image contents has been a substantial target for computer vision as well as
image processing researchers since last few decades. An image carries variety of information
regarding contour, colour, as well as orientation. The first step for contour extraction begins
with the detection of edges. This realism exposes the real significance of edge detection
techniques in image processing field. Edge detection has a wide range of applications in
image compression, enhancement of images, watermarking, morphological operations, and
restoration process and so on. The most important advantage of edge detection is that it
reduces the bulky data in an image, upholding the structural attributes for further processing.
The introduction of multi-sensory image fusion techniques have pointed towards a new
dimension of research work in edge detection process. This chapter of the research work
illustrates the development and implementation of some novel edge detection techniques
using image fusion algorithms.
3.1 Crack Detection Using Image Fusion
Since last few decades, Non Destructive Technique (NDT) has been concerning field of
research for quality evaluation of civil structures, aerospace engineering and industrial
products. In civil structures, the typical foundation crack will run vertically or at an angle.
Although human operator based crack detection methods have successfully illustrated that by
manually tracking the start and end of a crack, one can use pixel-based algorithms to define
the crack characteristics. Many literatures concerning tracking of defects in civil structures
are unable to identify the crack edges accurately due to poor contrast, uneven illumination
and noisy environment. Complications due to the inherent noise in the scanning process,
irregularly shaped cracks, as well as wide range of background patterns are also challenges
for error free detection in camouflaged environment. Therefore a new crack detection
technique is required which is based on Non Destructive Evaluation (NDE) along with some
efficient edge detection algorithms and an efficient image fusion technique to combat
contrast, noise sensitivity and uneven illumination. Since more than 25 years, so many
systems have been developed which basically deals with detection of linear features on optic
imaging [33]. Basically it has been tried to combine a local criterion using evaluating
radiometry and a global criterion using wide scale knowledge for edges to be detected. In
many cases local criterion are insufficient in detecting very fine crack edges. Some classical
gradient-magnitude (GM) methods [34], [35] are usually dependent on edge strength; hence,
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weaker edges due to texture may not be detected. An alternative method for detecting edges
regardless of their magnitude is being proposed [36]. It is based on the computation of the
cosine of the projection angles between neighbourhoods and predefined edge filters. So it is
otherwise known as an angle-based (AN) method. But this technique is very sensitive to
noise and uneven illumination. Local thresholding of image gradients are also sensitive to
uneven illumination since they inhibit low luminance regions. The improved method based
on phase congruency described the frequency domain image representation [37]. Since an
edge exists near points of maximum phase congruency, such methods are invariant towards
uneven illumination and low contrast. Due to the use of the log polar Gabor filter, they
produce poorer edge localization in those false edges and are detected in the vicinity of sharp
transitions. A contrast invariant edge detection method [38] based on the Helmholtz principle
describes edges as geometric structures with large deviations from randomness; but, sensitive
to the window size and edge localization. The other filter projected by Marr and Hildreth
suffers from the problems affined to zero-crossing approach [34]. This approach is basically
undeviating in edge localization, provided these are properly separated when the SNR in the
image is high. Again the localization of the real edge dislodges for a bounded width staircase
steps. The secondary issue is related to the identification of false edges. Laplacian of
Gaussian filter also can’t deal with the missing edges. However, merging Laplacian of
Gaussian filtering and zero crossing approach is a unmanageable job. Because, an edge does
not cope with a zero crossing for very confined number of steps. A robust edge detection
algorithm [39] produces superior result than the methods discussed above. This method
basically emphasizes on optimizing two of Canny’s criteria- accurate edge detection and
localization, without explicitly including the third criterion i.e. minimal response.
3.1.1 Proposed crack detection technique
We have proposed a model for an efficient and reliable crack detection, which combines
the best features of canny edge detection algorithm and Hyperbolic Tangent filtering
technique using an efficient Max-Mean image fusion rule. Here the detection architecture
consists of the some major steps as follows:
1. Acquisition of concerned wall image.
2. Crack detection using two efficient algorithms.
3. Wavelet decomposition and Fusion.
The proposed algorithm is shown in Fig.3.1
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Concerned Wall Image
Canny Edge
Detector
HBT Edge
Detector
HAAR DWT
Max-Mean Fusion
Inverse Wavelet Transform
Cracks Detected
Fig .3.1 Proposed crack detection algorithm
Acquisition of concerned wall image
Since the quality of detection result dominantly depend on the quality of the acquisition
process, the choice of acquisition system must be done carefully. Normally image acquisition
by means of 2D sensors needs image processing technique. In this experimental work , the
cracked wall image sample is acquired by means of a camera with focal length of 4mm,
exposure time: 0.002 sec, max aperture: 3.5. The lighting system should be designed in order
to preserve the crack edges which may not well contrast and negligible as compared to wall
image .The illumination problem can be solved by means of a stereoscopic system.
Crack Detection
The edge detection algorithm [39] is based on the actual profiles of image edges and it
optimizes only two of Canny’s criteria i.e. accurate edge detection and localization. It doesn’t
include the third criterion- minimal response i.e. a given edge in the image should only be
marked once, and where possible, image noise should not create false edges. So we have
selected canny detector to fulfil the third criterion. Again, from the spatial and frequency
properties of HBT filter, It is clearly observed that the family of FIR HBT filters has a narrow
bandwidth, indicating better noise reduction compared to Canny’s Gaussian first derivative.
Hence, our proposed edge detection architecture gives superior result by the fusion of
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common as well as complementary features of Canny and HBT based edge detection
techniques.
a) Canny edge detector
Canny considered three criteria desired for any edge detector such as good detection,
good localization, and minimal response. The technique is basically known as feature
synthesis. The image is smoothed using Gaussian convolution followed by a 2D first
derivative operator. Then, non-maximal suppression technique is applied using two
thresholds. Usually for good result, the upper tracking threshold can be set quite high and
lower threshold quite low [42]. A wide Gaussian kernel reduces the sensitivity of detector.
The edge detected by canny operator are much more smooth and hence more tolerance to
noise. So in this research work we have considered canny detector.
b) HBT Filter based edge detector
An edge similarity measurement based algorithm by Saravana Kumar [39] gives superior
result than GM and AN method. This technique is more rugged irrespective of diversity in
illumination, contrast and noise level. The filtering technique basically highlights the edge
similarities between image adjacency and directional finite impulse response by means of
hyperbolic tangent figuration. This edge detection technique based on similarity measurement
results an optimal identification of image edges by using principal component analysis. The
Principal Component Analysis is applied to a set of local neighbourhoods which can be
expressed as
2
bi  m  nj 1 uij e j
(3.1.1)
Where u ij is the projection of bi –m onto the jth Eigen vector e j and bi is of size n x n
.The PCAgenerates n² eigenvectors each of size n x n and { ei , 1 ≤ i ≤ n² }.
The average value of all local neighbourhoods (bi) is
m
1
N

