Development of Impulsive Noise Detection Schemes for Selective Filtering in Images

Development of Impulsive Noise Detection Schemes for Selective Filtering in Images
Development of Impulsive Noise Detection Schemes
for Selective Filtering in Images
Subrajeet Mohapatra
Department of Computer Science and Engineering
National Institute of Technology Rourkela
Rourkela–769 008, Orissa, India
September 2008
Development of Impulsive Noise Detection Schemes
for Selective Filtering in Images
Thesis submitted in partial fulfillment
of the requirements for the degree of
Master of Technology
(Research)
in
Computer Science and Engineering
by
Subrajeet Mohapatra
(Roll: 60606004)
Department of Computer Science and Engineering
National Institute of Technology Rourkela
Rourkela–769 008, Orissa, India
September 2008
Department of Computer Science and Engineering
National Institute of Technology Rourkela
Rourkela–769 008, Orissa, India.
Certificate
This is to certify that the work in the thesis entitled Development of Impulsive
Noise Detection Schemes for Selective Filtering in Images by Subrajeet Mohapatra
is a record of an original research work carried out by him under our supervision
and guidance in partial fulfillment of the requirements for the award of the degree
of Master of Technology (Research) in Computer Science and Engineering during
the session 2006–2008 in the department of Computer Science and Engineering,
National Institute of Technology Rourkela. Neither this thesis nor any part of it
has been submitted for any degree or academic award elsewhere.
Rameswar Baliarsingh
Assistant Professor
CSE department of NIT Rourkela
Place: NIT Rourkela
Date: 08 January 2009
Banshidhar Majhi
Professor
CSE department of NIT Rourkela
Acknowledgment
It will be simple to name all those people who helped me to get this thesis done,
however it will be tough to thank them enough. I will nevertheless try. . .
I would like to gratefully acknowledge the enthusiastic supervision and guidance
of Prof. Banshidhar Majhi for the ideas that led to this work, for his timely comments, guidance, support and patience throughout the course of this work. He is
my source of inspiration.
I am grateful to my co-supervisor Prof. R. Baliarsingh for his valuable suggestions,
and encouragements during this research period.
I am very much indebted to Prof. S. K. Jena for his continuous encouragement
and support. My sincere thanks goes to Prof. S. K. Rath for motivating me to
work harder.
Prof. A. K. Turuk and Prof. B. D. Sahoo were like two ceaseless source of power
for me. Their help can never be penned with words.
My sincere thanks goes to Prof. P.K. Nanda for his continuous encouragement. I
also thank Prof. J.K. Satpathy for serving on my Master Scrutiny Committee.
My overwhelming thanks goes to Prof. S. K. Patra, Prof. G. K. Panda, Prof. D.
P. Mahapatra, Prof. P. M. Khilar and Prof. S. Chinara, for being my knowledge
resource. Special thanks goes to Prof. P. K. Sa and Mr. R.Dash for appraising
my work critically.
I thank to all my friends for being there whenever I needed them. Thank you
very much Mrinal, Dilip, Swasti, Hunny, Baikuntha, Prem, Bandana, Jayprakash,
Dheeraj. I have enjoyed every moment I spent with you.
I must acknowledge the academic resource that I have got from NIT Rourkela.
Finally, I am forever indebted to my parents and my sister for their understanding
and encouragement when it was most required.
Subrajeet Mohapatra
Abstract
Image Noise Suppression is a highly demanded approach in digital imaging
systems design. Impulsive noise is one such noise, which is frequently encountered
problem in acquistion, transmission and processing of images. In the area of image
restoration, many state-of-the art filters consist of two main processes, classification (detection) and reconstruction (filtering). Classification is used to separate
uncorrupted pixels from corrupted pixels. Reconstruction involves replacing the
corrupted pixels by certain approximation technique. In this thesis such schemes
of impulsive noise detection and filtering thereof are proposed.
Impulsive noise can be Salt & Pepper Noise (SPN) or Random Valued Impulsive
Noise (RVIN). Only RVIN model is considered in this thesis because of its realistic
presence. In the RVIN model a corrupted pixel can take any value in the valid
range.
Adaptive threshold selection is emphasized for all the four proposed noise detection schemes. Incorporation of adaptive threshold into the noise detection
process led to more reliable and more efficient detection of noise. Based on the
noisy image characteristics and their statistics, threshold values are selected.
To validate the efficacy of proposed noise filtering schemes, an application to
image sharpening has been investigated under the noise conditions. It has been
observed, if the noisy image passes through the sharpening scheme, the noise
gets amplified and as a result the restored results are distorted. However, the
prefiltering operations using the proposed schemes enhances the result to a greater
extent.
Extensive simulations and comparisons are done with competent schemes. It is
observed, in general, that the proposed schemes are better in suppressing impulsive
noise at different noise ratios than their counterparts.
List of Acronyms
Acronym
AHE
CV
CV
DCT
FLANN
FP
FN
ISAT
MLP
MLPAT
MSE
PSNR
PSP
RBFN
RBFNAT
SPN
Description
Adaptive Histogram Equalisation
Coefficient of Variance
Coefficient of Variance Adaptive Thresholding
Discrete Cosine Transform
Functional Link Artificial Neural Network
False Positive
False Negative
Image Statistics based Adaptive Thresholding
Multilayer Perceptron
Multilayer Perceptron based Adaptive Thresholding
Mean Square Error
Peak Signal to Noise Ratio
Percentage of Spoiled Pixels
Radial Basis Functional Network
Radial Basis Functional Network based Adaptive Thresholding
Salt and Pepper Noise
List of Symbols
Symbol
µ
γ
Description
Statistical Mean of the Image
Standard Deviation
γ2
Variance
λ
Amplification factor
η
Noise
θopt
Optimum Noise Threshold value
c
Constant Factor
L
Maximum Gray Level of an Image
p
Noise Probability
r
Value of Image Pixel before Processing
s
Value of Image Pixel after Processing
List of Figures
1.1
Image Processing Tree . . . . . . . . . . . . . . . . . . . . . . . . .
1.2
(a) Model of the image degradation/restoration process, (b) Model
4
of the Noise Removal Process. . . . . . . . . . . . . . . . . . . . . . 13
1.3
Nonlinear Filter Family . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4
Representation of (a) Salt & Pepper Noise with Ri,j ∈ {nmin , nmax },
(b) Random Valued Impulsive Noise with Ri,j ∈ [nmin , nmax ] . . . . 18
1.5
PSNR (dB) variations of Lena image corrupted with RVIN by
Group-A schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.6
PSNR (dB) variations of Lena image corrupted with RVIN by
Group-B schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.7
PSNR (dB) variations of Lena image corrupted with RVIN by
Group-C schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.8
PSP variations of Lena image corrupted with RVIN by Group-A
schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.9
PSP variations of Lena image corrupted with RVIN by Group-B
schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
1.10 PSP variations of Lena image corrupted with RVIN by Group-C
schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
1.11 PSNR (dB) variations of Lena image corrupted with SPN
. . . . . 40
1.12 PSP variations of Lena image corrupted with SPN . . . . . . . . . . 40
1.13 Subjective Evaluation of Lena image subjected to Cascaded Noise
Reduction and Sharpness Enhancement schemes . . . . . . . . . . . 41
2.1
Gray level profile, first-order and second-order derivative of an image 44
2.2
Window Selection for an M × N Image . . . . . . . . . . . . . . . . 47
vii
2.3
Variation of MSE for different threshold values for 1% RVIN noise
for Lena image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.4
Variation of Optimum threshold for different noise % for Lena image. 48
2.5
Variation of Minimum MSE at different Threshold values . . . . . . 49
2.6
Variation of Optimum threshold with CV at different noise density
for Lena image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.7
Multi-Layer Perceptron Structure of Threshold (θ1 ) Estimator. . . . 52
2.8
Convergence Characteristics of Multilayer Perceptron Network . . . 53
2.9
Functional Link Artificial Neural Network (FLANN) Structure for
Threshold Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.10 Convergence Characteristics of FLANN structure . . . . . . . . . . 55
2.11 Radial Basis Functional Network (RBFN) Structure for Threshold
Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.12 Convergence Characteristics of Radial Basis Functional Network . . 57
2.13 PSNR (dB) variations of Restored Lena image corrupted with RVIN
of varying strengths by different adaptive threshold schemes . . . . 58
2.14 PSP variations of Restored Lena image corrupted with RVIN of
varying strengths by different adaptive threshold schemes . . . . . . 61
2.15 Impulsive Noise filtering of Lena image corrupted with 15% of RVIN
by different adaptive threshold schemes . . . . . . . . . . . . . . . . 62
2.16 Impulsive Noise filtering of Peppers image corrupted with 20% of
RVIN by different adaptive threshold schemes . . . . . . . . . . . . 63
3.1
Variation of Minimum MSE at different Threshold values . . . . . . 66
3.2
Functional Link Artificial Neural Network (FLANN) Structure for
Threshold Estimation using CV . . . . . . . . . . . . . . . . . . . . 69
3.3
Convergence Characteristics of the CV based FLANN . . . . . . . . 69
3.4
PSNR (dB) plot of Restored Lena image corrupted with RVIN of
varying strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.5
PSP plot of Restored Lena image corrupted with RVIN of varying
strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.6
Subjective comparison of impulsive noise removal of Lena image
corrupted with 15% of RVIN by different filters . . . . . . . . . . . 73
3.7
Subjective comparison of impulsive noise removal of Peppers image
corrupted with 20% of RVIN by different filters . . . . . . . . . . . 74
4.1
Variation of PSNR (dB) at different RVIN percentage on Lena image. 78
4.2
Computational time of proposed schemes for Lena (512 × 512) with
15% RVIN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.1
Linear Unsharp Masking scheme . . . . . . . . . . . . . . . . . . . . 82
5.2
Improved Unsharp Masking scheme . . . . . . . . . . . . . . . . . . 83
5.3
Comparison among different enhancement approaches for Lena image 84
5.4
Comparison among different enhancement approaches for Pepper
image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
List of Tables
1.1
Comparative Results in PSNR (dB) of different filters for Lena
image corrupted with RVIN of varying strengths . . . . . . . . . . . 35
1.2
Comparative Results in PSP of different filters for Lena image corrupted with RVIN of varying strengths . . . . . . . . . . . . . . . . 36
2.1
PSNR (dB) of different adaptive schemes at 15% and 20% of noise
on different images . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.2
PSP of different adaptive schemes at 15% and 20% of noise on
different images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.3
Computational time for different Schemes for removing impulsive
noise from Lena image corrupted with 15% of RVIN
3.1
. . . . . . . . 60
PSNR (dB) of different schemes at 15% and 20% of noise on different images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.2
PSP of different schemes at 15% and 20% of noise on different images 71
3.3
Computational time consumed by different Schemes for removing
impulsive noise from Lena image corrupted with 15% of RVIN
. . 71
4.1
Noise classification as per noise ratio . . . . . . . . . . . . . . . . . 75
4.2
Noise removal scheme chosen for comparison . . . . . . . . . . . . . 76
4.3
False Positive Percentage(FP%) and False Negative Percentage (FN%)
of proposed schemes for Lena (512 × 512) with 15% RVIN. . . . . . 77
4.4
Basis of comparison among the filtering schemes . . . . . . . . . . . 77
4.5
Comparison of schemes under low and medium noise conditions . . 78
4.6
Comparison of different schemes under high noise conditions . . . . 78
4.7
Computational overhead per pixel associated in filtering schemes
x
. 79
Chapter 1
Introduction
Within seconds of entering the world, those who are blessed with the gift of sight
start acquiring images. Human beings are primarily visual creatures who depends
solely on sense of vision. So vision allows humans to perceive and understand the
world surrounding them in a better manner. Hence, processing visual information
by computer has been drawing a very significant attention of the researchers over
the last few decades. The process of receiving and analyzing visual information by
the human species is referred to as sight, perception or understanding. Similarly,
the process of receiving and analyzing visual information by digital computer is
called digital image processing [1]. Before advancing more we should answer one
question ̏Why do we process images ? ˝
Image Processing has been developed in response to solve three major problems
concerned with pictures [2]:
• Picture digitization and coding to facilitate transmission, printing and storage of pictures.
• Picture enhancement and restoration in order for example, to interpret more
easily pictures of the surface of other planets taken by various probes.
• Picture segmentation and description as an early stage in machine vision.
An image may be described as a two-dimensional function I.
I = f (x, y)
(1.1)
where x and y are spatial coordinates. Amplitude of f at any pair of coordinates
(x, y) is called intensity I or gray value of the image. When spatial coordinates
1
and amplitude values are all finite, discrete quantities, the image is called digital
image [3]. The digital image I is represented by a single 2- dimensional integer
array for a gray scale image and a series of three 2- dimensional arrays for each
colour bands.
Digital image processing may be classified into various subbranches based on
methods whose [3]:
• input and output are images and
• inputs may be images where as outputs are attributes extracted from those
images.
Following is the list of different image processing functions based on the above
two classes.
• Image Acquisition
• Image Enhancement
• Image Restoration
• Color Image Processing
• Multi-resolution Processing
• Compression
• Morphological Processing
• Segmentation
• Representation and Description
• Object Recognition
For the first seven functions the inputs and outputs are images where as for
the rest three the outputs are attributes from the input images. With the exception of image acquisition and display most image processing functions are implemented in software. Image processing is characterized by specific solutions, hence
2
1.1 Image Enhancement
the technique that works well in one area can be inadequate in another. The
actual solution of a specific problem still requires a significant research and development [4]. Among the broad spectrum of applications remote sensing, medical
imaging, image morphing and warping are important. Figure 1.1 [2] depicts a pictorial representation of various image processing applications along with different
image processing functions.
Out of the ten sub-branches of digital image processing, cited above, this thesis
deals with image restoration and one of its application to enhancement. To be
precise, the thesis devotes on a part of the image restoration i.e. noise removal
from images, stated in the Problem Definition. Further, this thesis also discusses
how image noise removal can be utilized for high quality image enhancement.
This chapter is organized as follows. Section 1.1 is devoted to convey the basic
concepts of Image Enhancement and its various types, problems associated with
enhancement techniques are presented in Section 1.4. Image Restoration is discussed in Section 1.2 followed by a broad classification of filters in Section 1.3.
The problem definition associated with noise removal from images is described
in Section 1.4. Different performance measures for comparison are described in
Section 1.5. Review of different existing schemes and their performance analysis
is done in Section 1.6. Motivation behind carrying out the work is stated in Section 1.7. Organization of the thesis is outlined in Section 1.8. Finally, Section 1.9
provides the chapter summary.
1.1
Image Enhancement
Images are captured at low contrast in a number of different scenarios. The main
reason for this problem is poor lighting conditions (e.g., pictures taken at night
or against the sun rays). As a result, the image is too dark or too bright, and
is inappropriate for visual inspection or simple observation. Image enhancement
algorithms are used in a variety of image processing applications, primarily to improve or enhance the visual quality of an image by accentuating certain features [5].
Image processing modifies pictures to improve them (enhancement, restoration) to
3
1.1 Image Enhancement
Figure 1.1: Image Processing Tree
prepare suitable images for various applications from raw unprocessed images. Images can be processed by optical, photographic, and electronic means, but image
processing using digital computers is the most common method because digital
methods are fast, flexible, and precise. Image enhancement improves the quality
(clarity) of images for human viewing. Increasing contrast, and revealing details
are examples of enhancement operations where as removing blurring and noise
comes under the category Image restoration.
Planetary scientists were the first users of enhancement techniques to enhance
images of Mars,Venus and other planets. Radiologists, Doctors use this technology
frequently to manipulate CAT scans, MRI and X-ray images. Areas like forensic science use image sharpening(enhancement) techniques for criminal detection.
Enhancement algorithms are used extensively to enhance biometric (finger print,
4
1.1 Image Enhancement
iris) images in airport, banking security systems. Palm print manuscripts contain
religious texts and treaties on a host of subjects such as astronomy, astrology,
architecture, law, medicine and music. Most of these palm-leaves are nearing
the end of their natural lifetime or are facing destruction from elements such as
dampness, fungus, ants and cockroaches. enhancement algorithms are inevitable
members of the preservation projects to protect these valuable historical documents. Enhancement techniques are used to enhance the degraded documents so
as to enable retrieval of the written text from these documents. Printing technology also uses extensively the enhancement schemes to produce high quality
photographic prints. Acquisition of information of an object or phenomenon, by
the use of sensing devices that is not in physical or intimate contact with the object
i.e forest, vegetation, land utilization, sea changes etc. Various image processing
techniques are involved in analyzing the acquired data. Image enhancement is
one of the important image processing functions primarily done to improve the
appearance of the imagery to assist in visual interpretation and analysis. Image
restoration and enhancement are used usually in synchronization rather than as
an individual.
This class of image processing algorithms include image sharpening, contrast
and edge enhancement. Among the enhancement algorithms contrast enhancement is most important because it plays a fundamental role in the overall appearance of an image to human being. A human being’s perception is sensitive to
contrast rather than the absolute values themselves. So it is justified to increase
the contrast of an image for better perception. Section 1.1.1 provides a detail
classification for conventional enhancement schemes under the heading contrast
enhancement. This thesis devotes on image sharpening under impulse noise conditions. We concentrate on those noise removal algorithms which preserve edge
details as well remove noise using selective filtering technique. This helps the enhancement schemes to be cascaded along with noise removal algorithm to produce
better quality images with more edge details.