N
i 1 i
b
(3.1.2)
The Eigen values are in decreasing order of magnitude and eigenvector has similar
characteristics as a low pass filter. The eigenvector pairs are orthogonal to each other. The
PCA scheme is primarily based on successive approximation criterion. So, it gives an idea to
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use e j values so as to minimize the approximation error. Starting with eigenvector pairs (e2,
e3) and at higher ranges, it is found that, there is an accession of zero crossing points, which
signifies that the lower range eigenvectors contains more clues regarding the local
neighbourhoods at high frequency ranges. . Since the Eigen vectors e2, e3 assists in the
accurate approximation process of local neighbourhoods gray level alteration, our proposed
model deals with eigenvectors e2 and e3 for crack edge identification. From Fig.3.6 and
Fig.3.7, it is clear that e2 and e3 have blurred step edge profiles. Their approximated values
are as follows:
^
e2   21h1   22h2 And
^
e3   31h1   32 h2
(3.1.3)
Where { α } are weights and HBT filter pairs h1 , h2 are determined from a set of four
2D HBT filters oriented along 0 degrees, 45 degrees, 90 degrees, and 135 degrees .
The HBT profile h1 w.r.t h2 is expressed as
1  e   x  y 
Gw 
For |x|, |y| ≤ W and 0 otherwise.
1  e   x  y 
(3.1.4)
The region of support for Gw is confined within a window size W to guarantee edge
identification. By the sampling process of Gw at integer positions in a period [-w, w], h1 and
h2 filters are determined. The parameter  w determines the steepness of the profile at zero
crossing.  w is determined for a given filter width W so as to best approximate the natural
step edges in an image by means of the HBT filter pair correspondence to smallest
 total   2   3  . The weights  ij are determined by projecting both
Eigen values e2 and e3
onto orthogonal HBT filter pairs h1 and h2, i.e.
 ij 
ei , h j
hj , hj
(3.1.5)
The approximation error is given as
i 
ei  e j
ej
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Here the extra sensitivity to illumination can be mitigated by modifying their edgesimilarity measure with Ri with regularization parameter γ, an empirical constant c. The Ri is
expressed as,
Ri 
bi  bi  c , g
(3.1.7)
bi  bi  c . g
An estimate  , obtained by mean absolute deviation is given by
 
median(Yi : 1  i  N )
0.6745
Where Yi  2
1
n2
 b  j   b 
n2
j 1
2
i
i
(3.1.8)
(3.1.9)
i=1, 2… N.
Applying Ri to the sample wall image to compute four similarity maps where each map
corresponds to one of the four HBT filters equivalent similarity map is determined. By means
of suitable threshold value on local maxima, the edge pixels are determined.
3.1.2 Wavelet Decomposition and Fusion
After detection of crack edges by the different detectors, the next key issue is the type
and level at which the image fusion takes place. The wavelets-based approach is appropriate
for performing fusion tasks due to its multiresolution characteristics to deal with images at
varying resolution as described by Pajares et al. [41].The discrete wavelets transform (DWT)
performs theimage decomposition in different kinds of coefficients preserving the original
information of an image. The iterative decomposition helps in increasing the frequency
resolution. The approximation coefficients are then disintegrated through high and low pass
filters along with the down sampling operation as shown in fig.3.2.
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1
2
HH
1
ORIGINAL
WALL IMAGE
2
2
1 2
HL
1 2
LH
1 2
LL
1
Fig.3.2 Discrete wavelet filter banks
In the comparative study of image fusion algorithms by S. Krishnamoorthy et al.[42],
Haar Discrete Wavelet Transform based fusion method was evaluated as the outstanding
method in terms of subjective analysis. Like all wavelet transforms, the Haar transform
decomposes a discrete signal into two sub signals of half its length. One sub signal is a
running average or trend; the other sub signal is a running difference or fluctuation. Some of
the exclusive aspects of Haar wavelet transform are its efficient processing speed, simplicity,
memory management and reversibility. The Haar wavelet's mother wavelet function  t  can
be described as
 t 
=
1
0  t  0.5
-1
0.5  t  1
0
(3.1.10)
otherwise
Its scaling function  t  can be described as
 t  =
1
0
0  t  0.5
(3.1.11)
otherwise
The 2×2 Haar matrix associated with the Haar wavelet is
1 1 
H2  