5
1.1 Image Enhancement
1.1.1
Contrast Enhancement
Image enhancement usually employs various contrast enhancement schemes to increase the amount of visual perception. Different enhancement schemes emphasize
different properties or components of images [1, 3]. Contrast enhancement techniques can be broadly classified into two categories. For the first category, the
gray value of each pixel is modified based on the statistical information of the image. Power law transform [6], log transform [6], histogram equalization belong to
this category. In the second category the contrast is enhanced by first separating
the high and/or low frequency components of the image, manipulating them separately and then recombining them together with the different weights. Unsharp
Masking (UM) which emphasizes high frequency components of an image belongs
to this category. The pitfalls associated with unsharp masking is presented in
problem definition ( 1.4). One possible solution for this problem is narrated in
chapter 5. Some of the contrast enhancement methodologies are described below.
• Image Negative
The negative of an image with gray levels in the range [0, L-1] is obtained
by using the negative transformation, which is given by the equation 1.2.
s =L−1−r
(1.2)
where r & s denote the values of pixels before and after the processing and
L is the maximum Gray level intensity of the input image. Reversing the
intensity level of an image in this manner produces the equivalent of a photographic negative. This type of processing is particularly suited for enhancing
white or gray detail embedded in dark regions of an image.
• Logarthimic law
This is one of the simplest enhancement technique. It uses a log transform
to convert the input gray level to an output gray level to expand the values
6
1.1 Image Enhancement
of dark pixels in an image while compressing higher level values. The general
form of the log transformation can be represented using the relation:
s = c. log(1 + r)
(1.3)
where c is a constant and it is assumed that r ≤ 0. Where r and s are input
and output gray levels respectively.
• Power Law
Devices used for image capture, printing, and display respond according to
a power law given as:
s = c.r γ
(1.4)
By convention, the exponent in the power law equation is referred to as
gamma. The process used to correct this power law response is called gamma
correction. Images not corrected properly can look bleached out or dark. So
proper gamma adjustment must be done to produce the gray levels accurately and produce appropriate brightness.
• Histogram Equalization
The luminance histogram of a typical natural scene that has been linearly
quantized is usually highly skewed toward the darker levels; a majority of
the pixels possess a luminance less than the average. In such images, detail in the darker regions is often not perceptible. One means of enhancing
these types of images is a technique called histogram modification, in which
the original image is rescaled so that the histogram of the enhanced image
follows some desired form [6]. This method also assumes the information
carried by an image is related to the probability of occurrence of each gray
level. To maximize the information, the transformation should redistribute
the probabilities of occurrence of the gray level to make it uniform. In this
way, the contrast at each gray level is proportional to the height of the
image histogram [7]. Various modifications of histogram equalization are
7
1.2 Image Restoration
also available which increases its potential of contrast enhancement. Adaptive histogram equalization (AHE) [8], Contrast limited adaptive histogram
equalization (CLAHE) [9] belong to that category which apply histogram
equalization locally on the image and provides better contrast.
• Unsharp Masking
Unsharp masking (UM) is an image manipulation technique which was first
used in Germany in the 1930s as a way of increasing the acutance, or apparent sharpness, of photographic images. In Unsharp masking scheme, a high
pass filtered scaled version of an image is added to the image itself. It is desired when a particular application requires the high frequency components
of an image. One of its principal application is dark room photography [3].
The process can be represented with the help of the following equation.
= Ix,y + λI x,y
Ix,y
(1.5)
are original and enhanced images respectively. Ix,y
is the high
where Ix,y , Ix,y
pass component of the original image which is scaled with an amplification
.
factor λ as per requirement to obtain the enhanced image Ix,y
1.2
Image Restoration
The field of digital image restoration had its first encounter with the starting of
space program by the scientists involved of United States of America and the former Soviet Union in the 1950s and early 1960s. The first images of the Earth, Moon
(mainly of the opposite side), and planet Mars were, at that time, of unimaginable
resolution which were obtained under big technical difficulties. These programs
were responsible for producing many incredible images of our solar system, which
were at that time unimaginable. However, the images obtained from the various
planetary missions of the time were subject to many photographic degradations.
The need to retrieve as much information as possible from such degraded images
was the aim of the early efforts to adapt the one-dimensional signal processing
algorithms to images, creating a new field that is today known as digital image
8
1.2 Image Restoration
restoration. The 22 pictures produced during the Mariner IV flight to Mars in
1964 were later estimated to cost almost $10 million just in terms of the number
of bits transmitted alone [10].
In astronomical imaging the ultimate goal is to recover the original celestial
image from the degraded one. The degradations were as a result of relative motion
between camera and the original scene, defocusing of the lens system because of
vibration in machinery and spinning and tumbling of the spacecraft or because of
substandard imaging environment. In addition to blurring the space images are
also corrupted with additive random noise. Rapidly changing refractive index of
the atmosphere was also one of the reasons for the degradation. Pictures from
the manned space mission were also blurred due to the inability of the astronaut
to steady himself in a gravitation less environment while taking photographs.
Extraterrestrial observations were degraded by motion blur as a result of slow
camera shutter speed, relative to rapid spacecraft motions. The degradation of
images was no small problem. Any loss of information due to image degradation is
devastating as it reduces the scientific value of these images. There is no surprise
that astronomical imaging is still one of the primary applications of digital image
restoration today.
The rapid growth of medical imaging equipment which capture, record, and
redisplay in a non-invasive manner the internal structure of living matter or patients, has composed a great challenge and opportunity to image processing tasks.
Providing better diagnosis facility would have been a tedious job without image
restoration. X-rays, mammograms, and digital angiographic images [11] without filtering would have been of no use since the acquiring methods are usually
associated with various degradation phenomenon like noise. Sophisticated imaging techniques like PET (Positron Emission Tomography) and SPECT (Single
Photon Emission Computed Tomography) are two methods to obtain images noninvasively from the interior of a patient which extensively use restoration schemes
to improve resolution in order to perform better diagnosis. Other than this it
also finds its utility in Magnetic Resonance Imaging (MRI) [12]. Digital image
9
1.2 Image Restoration
restoration techniques can contribute significantly for this [13].
Films reflects the culture from which it is stemmed and records our history,
represent contemporary culture and have great artistic value. Thus, they are precious cultural assets which must be preserved. Unfortunately, because of aging,
improper storage conditions and other reasons, old films are threaten with defects caused by decaying, dust, dirt, scratch and mold [14]. Consequently, digital
film restoration, repairing defects in films, has been recognized as an important
issue by archives, content owners and film companies. Motion picture restoration
is not limited to eliminate scratches and dust from old movies, but also to colorize black-and-white films like Mughal-e-Azam. Only a small subset of the vast
amount of work being done in this area can be classified under the category of
image restoration. Much of this work belongs to the field of computer graphics
and enhancement. Nonetheless, some very important work has been done recently in the area of digital restoration of films. Digital restoration of the film
̏Snow White˝and the ̏Seven Dwarfs˝by Walt Disney, which originally premiered
in 1937 [15] are few to cite.
Image restoration has also received some notoriety in the media, and particularly in the movies of the last decades. The climax of the 1987 movie ̏No Way
Out˝was based on the digital restoration of a blurry Polaroid negative image [16].
The 1991 movie ̏JFK˝made substantial use of a version of the famous Zapruder
8mm film of the assassination of the US President John F. Kennedy. It is no surprise that digital image restoration has been used in law enforcement and forensic
science for a number of years. Complex problems like solving a crime often requires
security video tapes, blurry photographs of license plates and crime scenes to be
properly visualized for proper investigation. Image restoration helps in improving
the quality of such images which are often needed when such photographs can
provide the only link for solving a crime. Clearly, law enforcement agencies all
over the world have made, and continue to make use of digital image restoration
ideas in many forms.
Image and video coding is one of the exciting applications of image restora-
10
1.2 Image Restoration
tion. Even though coding efficiency has improved and bit rates of coded images
have reduced, there is another problem of blocking artifacts which needs significant improvement. These are as a result of the coarse quantization of transform
coefficients used in typical image and video compression techniques. Usually, a
Discrete Cosine Transform (DCT) will be applied to prediction errors on blocks
of 8 × 8 pixels. Intensity transitions between these blocks become more and more
apparent when the high-frequency data is eliminated due to heavy quantization.
Already, much has been accomplished to model these types of artifacts, and develop ways of restoring coded images as a post-processing step to be performed
after decompression [17–19].
Digital image restoration is being used in many other applications as well. Just
to name a few, restoration has been used to restore blurry X-ray images of aircraft
wings to improve aviation inspection procedures. It is used for restoring the motion
induced effects present in still composite frames, and, more generally, for restoring
uniformly blurred television pictures. Printing applications often require the use
of restoration to ensure that halftone reproductions of continuous images are of
high quality. In addition, restoration can improve the quality of continuous images
generated from halftone images. Digital restoration is also used to restore images
of electronic piece parts taken in assembly-line manufacturing environments. Many
defense-oriented applications require restoration, such as that of guided missiles,
which may obtained distorted images due to the effects of pressure differences
around a camera mounted on the missile. All in all, it is clear that there is a very
real and important place for image restoration technology today.
Image restoration is distinct from image enhancement techniques, which are
designed to manipulate an image in order to produce results more pleasing to
an observer, without making use of any particular degradation models. Image
enhancement refers to the techniques by which we try to improve an image such
that it looks subjectively better by improving the visual appearance of the image.
On the other hand restoration emphasizes on getting back the original image as
far as possible from the degraded one. Thus the goal of image enhancement is
11
1.2 Image Restoration
very different from that of restoration. Better representation of image is obtained
through image enhancement techniques, however, it would not be possible to define
what enhancement exactly means, as an enhancement to one may be a noise to
another [20]. Applying image enhancement scheme is of no use if the image which
we want to enhance is of low quality or is degraded due to presence of noise
or is an blurred image. So cascading schemes combining image noise removal
followed by enhancement is among one of the solution for better visual perception.
In this thesis we use such restoration techniques such that it can be used as a
preprocessing step for enhancement producing better quality images.
Image reconstruction techniques operate on a set of image projections and not
on a full image. Restoration and reconstruction techniques do share the same
objective, however, which is that of recovering the original image, and they end
up solving the same mathematical problem, which is that of finding a solution to
a set of linear or nonlinear equations.
Digital image restoration is a field of engineering that studies methods used
to recover an original scene from degraded observations. Developing techniques
to perform the image restoration task requires the use of models not only for
the degradations, but also for the images themselves. Image restoration problem
is a subset of Inverse Problem. In general, in inverse problems, the values of a
certain set of functions are estimated from the known properties of other functions.
Consider the following relationship
L({fi }, {gj }) = 0
(1.6)
where L is an operator, the function, {fi }, are sought, and the values of the functions, {gj }, are known. When the problem is well posed, the existence of solution
is assured. Also there exists a unique solution for a given problem. However, in
the presence of noise, the uniqueness of solution is not assured.
The image degradation and subsequent restoration may be depicted as in Figure 1.2(a). In this thesis, however, only noise part of entire degradation is dealt
with, which is shown in Figure 1.2(b). We consider such noise removal schemes
such that the output can be useful for further image enhancement while preserv12
1.3 Filters
ing image details during noise removal process. The following section provides a
broad classification of restoration filters.
g( x, y)
True
f ( x, y)
Image
Restoration
Degradation
Function H
Restored
^
Image f ( x, y)
Filter (s)
Noise
η( x, y)
(a)
g( x, y)
Restoration
Filter (s)
True f ( x, y)
Image
Restored
Image
Noise
η( x, y)
(b)
Figure 1.2: (a) Model of the image degradation/restoration process, (b) Model of
the Noise Removal Process.
1.3
Filters
Image restoration, usually, employs different filtering techniques. Filtering may
be done either in spatial domain or in frequency domain. In this thesis different
spatial domain filtering techniques have been studied and proposed. Broadly,
filters may be classified into two categories: Linear and Nonlinear. The filtering
methodologies are described below.
1.3.1
Linear Filters
In the early development of image processing, linear filters were the primary tools.
Their mathematical simplicity with satisfactory performance in many applications
made them easy to design and implement. However, in the presence of noise the
performance of linear filters is poor. In image processing applications they tend
to blur edges, do not remove impulsive noise effectively, and do not perform well
in the presence of signal dependent noise [21].
Mathematically, a filter may be defined as an operator L(· ), which maps a
signal x into a signal y:
y = L(x)
(1.7)
When the operator L(· ) satisfies both the superposition and proportionality principles, the filter is said to be linear. Two-dimensional and m-dimensional linear
13
1.3 Filters
filtering is concerned with the extension of one-dimensional filtering techniques
to two and more dimensions. If impulse response of a filter has only finite number of non-zero values, the filter is called a finite impulse response (FIR) filter.
Otherwise, it is an infinite impulse response (IIR) filter [22].
If the filter evaluates the output image only with the input image, the filter
is called non-recursive. On the other hand, if the evaluation process requires
input image samples together with output image samples, it is called recursive
filter [4, 21, 23]. Following are the few main types of filters:
• Low-pass filter: Smooths the image, reducing high spatial frequency noise
components.
• High-pass filter: Enhances very low contrast features, when superimposed
on a very dark or very light background.
• Band-pass filter: Tends to sharpen the edges and enhance the small details
of the image.
1.3.2
Nonlinear Filters
Nonlinear filters also follow the same mathematical formulation as in (1.7). However, the operator L(· ) is not linear in this case. Convolution of the input with
its impulse response does not generate the output of a nonlinear filter. This is
because of the non-satisfaction of the superposition or proportionality principles
or both [21–23].
Gray scale transformations [1, 3, 6] are the simplest possible nonlinear transformations of the form (1.7). This corresponds to a memory less nonlinearity that
maps the signal x to y. The transformation
y = t(x)
(1.8)
may be used to transform one gray scale x to another y. This type of gray level
transform are extensively used for enhancing the subjective quality of the images
as per the need of the application. Histogram modification is another form of
14
1.3 Filters
intensity mapping where the relative frequency of gray level occurrence in the image is depicted. An image may be given a specified histogram by transforming the
gray level of the image into another. Histogram equalization is one such methods
that is used for this purpose. The need for it arises when comparing two images
taken under different lighting conditions. The two images must be referred to the
same base, if meaningful comparisons are to be made. The base that is used as
standard has a uniformly distributed histogram [1, 3, 6]. Of course, a uniform histogram signifies maximum information content of the image [24]. Histogram based
approaches as discussed above are used as simple image enhancement techniques
in various applications. Figure 1.3 gives a graphical representation of the various
families of nonlinear filters [21].
Order Statistics Filters
Morphological
Filters
Median
Filters
NONLINEAR FILTERS
Nonlinear
Mean
Filters
Polynomial
Filters
Quadratic
Filters
Homomorphic
Filters
FILTERS
Figure 1.3: Nonlinear Filter Family
Order statistic filters [21,23] for noise removal are the most popular class nonlinear filters. A number of filters belongs to this class of filters, e.g., the median
filter, the stack filter, the median hybrid filter etc. Nonlinear filters based on order
statistics have excellent robustness properties in the presence of impulsive noise.
They tend to preserve edge information, which is very important for human perception. Even there computation is relatively easy and fast as compared to some
15
1.3 Filters
linear filters. Such properties of those filters have created numerous applications
in digital image processing.
There exists some approaches that utilizes geometric features of signals rather
than analytic features of signals. Their origin is basic set operations for image
processing. These filters are called morphological filters and find applications in
image processing and analysis. Biomedical image processing, shape recognition,
edge detection, image enhancement are few other areas, where it is used extensively
[1, 3, 6, 21, 23].
One of the oldest class of nonlinear filters, which have been used extensively
in digital signal and image processing, are homomorphic filters and their extensions. These filter class find its applications in image enhancement, multiplicative
and signal dependent noise removal, speech processing and also in seismic signal
processing [1, 3, 6, 21, 23].
Adaptive filtering has also taken advantage of nonlinear filtering techniques.
Non-adaptive nonlinear filters are usually optimized for a specific type of noise
and signal. When, however, the filter is required to operate in an environment of
unknown statistics or a non stationary environment, an adaptive filter provides
an elegant solution to this more difficult problem. Images can be modeled as
two-dimensional stochastic processes, whose statistics vary in the various image
regions and also from applications to applications. In such situations, adaptive
filters become the natural choice and their performance depends on the accuracy
of estimation of certain signal and noise statistics [1, 3, 6, 21, 23]. The filter starts
from an arbitrary initial condition, knowing nothing about the environment, and
proceeds gradually towards an optimal solution.
Considerable attenuation has been given nonlinear estimation of signals corrupted with noise. Despite impressive growth in last few decades, nonlinear filtering techniques still lack a unifying theory that encompasses existing nonlinear
processing techniques.
16
1.4 Problem Definition
1.4
Problem Definition
Different types of noise frequently contaminate images. Impulsive noise is one
such noise, which may affect images at the time of acquisition due to noisy sensors
or at the time of transmission due to channel errors or in storage media due to
faulty hardware. Two types of impulsive noise models are described below.