1  1
(3.1.12)
The coefficients derived from input images can be suitably integrated to acquire new
coefficients; retaining crude information of the original images. Once the coefficients are
merged, then fused image is achieved through the inverse discrete wavelets transform
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(IDWT), where the information in the merged coefficients is also preserved. The key step in
image fusion based on wavelets is to merge coefficients in an appropriate way in order to
obtain the best quality in the fused image. The hybrid fusion algorithm [43] combines the
advantages of both pixel and region based fusion by selecting maximum approximations,
averaging of detail coefficients.
3.1.3 Results & Discussion
In this edge detection technique the concerned wall image acquisition is done by means of
a camera with focal length of 4mm, exposure time: 0.002 sec, max aperture: 3.5. The image
is resized to 256X256 for ease of processing and is shown in Fig.3.3. Our proposed method is
based on crack detection process using two efficient and reliable edge detection algorithms
such as canny edge detection and HBT filtering. Canny detector response fulfils the three
criteria desired for any edge detector such as good detection, good localization, and minimal
response as shown in Fig.3.4; whereas HBT filtering technique highlights the edge
similarities between image adjacency and directional finite impulse response as shown in
Fig.3.5. In the Fig.3.6, 3.7, the second and third largest PCA Eigen values are plotted in
spatial domain respectively. The Total error vs.  w plot in Fig.3.8 shows that  w value of 0.48
best approximates the natural step edges in an image by means of the HBT filter pair
correspondence to smallest approximate error value of 0.1680. We have considered three
levels Haar DWT decomposition technique shown in Fig.3.9 using Graphical User Interface
(GUI). In the next stage, the decomposition results of individual cracked images are fused
using an efficient fusion rule. Here we have selected maximum-approximation and meandetail fusion selection algorithm. The high pass filter mask enhances the edges whereas
averaging filter mask helps in removing noise by taking mean of gray values surrounding the
center pixel of the window. Finally by the application of Inverse DWT, the synthesized fused
image is recovered to identify the cracks more accurately. The proposed crack detection
technique produces a crack detected image with improved PSNR, Entropy, Normalized
Absolute Error value and the Feature Similarity Index (FSIM), which is based on phase
congruency. The performance metrics is shown in Table. I. Here the overlapped crack edges
of both detectors highlight the genuine crack locations in the original image avoiding the
false edges, which is shown in Fig.3.11.
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Fig.3.3 Original Wall image showing a hairline crack
Fig.3.4 Canny Edge detector response
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Fig.3.5 HBT filter response with sigma = 0.48 ,Total minimum error = 0.168, gamma = 0.0208, Threshold
= 0.83
Fig.3.6 Second largest PCA Eigen values in spatial domain for wall image
Fig. 3.7 Third largest PCA Eigen values in spatial domain for wall image
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Fig.3.8 Total minimum error as a function of
w
Fig.3.9 GUI for Image Fusion
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Fig.3.10 Fusion with 3 level Haar DWT decomposition using GUI
Fig.3.11 Image Fusion Response using GUI
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Table I
Performance Metrics
Quality
Indices
PSNR
JOINT
NORMALIZED
(dB)
ENTROPY
ABSOLUTE
FSIM
Methods
ERROR
Canny
Edge Detector
10.5183
5.9816
0.3947
0.6429
10.8215
6.1161
0.3875
0.6319
11.1523
6.4054
0.3699
0.6602
HBTEdge
Detector
Proposed
Technique
3.1.4 Summary
In this research work, we proposed novel crack detection technique based on two efficient
crack detection algorithms along with an efficient image fusion by means of Haar discrete
wavelet transform. HBT filtering method emphasizes on optimization of two of Canny’s
criteria- accurate edge detection and localization, without explicitly including the minimal
response criterion and Canny Edge detector avoids the false edge detection. In our proposed
technique for crack detection, both Canny and HBT based filter responses are fused together
resulting an optimized edge detection technique. Here, we have chosen maximumapproximation and mean-detail fusion selection algorithm. The high pass filter mask
enhances the edges whereas averaging filter mask helps in removing noise by taking mean of
gray values surrounding the centre pixel of the window. Here the image fusion response is
having higher values of PSNR, Entropy and Feature Similarity Index as compared to canny
as well as HBT edge detector responses. The Normalized Absolute Error also gets reduced.
Finally, the smoothness parameter should be taken relatively high value to decrease the slope
of the filter function reducing the oscillations of the filter response function in the time
domain.
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3.2 Edge Detection for Multi-Focus Images using Image
Fusion
Several researchers have proposed many edge detection techniques since three decades.
The classical edge detector such as Sobel, Prewitt, Kirsch, Robinson and Frei-Chen [36] are
preferred due to their simplicity in detecting the edges and their orientations. However, due to
the absence of smoothing filter, their performance degrades appending noise and inaccuracy.
The zero crossing algorithms such as Laplacian, second directional derivative have fixed
characteristics in all directions. However, these are having low noise performance. Laplacian
of Gaussian (LoG) by Marr-Hildreth [34] uses laplacian filter. Therefore, it malfunctions at
the corners, curves and fails to find the real edge orientation. The Gaussian algorithms such
as Canny and Shen-Castan [35] are having complex computations, delusive zero crossing and
time consuming. Lacroix [44] proposed an algorithm base on canny’s method that voids the
issue of splitting edges. But, it introduces localization error. Jeong and Kim [45] proposed an
automatic optimum determination of scales for each pixel. However, this technique has a low
execution speed. The angle-based technique is tender to noise and uneven light. The
improved method [37] based on phase congruency are invariant towards uneven illumination
and low contrast. It is found that the edge detection techniques, which are robust towards
contrast variation, are prone to be stirred by noise. A robust edge detection algorithm [39]
produces superior performance compared to methods discussed above. Focusing onto the
image fusion techniques, several algorithms have been proposed. Spatial domain is simple
and computationally efficient for image fusion. Low performances as well as blocking effects
[46] are the main constraint for spatial domain. Again, the multi resolution pyramid based
algorithms are redundant and bad orientation selectivity [19]. The widely used DWT based
MRA [47, 48, 49] technique have the advantage of good time-frequency analysis and nonredundancy. The DWT suffers from the following hazards: shift variance, non-directionality,
oscillations and aliasing [50]. The Dual-Tree Complex Wavelet Transform is having the
property of shift invariance and directional selectivity. Therefore, it takes the advantage over
DWT. In this research work, a multi-focus image fusion algorithm with Dual-Tree Complex
Wavelet Transform (DT-CWT) [51] is implemented followed by Hyperbolic Tangent based
edge detection technique followed by an adaptive thresholding method [53].
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3.2.1 Proposed technique
We have proposed a new approach for efficient and reliable edge detection in multi-focus
images, which is a challenging task due to blurring effect. It uses the Dual-Tree Complex
Wavelet Transform (DT-CWT) based image fusion followed by a Hyperbolic Tangent
filtering technique. Here image-I, II are the multi-focus image.
The edge detection
architecture is shown in Fig.3.12.
Image-I
Image- II
Image Fusion using DT-CWT
Fused Image
Edge Detection using HBT Filter
with Adaptive Thresholding
Detected Edges
Fig. 3.12 Flow chart for proposed Edge Detection Technique
3.2.2 DT-CWT based image fusion
Nick Kingsbury was the first pioneer of DT-CWT technique in 1998. It possesses the
competitive attributes such as approximate shift invariance and improved directional
selectivity [50]. The DT-CWT employs two real Discrete Wavelet Transform by splitting the
real and imaginary parts of transform into two trees as shown in Fig.3.13. The technique uses
delayed samples between the real part and its correspondence imaginary part in each level in
combination with the alternate odd length and even length linear phase filters. To avoid the
issue regarding the non-symmetrical and non bi-orthogonal property of DT-CWT, a Q-shift
dual tree has been proposed [51]. Here the first level filters are even length. A quarter (q)
group delays are implemented followed by 2q delay and so on as shown in Fig.3.13. This
upholds the shift-invariance as well as directional selectivity attributes.
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Fig.3.13 Dual Tree Q-shift CWT
Fusion Rules
Following an optimum rule [54] is one of the most important parts of image fusion based
on multi resolution analysis. The low frequency coefficients represent the texture information
of background image. So the rule for low frequency components is based on neighbourhood
due to high correlation among the pixels. Since we are concerned for the multi-focus image
fusion to have an improvement of blurred regions, the weighted scheme based neighbourhood
rule is implemented for low frequency coefficients. Here the neighbourhood maximum
selectivity (NGMS) rule is enforced. The neighbourhood gradient is computed as follows.
Gi (m, n) 
 H (m' , n' )L (m  m' , n  n' )
m' , n '  s
i
(3.2.1)
Where i =A or B, are the input images.
Li (m, n) is the coefficient at (m, n) and ‘S’, ‘H’ represents the neighbourhood and the
corresponding mask.
The laplacian mask used here is
 1  1  1
H   1 8  1
 1  1  1
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(3.2.2)
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The edges and detail information is presented by means of high frequency coefficients. In
general imaging techniques, the in-focus image system functions are wider as compared to
the out of focus images. Due to the high correlation pixel property, an absolute value
maximum selection (AVMS) technique is preferred for high frequency components. The
actual fusion rule is as follows
S Aj , i (m, n) if S Aj , i (m, n) ≥ S Bj , i (m, n)
S fj , i (m, n) =
(3.2.3)
S Bj ,i (m, n) if S Aj ,i (m, n) ≤ S Bj ,i (m, n)
Where j=1, 2…N, represents the level of the decomposition,
i=1, 2…6, represents the level wise direction of high frequency coefficients.
3.2.3 Edge detection using HBT filter
An edge similarity measurement based algorithm by Saravana Kumar [39] gives superior
result than GM and Angle based method. This technique is more rugged irrespective of
diversity in illumination, contrast and noise level. The filtering technique highlights the edge
similarities between image adjacency and directional finite impulse response by means of
hyperbolic tangent figuration. This edge detection technique based on similarity measurement
results an optimal identification of image edges by using principal component analysis. The
Principal Component Analysis (PCA) is implemented onto a set of local neighbourhoods,
which can be expressed as
2
bi  m  nj 1 uij e j
(3.2.4)
Where u ij is the projection of bi –m onto the jth Eigen vector e j and bi is of size n x n
.The PCA generates n² eigenvectors each of size n x n and { ei , 1 ≤ i ≤ n² }. The average
value of all local neighbourhoods (bi) is
m
1
N