Let Yi,j be the gray level of an original image Y at pixel location (i, j) and
[nmin , nmax ] be the dynamic range of Y . Let Xi,j be the gray level of the noisy
image X at pixel (i, j) location. Impulsive Noise may then be defined as:
⎧
⎨ Y
with 1 − p
i,j
Xi,j =
⎩ R
with p
(1.9)
i,j
where, Ri,j is the substitute for the original gray scale value at the pixel location
(i, j). When Ri,j ∈ [nmin , nmax ], the image is said to be corrupted with Random
Valued Impulsive Noise (RVIN) and when Ri,j ∈ {nmin , nmax }, it is known as Fixed
Valued Impulsive Noise or Salt & Pepper Noise (SPN).
The difference between SPN and RVIN may be best described by Figure 1.4. In
the case of SPN the pixel substitute in the form of noise may be either nmin (0) or
nmax (255). Where as in RVIN situation it may range from nmin to nmax . Cleaning
such noise is far more difficult than cleaning fixed-valued impulse noise since for
the latter, the differences in gray levels between a noisy pixel and its noise-free
neighbors are significant most of the times. In this thesis, we focus only on random
valued impulse noise (RVIN) and schemes are proposed to suppress RVIN.
One common drawback of typical image sharpening (enhancement) methods
is that they tend to boost noise while amplifying the image details making the
image more noisy. This undesirable amplification limits the real time applications
of sharpening algorithms. Typical solution to deal with noise amplification when
performing enhancement is perform noise reduction prior to enhancement. However, noise filters not only suppress noise but also tend to blur the image details
producing low quality images [25]. This is because noise reduction is commonly a
low pass filtering operation, whereas sharpening is a high-pass operation. Hence,
there is a conflicting spectral demand on both filters, and generally, the optimiza17
1.5 Performance Measures
0
{0,255}
255
(a)
0
[0,255]
255
(b)
Figure 1.4: Representation of (a) Salt & Pepper Noise with Ri,j ∈ {nmin , nmax },
(b) Random Valued Impulsive Noise with Ri,j ∈ [nmin , nmax ]
tion of one leads to deterioration of the other [26].
1.5
Performance Measures
The metrics used for performance comparison of different filters (exists and proposed) are defined below.
a. Peak Signal to Noise Ratio (P SNR)
P SNR analysis uses a standard mathematical model to measure an objective
difference between two images. It estimates the quality of a reconstructed
image with respect to an original image. The basic idea is to compute a single
number that reflects the quality of the reconstructed image. Reconstructed
images with higher PSNR are judged better. Given an original image Y of
size (M × N) pixels and a reconstructed image Ŷ , the P SNR(dB) is defined
as:
⎛
⎞
⎜
P SNR(dB) = 10 log10 ⎝
2552
⎟
2 ⎠
M N i=1
j=1 Yi,j − Ŷi,j
1
M ×N
(1.10)
b. Percentage of Spoiled Pixels (P SP )
P SP is a measure of percentage of non-noisy pixels change their gray scale
values in the reconstructed image. In other words it measures the efficiency
18
1.6 Literature Survey
of noise detectors. Hence, lower the P SP value better is the detection, in
turn better is the filter performance.
P SP =
number of non-noisy pixels changed their gray value
× 100 (1.11)
total number of non-noisy pixels
c. Subjective or Qualitative measure
Along with the above performance measure subjective assessment is also
required to measure the image quality. Unavailability of quantitative performance measure in case of image enhancement (sharpening) subjective
or qualitative measure is the only option left for measurement [27]. In a
subjective assessment measures characteristics of human perception become
paramount, and image quality is correlated with the preference of an observer or the performance of an operator for some specific task. Hence as
an usual case of image enhancement there is no quantitative performance
evaluation measure because no ideal image can be used as reference. Any
reasonable measure should be tuned to the human visual system. However
perceptual quality evaluation is not a deterministic process. So subjective
evaluation is the only way to prove the performance. Hence human observer
is the only way by which enhanced image quality can be measured. All the
proposed schemes are hence compared with the subjective results of well
accepted schemes.
In the thesis, Chapter 5 deals with image sharpening (enhancement) under
noisy conditions and no reference ideal image is available for comparison
of objective indices. In such a situation the subjective measure is the only
alternative to be used.
1.6
Literature Survey
In this section literature survey is presented under two heads noise removal and
prevention of noise boosting in contrast enhancement. Noise removal from a contaminated image signal is still a challenging problem for researchers. Many researchers have suggested a large number of algorithms and compared their results.
19
1.6 Literature Survey
The main thrust on all such algorithms is to remove impulsive noise while preserving image details. These schemes differ in their basic methodologies applied to
suppress noise. Some schemes utilize detection of impulsive noise followed by filtering whereas others filter all the pixels irrespective of corruption. In this section
an attempt has been made for a detail literature review on the reported articles
and study their performances through computer simulation. We have classified the
schemes based on the characteristics of the filtering schemes and described are below. We also describe some of the conventional contrast enhancement techniques
in this section, boosting in images can be prevented with proper
1.6.1
Impulsive Noise Removal
A. Filtering without Detection
In this type of filtering a window mask is moved across the observed image.
The mask is usually of size (2N +1)2 , where N is a positive integer. Generally
the center element is the pixel of interest. When the mask is moved starting
from the left-top corner of the image to the right-bottom corner, it performs
some arithmetical operations without discriminating any pixel.
B. Detection followed by Filtering
This type of filtering involves two steps. In first step it identifies noisy pixels
and in second step it filters those pixels. Here also a mask is moved across
the image and some arithmetical operations is carried out to detect the noisy
pixels. Then filtering operation is performed only on those pixels which are
found to be noisy in the previous step, keeping the non-noisy intact.
C. Hybrid Filtering
In such filtering schemes, two or more filters are suggested to filter a corrupted location. The decision to apply a particular filter is based on the
noise level at the test pixel location or performance of the filter on a filtering
mask.
20
1.6 Literature Survey
All those filtering schemes that are reviewed are described in this section under
their respective head.
A. Filtering without Detection
As discussed in the previous section, this technique does not detect contaminated
pixels. It applies the filtering mechanism through out the subject without discriminating any pixel.
A1.
Moving Average [3]
This is a simple linear filter. Average of all pixels of a sliding window is replaced
with the pixel of interest.
Ŷi,j =
1
m×n
Xu,v
(1.12)
(u,v)∈Smn
where, X is the noisy image, Ŷ is the restored image and Smn is the sliding window
of size m × n centered around (i, j). Its performance both in subjective as well as
objective way is very poor.
A2.
Median (3 × 3)
A3.
Median (5 × 5) [3]
The median filter (1.13) is one of the most popular nonlinear filters. It is very
simple to implement and much efficient as well. But the cost is that it blurs the
image and edges are not preserved. It acts like a low pass filter which blocks all
high frequency components of the image like edges and noise, thus blurs the image.
Ŷi,j = MEDIAN(u,v)∈Smn (Xu,v )
(1.13)
Depending upon the sliding window mask there may be many variations of
median filter. Here we have reviewed two such variations. Median (3 × 3) filter
makes use of a 3×3 sliding window, whose center pixel is replaced with the median
value of all the 9 pixels of the window. This kind of filter is helpful when noise is
scattered throughout the image. Whereas median (5 × 5) filter replaces the pixel
of interest i.e. the center pixel with the median value of all the 25 pixels of the
sliding window. When noise appears in blotch, this type of filter works better.
But for other situations it produces disappointing results.
21
1.6 Literature Survey
A4.
WM1 k = 1
A5.
WM k = 2 [28–31]
This is another nonlinear median filter, which favors the center pixel than others.
Let the window size be (2n + 1)2 and L = 2n(n + 1). The filter is defined as:
2k
= MEDIAN{Xi−u,j−v , (2k) 3Xi,j | − h ≤ u, v ≤ h}
Ŷi,j
(1.14)
where 2k is the weight given to pixel (i, j), and 3 represents the repetition opera2k
tion. Hence in a 3 × 3 window Ŷi,j
is the median of (9 + 2k) gray values with the
0
is the standard median
center value of the window repeated (2k + 1) times. Ŷi,j
2k
becomes identity filter when k ≥ L. Two variations of WM
filter, where as Ŷi,j
(with k = 1 and k = 2) have been simulated. When the noise percentage is low,
both the filters work better but beyond 10% of noise the performance starts deteriorating. If noise appears as blotch in a window, it leaves the blotch as it is as if
no filtering has been done.
B. Detection followed by Filtering
Such filtering schemes differentiate between noisy and non-noisy pixels. These
filters, in general, consist of two steps. Detection of noisy pixels is followed by
filtering. Filtering mechanism is applied only to the noisy pixels.
B1.
Rank-Ordered Mean [32]
This is an adaptive approach to solve the restoration problem in which filtering
is conditioned on the current state of the algorithm. The state variable is defined
as the output of a classifier that acts on the differences between the current pixel
value and the remaining ordered pixel values inside a window centered around the
pixel of interest.
This scheme is undoubtedly one of the robust and simple scheme but it fails
in preserving the finer details of the image.
B2.
Progressive-Switching Median [33]
It is a median based filter, which works in two stages. In the first stage an impulse
detection algorithm is used to generate a sequence of binary flag images. This
1
WM: Weighted Median
22
1.6 Literature Survey
binary flag image predicts the location of noise in the observed image. In the
second stage noise filtering is applied progressively through several iterations.
This filter is a very good filter for fixed valued impulsive noise but for random
values the performance is abysmal.
B3.
Adaptive Center Weighted Median Filter [29]
This work is an improvement of previously described Center Weighted Median
(CWM) filter. It works on the estimates based on the differences between the
current pixel and the outputs of the CWM filters with varied center weights.
These estimates decide the switching between the current pixel and median of the
window.
This is a good filter and is robust for a wide variety of images. But it is
inefficient in recovering the exact values of the corrupted pixels.
As the name suggests it employs median filter on the noisy image twice. This
adaptive system tries to correct for false replacements generated by the first round
of median filtering operation. Based on the estimated distribution of the noise,
some pixels changed by first median filter are replaced by their original values and
kept unchanged in the second median filtering. And in the second round it filters
out the remaining impulses.
Even though the filter gives some good results in terms of noise suppression
but spoiling of good pixels is more and it results in overall poor performance.
B5.
Accurate Noise Detector [34]
This filter justifies its name by detecting noise to the perfection. Based on Progressive Switching Median Filter, it generates an edge flag image to classify the
pixels of noisy image into ones in the flat regions and edge regions. The two types
of pixels are processed by different noise detector. When noise is very high prevention of false-detection and non-detection becomes difficult. Therefore, another
iteration is dedicated for verification of the noise flag image.
This scheme exhibits good performance on images not only with low noise
density but also with high percentage of corruption. But all these come at the
23
1.6 Literature Survey
cost of computational complexity which is very high and not at all suitable for
real time applications.
B6.
SM2 (5 × 5)
B7.
SM (7 × 7)
B8.
SM (9 × 9) [35]
This is also a two stage process, where in the first stage noise detection is carried
out and in the second stage filtering is done. The noisy image is convolved with a
set of convolution kernels. Each of the kernels are sensitive to edges in a different
orientation. The minimum absolute value of these four convolutions is used for
impulse detection by comparing with a threshold. By varying the size of kernel
different variations of SM may be obtained. Three such variations of SM are
reviewed here in this paper.
Because of its four kernels it detects noise effectively even in those images
where the edge density is more. But when the kernel size increases to 7 × 7 and
9 × 9 it fails in doing so. Also it fails in preserving finer details.
B9.
Differential Ranked Impulse Detector [36]
This is another nonlinear technique which also works in two stages. It aims at
filtering only corrupted pixels. Identification of such pixels is done by comparing
signal samples within a narrow rank window by both rank and absolute value.
The first estimate is based on the comparison between the rank of the pixel of
interest and rank of the median. The second estimate is based on the brightness
value which is analyzed using the median.
It is a good filter in low noise conditions but the performance slightly degrades
in beyond 20% of noise. It also leaves noise blotch without correcting.
B10.
Enhanced Ranked Impulse Detector [36]
This scheme is an alteration of the scheme described above. Here the brightness is
analyzed by calculating the difference of pixel of interest with its closest neighbors
in the variational series.
Its performance is very good at low noise but fails miserably at noise density
more than 20%.
2
SM: Switching Median
24
1.6 Literature Survey
B11.
Advanced Impulse Detection Based on Pixel-Wise MAD [37]
This scheme is based on modified median of absolute deviation from median
(MAD). MAD is used to estimate the presence of image details. An iterative
pixel wise modification of MAD is used here that provides a reliable removal of
impulses. Its performance is more than average and fails when the edge density is
more.
B12.
Minimum-Maximum Exclusive Mean [38]
This is a simple nonlinear, robust filter that centers around two windows of size
3×3 and 5×5. It checks for a particular range of gray level in the 3×3 windows. If
it fails it goes to 5 × 5 window. If average of all the pixels of that particular range
is more than certain value then that pixel is replaced with the average, otherwise
it is left intact. This is one of the good schemes because of its simplicity and easy
implementation.
B13.
Peak and Valley [39]
This recursive nonlinear filter is composed of two conditional rules. It compares the
test pixel with surrounding neighbor pixels for some conditions. It then replaces
the pixel of interest with the most conservative surrounding pixel. This scheme
is computationally efficient over others but at the same time it spoils non-noisy
pixels to a greater extent.
B14.
Detail preserving impulsive noise removal [40]
Unlike thresholding techniques, it detects noisy pixels non-iteratively using the
surrounding pixel values. It is based on a recursive minimum maximum method
of Peak and Vally scheme. When the image contains numerous edges like Babbon,Clown etc. this technique totally fails.
B15.
Signal-Dependent Rank Ordered Mean [41]
This is one of the most efficient nonlinear algorithms to suppress impulsive noise
from highly corrupted images. Based on detection-estimation strategy, this algorithm replaces the identified noisy pixel with rank ordered mean of it surroundings.
25
1.6 Literature Survey
C. Combined Filtering
Two or more filters are employed in this type of filtering mechanism. In addition
to this a switch is used whose logic helps in switching among the employed filters.
The switch may take output of individual filter into consideration or by some other
means to decide which filter should be employed for a particular window such that
the final output would be the best.
C1.
Tri-State Median Filtering [42]
This combined filter comprises of standard median filter, identity filter, center
weighted median filter and a switching logic. Noise detection is realized by an
impulse detector, which takes the outputs from the standard median and center
weighted median filters and compares them with the center pixel value in order to
make a tri-state decision. The switching logic is controlled by a threshold value.
Depending on this threshold value, the center pixel value is replaced by the output
of either SM filter or CWM filter or identity filter. This is one of the good schemes
reviewed in this paper.
C2.
Two-Output Filter [43]
The two-output nonlinear filter is based on the subsequent activation of two recursive filtering algorithms that operates on different subsets of input data. One
subset is the right-bottom 3×3 sub-window and the other one is left-top 3×3 subwindows of a 4×4 sliding window. Two center pixels of both 3×3 sub-windows are
updated at each step. Rank ordered filtering is used to remove impulsive noise.
This is a good scheme and gives very good result under fixed valued impulsive
noise conditions. But under random valued impulsive noise it fails miserably.
C3.
MRHF3 -1
C4.
MRHF-2
C5.
MRHF-3 [44]
This is a class of non-linear filters called Median Rational Hybrid Filters based on
a rational function. The filter output is the result of a rational operation taking
into account three sub function. In all the three operations the central operation
3
MRHF: Median Rational Hybrid Filter
26
1.6 Literature Survey
is CWM.
In MRHF-1 the CWM gives φ2 and two FIR sub filters give φ1 and φ3 . The
rational function on φ1 , φ2 and φ3 decides which of the filter is most suitable.
In MRHF-2 the sub-filters are four unidirectional median filters. Mean of two
median filters gives φ1 and mean of other two gives φ3 . And the CWM gives φ2 .
The rational function decides based on these three φ values.
In MRHF-3 two bidirectional median filter give φ1 and φ3 . Together with φ2 from
CWM the rational function takes the decision.
Spoiling of non-noisy pixels is high in all the three filters. When compared among
the three, the MRHF-2 outperforms other two.
1.6.2
Prevention of Noise Amplification in Image Sharpening
Loss of sharpness can be caused by poor resolution of the imaging device, limited transmission bandwidth, reflections or echoes in the channel, or poor display.
These anomalies can be improved upon by applying image enhancement techniques. The techniques to achieve enhancement usually separate the high and/
or low frequency components of the image, manipulating them separately and
recombine them together with desired weights. The UM or the high frequency
emphasizing methods which belongs to this category faces a severe drawback that
is noise amplification. Applying those schemes to low contrast noisy images produces undesirable artifacts resulting low quality images. These artifacts become
too strong in particularly in dark regions resulting visually less pleasing enhanced
images. Performance of UM is improved using non linear filters like quadratic
filters [45], Volterra filters [45], morphology based nonlinear filters [46] instead of
linear high pass filters. In an alternate approach the amplification factor is estimated recursively by considering the statistics of neighboring pixel values. Adaptive Unsharp Masking [47] controls the contributions of the amplification factor
in such a way that image enhancement occurs in high detail areas and little or
no image sharpening occurs in smooth areas. Another solution for noise amplification is cascading of noise filters with UM. This scheme does not gives the best
27
1.6 Literature Survey
performance always. Since noise filters tend to blur image details, while UM tend
to increase noise so spectrally this arrangement cannot produce an optimal result.