N
i 1 i
b
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(3.2.5)
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The Eigen values are in decreasing order of magnitude and eigenvector has similar
characteristics as a low pass filter. The PCA scheme is primarily based on successive
approximation criterion. Therefore, it gives an idea to use e j values to minimize the
approximation error. Starting with eigenvector pairs (e2, e3) and at higher ranges, it is found
that the lower range eigenvectors contains more clues regarding the local neighbourhoods at
high frequency ranges. . Since the Eigen vectors e2, e3 assists in the accurate approximation
process of local neighbourhoods gray level alteration, our proposed model deals with
eigenvectors e2 and e3 for crack edge identification. It is observed that e2 and e3 have
blurred step edge profiles. Their approximated values are as follows:
^
^
e2   21h1   22h2 And
e3   31h1   32 h2
(3.2.6)
Where { α } are weights and HBT filter pairs h1 , h2 are determined from a set of four
2D HBT filters oriented along 0 degrees, 45 degrees, 90 degrees, and 135 degrees .
The HBT profile h1 w.r.t h2 is expressed as
Gw 
1  e   x  y 
1  e   x  y 
0
For |x|, |y| ≤ W
(3.2.7)
otherwise.
The region of support for Gw is confined within a window size W to guarantee edge
identification. By the sampling process of Gw at integer positions in a period [-w, w], h1 and
h2 filters are determined. The parameter  w determines the steepness of the profile at zero
crossing.  w is determined for a given filter width W so as to best approximate the natural
step edges in an image by means of the HBT filter pair correspondence to smallest
 total
 2  3 .
The weights  ij are determined by projecting both Eigen values e2 and e3
onto orthogonal HBT filter pairs h1 and h2, i.e.
 ij 
ei , h j
(3.2.8)
hj , hj
The approximation error to be minimized is given as
i 
ei  e j
(3.2.9)
ej
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Here the extra sensitivity to illumination is mitigated by modifying Ri with a
regularization parameter γ, an empirical constant c. Now Ri is represented by,
Ri 
bi  bi  c , g
bi  bi  c . g
(3.2.10)
An estimate  , obtained by mean absolute deviation is given by
 