There is a conflicting spectral demand on both hence optimization of one leads to
deterioration of the other. Little variation of this approach is noise filtering after
UM, this is seldom preferred because the noise filter will remove the sharpness
enhancement created by UM [5]. So noise filtering followed by UM is a simple
enhancement method, but proper filter must be chosen so that it preserves image
details while filtering noise. Hence, proper compromise between image smoothing (noise removal) and sharpening must be done to obtain an image for better
perception.
Procedures for sharpening images under noisy conditions can be classified under two heads:
α. Integrated Noise Reduction and Sharpness Enhancement
β. Cascaded Noise Reduction and Sharpness Enhancement
α. Integrated Noise Reduction and Sharpness Enhancement
Under this category no specialized filter or method is applied to remove noise
before UM. In this approach importance is given to noise sensitivity or to avoid
such image regions which may be noisy.
α1.
Quadratic Filter [25]
Quadratic filters are the simplest non linear time-invariant systems and correspond
to the second term of the Volterra expansion [48]. Such filters are completely
defined by their kernel which is a symmetric finite of infinite square matrix. Inspite
of their nonlinear properties they behave like linear high pass filter. One of them
can be formulated as [49]:
ˆ − Ii+1,j
ˆ − Yi,j−1
ˆ − Ii,j+1
ˆ
Hi,j = 4Iˆi,j − Ii−1,j
(1.15)
Using these filters in UM may still introduce some visible noise, depending on the
amplification factor. To have better performance the output of high pass filter can
be multiplied by a control signal obtained from an edge sensor.
28
1.6 Literature Survey
α2.
Normalized Nonlinear UM [50]
This is an alternate approach to reduce the noise effects and to modify the UM
structure by replacing the sharpening components of simple linear UM scheme by
an enhancement fraction derived from quadratic filters.
α3.
Adaptive UM [51]
In this new approach sharpening action is performed only in locations where the
image exhibits significant dynamics. Hence, the amplification of noise in smooth
areas is reduced. All this is achieved by proper tuning of amplification factor λ. In
the previous schemes the factor λ was fixed for the whole image. In adaptive UM,
the factor λ is controlled by values of the pixels in a neighborhood. Low contrast
details are much more enhanced than the high contrast details in adaptive UM.
β.Cascaded Noise Reduction and Sharpness Enhancement
Cascaded noise reduction and sharpness enhancement algorithms have been implemented to have images of high quality for human as well as machine perception.
This combination of smoothing and sharpening is achieved by using noise filters
along with UM [11,52]. The type of filter to be used depends on the allowed noise
level of the output image. The complete cascaded scheme can be narrated as filtering out impulse noise (smoothing) and sharpening image details. Noise smoothing
and edge enhancement are inherently conflicting processes, since smoothing a region might destroy an edge and sharpening may lead to unnecessary noise amplification. A plethora of such techniques have been proposed in the literature [53,54].
Common filters used here to reduce impulse noise belongs to the category filtering
without detection, because of there simplicity. It can be easily realized from the
previous schemes that noise removal is very important before image enhancement.
Slight amount of noise can even degrade the quality of an image drastically after
enhancement. In this section, we discuss those techniques which uses a particular
filter to remove noise followed by UM. The performance of cascading algorithms
depend mostly on the filtering scheme. The objective is to preserve the image details while filtering noise so that enhancement algorithms can enhance the images
29
1.6 Literature Survey
properly. As per the review under the section impulse noise removal it is observed
that detection followed by filtering scheme is the best. So as per this we can have
different combination of filters with well known unsharp masking. The quality of
enhancement will depend upon the amount of noise removed by the filter. Few
combinations of simple filtering schemes along with UM is discussed below.
β1.
Median Filtering followed by Unsharp Masking [45]
All the steps of unsharp masking remains same except a non linear median filter [3]
output is used as the input to the unsharp masking stage. This filter is able to
remove noise up to some extent but it also blurs the edges since filtering is applied
to all the pixels. Since the image details are lost while filtering the enhanced
images are not satisfactory and it only works under low noise condition.
β2.
Weighted Median Filtering followed by Unsharp Masking [55]
There have been several variations on the median filter, for example the weighted
median filter [30, 56] selectively gives the neighboring pixels multiple entries to
the ordered list, usually with the center pixels of the neighborhood contributing
more entries. this performance is better in higher noise conditions. The higher the
weighting given to the central pixel, the better the filter is at preserving corners,
but the less the smoothing effect is. So its output can be used for getting enhanced
images using UM but not in high noise conditions.
β3.
PWMAD Filtering followed by Unsharp Masking
As an alternate to median filtering and its variations an advanced selective filtering
scheme is applied along with UM. PWMAD [37] is based on modified median of
absolute deviation from median (MAD). Its performance in filtering and hence
with UM is more than average and the filtering fails when the edge density is
more.
30
1.6 Literature Survey
1.6.3
Simulation of Existing schemes, Results and Discussion
Lena image corrupted with RVIN (1% to 30% of noise) is subjected to the different
filtering schemes discussed above and their performance is measured using metrics
(1.10) and (1.11). Table-1.1 lists the P SNR where as Table-1.2 lists the P SP of
different filters. Figures 1.5– 1.7 depict the performance of each scheme in their
respective groups.
The performance in P SNR of Group-A schemes is depicted in Figure 1.5.
The performance of A1 is very poor in comparison to others. A3’s performance
is steady, which is around 30dB. A5 is in commanding position at very low noise
density but flunks at other situations. A2 is better in the upper half where as A4
is better in the lower half of noise density.
Group-B performance is depicted in Figure 1.6. B15 is one of the filters that
outperforms rest all. When comparing other schemes it can be seen that, in the
very low noise density (around 1%) B6 and B9 outperforms all others. When the
density increases (low noise, 5%–15%) B3, B4, B10 and B11 performs equally good
but B6 and B9 decline drastically. When the density further increases (medium
noise, 20%–30%), all the schemes perform more or less same. But B3 and B4 are
slightly better than others in this range of noise.
Figure 1.7 unequivocally depicts that C1 is not only the winner in Group-C
but also outperforms all other schemes in the same group. Performances of C3,
C4 and C5 are almost same where as C2 produces very poor results.
Some of the schemes, whose performance is better in SPN model of noise are
also compared. Figure 1.11 shows the PSNR (dB) variations and Figure 1.12 PSPs
of such schemes.
However, an inherent difficulty in image sharpening or enhancement is unavailability of mathematical criterion for visual quality. As a result final assessment
can only be performed by human observer. Subjective evaluation of Image Sharpening is depicted in Figure 1.13. Subjective evaluation of the images in Figure 1.13
shows that β3 has better performance in comparison to α1, α2, β1 and β2 under
noisy conditions.
31
1.7 Motivation
1.7
Motivation
In the literature, for suppression of impulsive noise mostly the filtering schemes
fall under two categories. First, filtering without detection of noise, where as the
second category filters apply detection mechanism [29, 34–37, 40, 41, 43, 44, 57, 58].
The later schemes are superior to former ones in terms of noise rejection as well
as retention of edges in restored images. It is also observed the performance of
any filtering scheme is dependent on the detection mechanism. The better is the
detector, the superior is the filtering performance. Hence the performance of a
detector plays a vital role. In turn, the detector performance is solely dependent on
a threshold value which is compared with aprecomputed numerical value. Mostly
the reported schemes use a fixed threshold which do not serve the purpose at
various noise conditions as well as in different images. Hence to improve the
detector performance need for an adaptive threshold is an utmost necessity which
can be automatically determined from the charecterstics of an image and the noise
present in it. In this thesis, attemts have been made to determine an threshold
from an observed noisy image. This problem has been formulated as an prediction
problem and various neural network models have been chosen as tools based on
statistical parameters derived from the input noisy images.
In summary, the thesis objectives is listed as:
• to use better image statistics for identifying contaminated pixels and decrease computational complexity.
• to work towards improved and efficient detectors for identifying contaminated pixels using different neural detectors.
• to devise adaptive thresholding techniques so that noise detection would be
more reliable.
• to explore the utilities of selective filtering to image sharpening to produce
high quality images with preserved image details.
32
1.8 Thesis Organization
1.8
Thesis Organization
The rest of the thesis is organized as follows.
Chapter 2 proposes restoration schemes for images contaminated with Random Valued Impulsive Noise. The proposed schemes are based on second order difference of pixels. An adaptive threshold value is used to determine the
noise status of each pixel. Mean and variance are used to train the neural detectors. Three different ways of selecting the threshold value are presented.
The first approach uses an Multilayer Perceptron network trained with back
propagation algorithm to detect noisy pixels. The second approach uses an
Functional Link Artificial Neural Network to determine the noise threshold.
And the last scheme uses a Radial Basis Functional Network to estimate the
sanctity of a test pixel. Comparative analysis with most recent techniques
reveal that the proposed techniques are better in terms of noise suppression.