Where Yi  2 1
2
n
median (Yi : 1  i  N )
0.6745
(3.2.11)
 b  j   b 
n2
j 1
2
i
i
Where i=1, 2… N.
Ri is applied to the fused image to compute four similarity maps where each map
corresponds to one of the four HBT profile orientations. Equivalent similarity map is
determined. A suitable threshold value is applied to have the edge pixels.
Adaptive thresholding
Thresholding is one of the important processes followed by image segmentation. It is an
effective way for separating the object from its background. The Chow and Kaneko approach
[52] fails due to its computational expensiveness. So it is not suitable for real time
applications. In this research work the adaptive thresholding method [53] is incorporated
followed by the edge detection using hyperbolic tangent profile. The adaptive thresholding
technique uses the local information and boundary characteristics of an image. Due to the
small size of intensity range and the resemblance of mean value with the central pixel value,
simple mean does not perform well. So the mean-c concept is implemented, where the
threshold value changes dynamically over the image, which ensures that it is best, suited for
the illumination variant imaging.
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3.2.4 Results & Discussion
In this edge detection technique, the simulation is done using multi-focus test images as
shown in Fig.3.14 and Fig.3.15. The multi-focus image-I and image-II are fused by means of
Dual-Tree Complex Wavelet Transform based image fusion to get the proper image with
focused features. Fig.3.14 (a, b) represents the multi-focus images of Clock and the fused
image is shown in Fig.3.14(c). Similarly the multi focus Coke-Can images are shown in
Fig.3.15 (a, b) and the fusion result is shown in Fig.3.15(c). The image fusion result is treated
through an HBT filter and the edges are tracked as depicted in Fig. 3.14(d) and Fig.3.15 (d).
The total min-error Vs. sigma plots for multifocal clock and multifocal Pepsi-Can image
using HBT filter optimization are shown in fig.3.16 and Fig.3.17 respectively. For clock
image, the edge is detected with
  0.55
and total minimum error of 0.1627. Again, the
Coke Can image is also treated by HBT profile with
  0.68 and
total min-error of 0.3626.
Here, the proposed multi focus image edge detection technique performs well with the
adaptive thresholding. The performance chart is shown in Table. I.
(a)
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(b)
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Image Fusion & Edge Detection
(c)
(d)
Fig.3.14 (a) Multi-Focus Image-I, (b) Multi-Focus Image-II, (c) Image Fusion result, (d) Edge Detection result
(a)
(b)
(c)
(d)
Fig.3.15 (a) Multi-Focus Image-I, (b) Multi-Focus Image-II, (c) Image Fusion result,
(d) Edge Detection result
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Image Fusion & Edge Detection
Fig.3.16 Total min-error Vs sigma plot for Clock image showing total min-error of 0.1627 at   0.55
Fig.3.17 Total min-error Vs sigma plot for Pepsi Can image showing total min-error of 0.3626 at   0.68
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Image Fusion & Edge Detection
Fig.3.18 (a) PCA Eigen value e2 for Fused Clock Image
(b) PCA Eigen value e3 for Fused Clock Image
Fig.3.19 (a) PCA Eigen value e2 for Fused Pepsi-Can Image, (b) PCA Eigen value e3 for Fused Pepsi-Can
Image
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Image Fusion & Edge Detection
Table I
Comparison Chart
PARAMETERS
IMAGES
PROPOSE
CANNY
SOBEL
METHOD
PSNR
Clock
11.4986
11.1355
11.1869
in dB
Can
12.0113
11.6394
11.9688
Total
Clock
74.4641
66.4037
37.2234
STD
Can
77.1899
70.2991
52.3905
Entropy
Clock
4.1011
2.5368
1.2697
Can
2.1793
1.5774
1.2510
3.2.5 Summary
Edge detection in multi-focus images has been one of the challenging tasks due to severe
blurring effects. In this research work, we have proposed a novel edge detection architecture,
which combines the individual advantages of Q-shift DT-CWT based image fusion and HBT
filtering based edge detection technique. The Q-shift DT-CWT removes the blocking effect,
ringing artefacts during fusion and improves the directional selectivity. The use of HBT
profile makes the edge detection technique more robust towards uneven illumination, contrast
variation and noise. The proposed technique performs superior as compared to classical sobel
method as well as canny algorithm in terms of PSNR, total standard deviation and Entropy.
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Image Fusion based on Bilateral Sharpness Criterion
CHAPTER 4
Image Fusion based on
Bilateral Sharpness in DT-CWT
Domain
Introduction
Dual Tree Complex Wavelet Transform
Proposed Image Fusion Technique
Simulation Results and Discussion
Summary
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Image Fusion based on Bilateral Sharpness Criterion
4. IMAGE
FUSION
BASED
ON
BILATERAL
SHARPNESS
CRITERION IN DT-CWT DOMAIN
Image fusion is basically the technique of merging several images from multi-modal
sources with respective complementary information to form a new image, which carries all
the common as well as complementary features of individual images. Image fusion has an
extensive area of application such as, multi-spectral remote sensing, target detection, military
surveillance systems medical imaging and so on. Various algorithms have been proposed for
effective fusion of multi-source images such as simple averaging, maximum and minimum
fusion rules. Afterwards, the fusion performance is improved by the introduction of Principal
Component Analysis (PCA) and Morphological processing algorithms [42].
Again, the fusion algorithms such as Brovey technique, PCA and Intensity-HueSaturation fail due to the characteristic spectral losses and color deformation. Data fusion by
means of pyramidal decomposition results in growth of redundancy and orientation
deficiency [19]. Further, with the development of Discrete Wavelet Transform (DWT) based
image fusion techniques, the perceptual quality has been enhanced upholding the spectral
information contents. The real DWT has the property of good compression of signal energy.
Perfect reconstruction is possible using short support filters. The unique feature of DWT is
the absence of redundancy and very low computation [49]. Therefore, DWT has been used
extensively for Multi Resolution Analysis (MRA) based image fusion. The Discrete Wavelet
Transform primarily suffers from the various problems [55] such as oscillations, aliasing,
shift variance and lack of directionality. The ringing artefacts introduced by DWT are also
completely eliminated by the implementation of Dual Tree Complex Wavelet (DT-CWT)
based image fusion methods.
In this research work, an improved version of Dual Tree Wavelet Transform based image
fusion algorithm is proposed. The fusion process is implemented using efficient fusion rules
for high frequency coefficients as well as low frequency coefficients depending on their
characteristics. The robustness of the proposed method is verified from Low Light Television
(LLTV) and Forward-Looking-Infrared (FLIR) image fusion, multi-spectral satellite image
fusion and CT-MR image fusion.
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4.1 Dual-Tree Complex Wavelet Transforms
The Dual-Tree Complex Wavelet Transform (DT-CWT) was first introduced by Nick
Kingsbury in the year 1998. The DT-CWT has been one of the most popular transform
domain techniques due to some of the unique features such as, good shift invariance, good
directional selectivity in 2-Dimensons as well as 3-Dimensons, perfect reconstruction using
short support filters, limited redundancy and low computation. The DT-CWT basically
utilizes two real DWTs. The first one yields the real part of the transform while the second
one yields the imaginary part.
In order to accomplish the perfect reconstruction, it is required to process signals with the
help of wavelets. The DT-CWT [55] accomplishes this by using two filter banks and thus two
bases. With the help of two filter banks { h0 (n) , h1 (n) } and
{ g 0 (n) , g1 (n) }, four DWTs,
Fhh , Fgg , Fgh and Fhg are generated. The Fgh component is extracted from the filters g i (n)
along the rows and filters hi (n) along columns. Since at each decomposition level of DWT,
three sub-bands are produced, there can be twelve sub-bands to generate six directionally
selective complex sub- bands, which are approximately analytic. These complex sub-bands
are basically oriented at ±15°, ±45°, and ±75°.
Mathematically the two dimensional DT-CWT decomposition of an image I(x, y) can be
expressed by means of the complex shifted and dilated mother wavelet  (x) and scaling
function  (x) as
I ( x, y)   S j0 ,l  j0 ,l ( x, y)    C j ,l j ,l ( x, y)
(4.1)
  j  j0 lz 2
lz 2
The mother wavelet is expressed as
 j ,l ( x)   jr ,l ( x)   1 ij ( x)
0
0
(4.2)
The scaling wavelet function is
 j ,l ( x)   rj ,l ( x)   1 ij ,l ( x)
(4.3)
Where ‘z’ is the natural number set.
S j0 ,l represents the scaling coefficient with shifting of ‘j’ and dilation of ‘l’.
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Image Fusion based on Bilateral Sharpness Criterion
C j ,l Shows the complex wavelet coefficients
r, i are the indexing for real and imaginary parts respectively.
The directionality of the six complex sub bands generated is guided along
    {15 ,45 ,75 } .
Thus, the two dimensional Dual Tree Complex Wavelet Transform gives rise to one
real low-pass image along with six complex high-pass sub-images at each decomposition
level. To obtain the final DT-CWT outcome, the difference between the filters in the two
trees is estimated. It is basically implemented by a delayed version of one sample between the
level-1 filters of the real as well as imaginary decomposition trees. The outcomes of
subsequent levels are obtained by the help of alternate odd-length and even-length linearphase filters. Unluckily the odd and even filtering techniques often suffer from the problems
like: unsymmetrical sub-sampling structure, frequency responses variation between
decomposition trees [50].
To beat these issues, a Q-shift dual tree [51] is implemented for this research work. This
novel algorithm proposes that, all the filters beyond level 1 has to be of even length without
any rigid linear phase condition with a group delay of nearly a quarter samples (q). Likewise,
other filters beyond level-1 are imitated from the orthonormal prototype set. A symmetric
sub-sampling arrangement takes care of the shift invariance as well as the directional
selectivity property of DT-CWT. The dual tree filters for Q-shift wavelet decomposition is
shown in Fig.3.2.2.
Fig.4.1 Dual tree of real filters for the Q-shift Wavelet Transform
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Image Fusion based on Bilateral Sharpness Criterion
4.2 Proposed Image Fusion using DT-CWT
At every decomposition level of DT-CWT, six directional high frequency wavelet
coefficients are generated along with two low frequency coefficients. Generally, the wavelet
coefficients of each band are blended using some suitable fusion rules. A new fused image is
reconstructed using inverse DT-CWT. The complete fusion process is shown in Fig.4.2.
Fig.4.2 DT-CWT fusion
4.2.1 Fusion rule for Low frequency coefficients
In an image, the background texture information is primarily highlighted by the low
frequency components. Appropriate fusion selection rule for low frequency components is
one of the important criterions during the fusion process. The rules can be classified as
maximum selection rule or weighted rule. In this research work, we have implemented the
weighted fusion scheme for low frequency components. The normalized weighting factor
selection for this research work is inspired by the maximum gradient based sharpness of the
neighbourhood pixels [57].
4.2.2 Gradient-based sharpness criterion
Sharpness has always been considered as one of the prime norm for image quality
measurement. The sharpness and information content of an image primarily depends on the
strength measures. Image fusion algorithms based on simple normalized aggregation of input
images fails since, the concerned high frequency regions are also weighted equally along with
the unimportant regions. To overcome such issues, an improved version of the novel
weighting criterion [57] has been implemented in this research work. Here, to measure the
structural contents of an image I(r, c) effectively, a gradient covariance matrix of a region is
specified by means of a local window of size MxN [58].
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The gradient covariance matrix is given by
  w I r2 (r , c)
C
  I r (r , c) I c (r , c)
 w

I (r , c) I c (r , c) 

 w I c2 (r, c) 
w r
(4.4)
Where I r (r , c) and I c (r , c) represent the row-gradient and column-gradient of the image
respectively. The gradient covariance matrix can be represented as
C  VDV  (v1
T
 1 0  v1T 
 T 
v2 )
0

2  v2 

(4.5)
Where the 2x2 matrix V consists of the eigen vectors v1 and v 2 along its columns. The
 1
2x2 matrix D  
0
0
 . Where 1 and  2 represents the Eigen values of the gradient
2 
covariance matrix [59].
The image gradient strength is represented as G(r , c)  1  2
The
maximum
gradient
strengths
of
input
images
can
(4.6)
be
calculated
as
Gmax  max(max( G(r, c)))
The maximum gradient strengths are computed for individual image-A and image-B
using the above formula. Now, the normalized weighting factors W A for image-A is laid out
by
WA 
Gmax A
Gmax A  Gmax B
(4.7)
Similarly, the normalized weighting factor for image-B can be represented as
WB 
Gmax B
Gmax A  Gmax B
(4.8)
The weights W A and WB corresponding to the image-A and image-B respectively, are
applied to the low frequency wavelet coefficients for the fusion process.
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Image Fusion based on Bilateral Sharpness Criterion
4.2.3 Fusion rule for High frequency coefficients
Recently, most of the fusion rules meant for high frequency coefficients are based on
neighbourhood characteristics such as neighbourhood energy, variance, etc. The high
frequency components basically describe the detail information of an image. In this research
work, the fusion of high frequency components is implemented by means of an effective
weighting scheme proposed by Jing Tian [57].
For high frequency wavelet component fusion process, the bilateral gradient-based
sharpness weighting method is implemented. This bilateral sharpness measurement comprises
of both gradient strength criterion from Eq. (4.6) and corresponding phase coherence
measurement. The local phase coherence criterion plays a vital role with respect to human
visual perception towards the fusion response [38]. The phase criterion is also robust towards
noise and gradient based illumination variation.
The phase coherence for image gradient can be presented as

P(r , c)   cos( (r , c)   (r , c))
(4.9)
Where  (r , c) evaluated from principal vector v1 , is the phase information at coordinates

(r, c).  (r , c) is the average phase of neighbouring pixels.
The maximum phase coherence value corresponds to the edge pixels. The bilateral
sharpness criterion is developed using the gradient sharpness criterion in Eq. (4.6) and its
corresponding phase coherence in Eq. (4.9). This can be expressed as
S  G  ( r , c) P  ( r , c)
(4.10)
The factors  and  can be tuned to some suitable values to maximize the contribution
of suitable sharpness criterions. In this experimental work,  and  values are set to 1 and
0.5 respectively confined in an window size of w=5 [57].
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Image Fusion based on Bilateral Sharpness Criterion
4.3 Simulation Results and Discussion
The Bilateral sharpness criterion based fusion in Dual Tree Complex Wavelet domain has
been performed using various multi-sensor images from a standard image database of Dr.
Oliver Rockinger. The robustness of the proposed fusion technique is verified successfully
with some multi-sensor images such as: LLTV sensor image, FLIR sensor image,
multispectral remote sensing images and medical images such as CT, MR images. The
original input images and their corresponding fusion results using the proposed technique are
depicted in Fig.4.3, Fig.4.4 and Fig.4.5.
(a)
(b)
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Image Fusion based on Bilateral Sharpness Criterion
(c)
Fig.4.3 (a) LLTV sensor image, (b) FLIR sensor image (c) Fused image using proposed method
(a)
Fig. 4.4(b) Multispectral sensor image-B
(b)
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Image Fusion based on Bilateral Sharpness Criterion
Fig. 4.4 (a) Multispectral sensor image-A, (b) Multispectral sensor image-B, (c) Fused image using proposed
method
(a)
(b)
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Image Fusion based on Bilateral Sharpness Criterion
(c)
Fig. 4.5 (a) CT image, (b) MRI image, (c) Fused image using proposed method
4.3.1 Quantitative evaluation
The quantitative evaluation of this research work using various multi-sensor images has
been shown in Table-I, Table-II and Table-III. The performance comparison of the proposed
method is accomplished with Discrete Wavelet Transform (DWT) and Dual Tree Complex
Wavelet Transform (DT-CWT) in terms of some non-referential image quality measures such
as entropy, average gradient, edge intensity and standard deviation. The superiority as well as
robustness of the proposed image fusion technique is evidently justified from the fused image
quality assessment tables. Some of the major non-referential image quality measures are
discussed below.
Entropy (E)
Entropy is considered as one of the vital image quality index to evaluate the information
content in an image.
N
It is formulated as
E   p( xi ) log p( xi )
(4.11)
i 0
Where x i is the gray level value at i th pixel with corresponding probability ‘p’. The
entropy value is larger for images containing more the information.
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Image Fusion based on Bilateral Sharpness Criterion
Average gradient
The detail contrast and texture variations in an image is usually indexed by means of
average gradient values and is given as
 f 
 f 


  

x


 y 
2
2
g
( M 1)( N 1)
1

( M  1)( N  1)
i 1
2
(4.12)
Edge intensity
The measurement of sharp discontinuities in an image can be considered as one of the
image quality assessment parameters. It can be easily accomplished using the Sobel edge
detection algorithm. It uses horizontal differentiation kernel g x and a vertical differentiation
kernel g y , which are presented as:
 1

gx   2
 1

  1  2  1


gy   0 0 0 
1 2 1


1

2 ,
1 
0
0
0
(4.13)
For an image I, the edge intensity values are given as:
S
G
2
x
 G y2

(4.14)
Where, Gx  I * g x , G y  I * g y `
Standard deviation
The Standard deviation is considered as one of the best metrics for contrast value
measurement for an image. High contrast level of an image can be make out from high
standard deviation value. It can be formulated as
j 
1
N
N
 (x
i 1
ji
  j )2
Where, the mean pixel value  j 
(4.15)
1
N
N
x
i 1
ji
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Image Fusion based on Bilateral Sharpness Criterion
Table. I Quantitative assessment for fusion of navigation images (LLTV and FLIR)
Quality
Entropy
Average
Gradient
Edge Intensity
Standard
Deviation
DWT
5.4799
3.8137
39.5306
80.7748
DT-CWT
5.4147
3.8473
39.7661
84.1700
PROPOSED
METHOD
5.7038
3.9373
40.7322
87.4002
I
Indices
Methods
Table..II Quantitative assessment for fusion of multispectral remote sensing images
Quality
Indices
Entropy
Average
Gradient
Edge Intensity
Standard
Deviation
DWT
5.4926
7.5051
74.6469
78.4850
DT-CWT
5.7928
7.6045
76.8336
80.2671
PROPOSED
METHOD
6.0335
7.7230
78.2545
81.9917
Methods
Table.III Quantitative assessment for fusion of medical images (CT and MR)
Quality
Indices
Entropy
Average
Gradient
Edge Intensity
Standard
Deviation
DWT
3.8010
3.9580
41.9148
91.7107
DT-CWT
3.9944
4.1174
43.7937
96.1673
PROPOSED
METHOD
4.1129
4.2091
44.8069
100.7343
Methods
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Image Fusion based on Bilateral Sharpness Criterion
4.4 Summary
An enhanced fusion scheme proposed in this research work implements a bilateral
gradient-based sharpness-weighting criterion in Dual-Tree Complex Wavelet Transform. The
proposed fusion technique compensates all the shortcomings of Discrete Wavelet Transform
by the implementation of Q-shift DT-CWT. It also removes the ringing artefacts introduced
in the fused image by assigning suitable weighting schemes to high pass wavelet coefficients
and low pass coefficients independently.
The normalized maximum gradient-based
sharpness criterion for low frequency coefficients enhances the background texture
information as well as improves the quality of the blurred regions in the fusion result. The
most vital information contents concealed in the high frequency coefficients are also boosted
up by the implementation of bilateral sharpness criterion. From the image quality assessment
tables, it is clear that the proposed fusion technique outperforms other methods in terms of
Entropy,
Average
Gradient,
Edge
Intensity
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and
Standard
deviation.
Page 67
Conclusions
CHAPTER 5
Conclusion
Conclusions
Suggestions for Future Work
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Conclusions
5. CONCLUSIONS
This chapter describes the conclusion about the research work and gives the suggestions
for future work.
5.1 Conclusions
In this research work, attention was drawn towards the current trend of the use of
multiresolution image fusion techniques, especially approaches based on discrete wavelet
transforms and Dual Tree Complex Wavelet Transforms. The work started with the review of
several image fusion algorithms and their implementation. The significance of image fusion
in edge detection has been illustrated with some proposed techniques in chapter-3. A novel
crack detection technique has been proposed here, which is based on two efficient crack
detection algorithms along with an efficient image fusion by means of Haar discrete wavelet
transform. HBT filtering method emphasizes on optimization of two of Canny’s criteriaaccurate edge detection and localization, without explicitly including the minimal response
criterion and Canny Edge detector avoids the false edge detection. In our proposed technique
for crack detection, both Canny and HBT based filter responses are fused together resulting
an optimized edge detection technique. A maximum-approximation and mean-detail fusion
selection rule has been implemented. The high pass filter mask enhances the edges whereas
averaging filter mask helps in removing noise by taking mean of gray values surrounding the
centre pixel of the window. The response of image fusion is found to have higher values of
PSNR, Entropy and Feature Similarity Index as compared to canny as well as HBT edge
detector responses. The Normalized Absolute Error also gets reduced. Finally, the
smoothness parameter should be taken relatively high value to decrease the slope of the filter
function reducing the oscillations of the filter response function in the time domain.
Edge detection in multi-focus images has been one of the challenging tasks due to severe
blurring effects. In this research work, we have proposed a novel edge detection architecture,
which combines the individual advantages of Q-shift DT-CWT based image fusion and HBT
filtering based edge detection technique. The Q-shift DT-CWT removes the blocking effect,
ringing artefacts during fusion and improves the directional selectivity. The use of HBT
profile makes the edge detection technique more robust towards uneven illumination, contrast
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Conclusions
variation and noise. The proposed technique performs superior as compared to classical sobel
method as well as Canny algorithm in terms of PSNR, total standard deviation and Entropy.
An enhanced fusion scheme proposed in chapter-4 implements a bilateral gradient-based
sharpness-weighting criterion in Dual-Tree Complex Wavelet Transform. The proposed
fusion technique compensates all the shortcomings of Discrete Wavelet Transform by the
implementation of Q-shift DT-CWT. It also removes the ringing artefacts introduced in the
fused image by assigning suitable weighting schemes to high pass wavelet coefficients and
low pass coefficients independently. The normalized maximum gradient based sharpness
criterion for low frequency coefficients enhances the background texture information as well
as improves the quality of the blurred regions in the fusion result. The most vital information
contents concealed in the high frequency coefficients are also boosted up by the
implementation of bilateral sharpness criterion. From the image quality assessment tables, it
is clear that the proposed fusion technique outperforms other methods in terms of Entropy,
Average Gradient, Edge Intensity and Standard deviation.
5.2 Suggestions for Future Work
Image Registration has significant contribution towards the enhancement of image fusion
quality. Image Registration has not been incorporated in this research work. By the
Implementation of suitable image registration techniques, the competitiveness of the
proposed image fusion methods can be properly justified with some more set of sample
test/perfect images.
The number of decomposition levels in the Multiresolution analysis has a great impact on
image fusion performance. However, using more decomposition levels do not necessarily
implies better results. Therefore methods for selection ofoptimized number of decomposition
levels can be explored.
A learning algorithm like neural networks and more specifically Support Vector Machine
could be devised for assigning weightage to the image quality metrics so as to assess them. A
more extensive number of image sets could be considered initiating a learning process using
SVM, based on which the metrics could be provided with weighted ranks.
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Future Work
The final aspect in future development and improvement is how to estimate and evaluate
the quality of afused image. As we have discussed in the previous chapter, depending on the
applications, some fusion system might not have a perfect ground truth reference image for
objective evaluation. Therefore, access methods without reference image are important for
our concern in multi-camera imaging system.
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Bibliography
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Dissemination of the Research Work
Dissemination of the Research Work
[1].
P.R. Muduli and U.C. Pati, “A Novel Technique for Wall Crack Detection Using Image
Fusion”, Proc. of IEEE International Conference on Computer Communication and
Informatics (ICCCI-2013), Jan-2013, Coimbatore, India.
[2].
P. R. Muduli and U.C. Pati, “A Novel Edge Detection Technique for Multi-Focus Images
Using Image Fusion”, Advances in Intelligent and Soft Computing, Springer Publication,
ISSN: 1867-5670, 2013. (Accepted)
[3].
P. R. Muduli and U.C. Pati, “Image Fusion based on Bilateral Sharpness Criterion in DTCWT Domain“, International Journal of Computational Vision and Robotics,
INDERSCIENCE Publishers, ISSN: 1752-9131, 2013. (Communicated)
[4].
V. S. Bind, P. R. Muduli and U. C. Pati, “A Robust Technique for Feature-based Image
Mosaicing using Image Fusion”, International journal of Advanced Computer Research
(IJACR), Vol.3, Issue-8, pp.263-268, Mar 2013.
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Page 77
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