In Chapter 3 again we use a Functional Link Artificial Neural Network to
determine the threshold with reduced input parameters. Emphasis is given
on the use of better image statistics for training the neural detector. A
single parameter coefficient of variance (CV) of the noisy image is used in this
scheme, which reduces the training time considerably and the noise detection
becomes more accurate. Exhaustive simulations on different standard images
and subsequent comparisons reveal that this proposed scheme outperforms
existing schemes both qualitatively as well as quantitatively.
The objective of Chapter 4 is to critically study the comparative filtering
performance amongst the various methods proposed in this thesis. A conclusion has also been drawn to choose a method for impulse noise filtering
under a particular noise situation.
Chapter 5 covers the topic image sharpening under impulsive noise condition. Prevention of noise amplification and image detail preservation in
image sharpening schemes i.e. Unsharp Masking is achieved using selective
33
1.9 Summary
filtering. Subjective comparison of the proposed scheme resulted with well
accepted result in comparison to existing schemes.
Finally Chapter 6 presents the concluding remark, with scope for further
research work.
1.9
Summary
The fundamentals of digital image processing, sources of noise and types of noise
in an image, the existing filtering schemes and their merits and demerits and
the various image metrics are studied in this chapter. Applications of neural
architectures have been underutilized in the surveyed schemes. To derive the
benefits of this paradigm, investigation has been made in this thesis to develop
some novel schemes in the area of image restoration. Further applications of
selective filtering to image enhancement is also been explored in this thesis.
34
1.9 Summary
Table 1.1: Comparative Results in PSNR (dB) of different filters for Lena image
corrupted with RVIN of varying strengths
N oise ⇒
1%
5%
10%
15%
20%
25%
30%
A1
28.16
26.76
24.19
22.44
21.07
20.01
19.11
A2
35.04
33.96
32.81
31.65
30.25
28.94
27.39
A3
30.95
30.4
29.82
29.22
28.48
27.96
27.32
A4
38.19
36.11
33.99
31.76
29.32
27.30
25.25
A5
41.16
36.05
31.26
27.73
24.87
22.70
20.88
B1
31.64
31.01
30.25
29.60
28.86
28.15
27.39
B2
31.95
31.28
30.81
30.05
29.27
28.54
27.84
B3
36.08
34.77
33.37
32.21
31.12
29.02
28.02
B4
35.32
34.15
32.94
31.88
30.59
29.40
28.19
B5
31.51
30.33
29.03
28.23
27.18
26.59
25.84
B6
40.55
35.01
31.84
29.71
27.97
26.66
25.43
B7
33.9
31.86
30.3
29.01
27.57
26.59
25.60
B8
30.48
29.31
28.09
27.11
26.03
25.18
24.22
B9
42.08
36.01
32.12
28.89
26.40
24.35
22.68
B10
39.21
36.06
33.85
31.64
30.80
28.91
27.22
B11
37.10
35.47
33.55
31.72
29.52
27.34
25.39
B12
38.93
33.47
30.06
27.63
25.67
24.13
22.73
B13
35.99
34.68
32.89
30.93
28.36
26.48
24.35
B14
36.87
33.34
29.53
26.62
24.37
22.64
21.07
B15
42.90
38.68
35.80
33.95
32.24
30.90
29.63
C1
39.49
36.06
34.01
31.61
29.09
28.46
27.88
C2
31.92
24.92
21.97
20.21
18.91
17.95
17.06
C3
30.97
29.38
27.03
24.89
23.02
21.46
20.13
C4
32.01
30.24
27.73
25.47
23.50
21.84
20.42
C5
31.59
30.02
27.73
25.56
23.62
22.02
20.60
F ilters ⇓
35
1.9 Summary
Table 1.2: Comparative Results in PSP of different filters for Lena image corrupted
with RVIN of varying strengths
N oise ⇒
1%
5%
10%
15%
20%
25%
30%
A1
98.99
99.08
99.13
99.18
99.32
99.45
99.56
A2
66.71
67.4
68.12
68.45
69.14
69.63
69.97
A3
78.23
78.84
79.43
79.73
80.34
80.77
80.98
A4
40.58
40.28
39.7
39.34
38.99
38.67
38.27
A5
22.84
21.77
20.60
19.52
18.40
17.61
16.92
B1
96.85
97.03
97.25
97.39
97.53
97.78
97.96
B2
00.00
00.05
00.09
00.05
00.11
00.00
00.22
B3
06.36
06.70
07.06
07.55
07.89
08.57
09.38
B4
59.01
59.52
60.05
60.56
61.14
61.74
62.29
B5
00.00
00.00
00.02
00.05
00.08
00.06
00.00
B6
00.13
00.17
00.21
00.26
00.32
00.44
00.58
B7
01.27
01.49
01.62
01.96
02.29
02.88
03.37
B8
03.63
04.06
04.49
05.22
06.03
07.13
08.47
B9
00.09
00.09
00.1
00.12
00.12
00.16
00.17
B10
01.17
01.21
01.33
01.49
01.79
02.21
02.75
B11
08.70
08.81
08.90
09.05
09.20
09.50
10.08
B12
00.33
00.60
01.24
02.21
03.62
05.37
07.68
B13
51.46
51.86
52.31
52.71
53.43
53.85
54.41
B14
25.63
23.87
21.98
19.93
18.25
17.13
15.63
B15
0.28
0.28
0.33
0.32
0.34
0.40
0.47
C1
00.74
00.79
00.89
00.99
01.16
01.14
01.59
C2
00.01
00.03
00.05
00.06
00.09
00.09
00.13
C3
99.12
99.15
99.18
99.19
99.2
99.21
99.22
C4
92.79
93.34
93.87
94.39
94.99
95.34
95.87
C5
92.28
92.72
93.16
93.62
94.14
94.45
94.91
F ilters ⇓
36
1.9 Summary
45
A1
A2
A3
A4
A5
40
PSNR (dB)
35
30
25
20
15
0
5
10
15
Noise Percentage
20
25
30
Figure 1.5: PSNR (dB) variations of Lena image corrupted with RVIN by Group-A
schemes
45
B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
B11
B12
B13
B14
B15
PSNR (dB)
40
35
30
25
20
0
5
10
15
20
Noise Percentage
25
30
Figure 1.6: PSNR (dB) variations of Lena image corrupted with RVIN by Group-B
schemes
37
1.9 Summary
40
C1
C2
C3
C4
C5
PSNR (dB)
35
30
25
20
15
0
5
10
15
Noise Percentage
20
25
30
Figure 1.7: PSNR (dB) variations of Lena image corrupted with RVIN by Group-C
schemes
100
A1
A2
A3
A4
A5
90
80
PSP
70
60
50
40
30
20
10
0
5
10
15
20
Noise Percentage
25
30
Figure 1.8: PSP variations of Lena image corrupted with RVIN by Group-A
schemes
38
1.9 Summary
100
B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
B11
B12
B13
B14
B15
90
80
70
PSNR (dB)
60
50
40
30
20
10
0
0
5
10
15
Noise Percentage
20
25
30
Figure 1.9: PSP variations of Lena image corrupted with RVIN by Group-B
schemes
100
C1
C2
C3
C4
C5
90
80
70
PSP
60
50
40
30
20
10
0
0
5
10
15
20
Noise Percentage
25
30
Figure 1.10: PSP variations of Lena image corrupted with RVIN by Group-C
schemes
39
1.9 Summary
45
SM(5X5)
MED(3X3)
MED(5X5)
PnV
WM(k=1)
WM(k=2)
TMED
ATMED
40
PSNR (dB)
35
30
25
20
15
0
5
10
15
Noise Percentage
20
25
30
Figure 1.11: PSNR (dB) variations of Lena image corrupted with SPN
100
SM(5X5)
MED(3X3)
MED(5X5)
PnV
WM(k=1)
WM(k=2)
TMED
ATMED
90
80
70
PSP
60
50
40
30
20
10
0
0
5
10
15
Noise Percentage
20
25
30
Figure 1.12: PSP variations of Lena image corrupted with SPN
40
1.9 Summary
(a) α1
(d) β1
(b) α2
(e) β2
(c) α3
—
(f) β3
Figure 1.13: Subjective Evaluation of Lena image subjected to Cascaded Noise
Reduction and Sharpness Enhancement schemes
41
Chapter 2
Adaptive Threshold for Impulsive
Noise Detection
The pending problem that research in Random Valued Impulsive Noise (RVIN)
filtering has been facing is the inability to distinguish noisy values that do not
occur as extreme outliers in comparison with surrounding pixels. Salt and Pepper
(SPN) handling is easy whereas RVIN noise cases are difficult to deal with and
most research directions triala are towards removal of RVIN noise from images.
we have observed few contribution in this directions which has been discussed in
this chapter and the following chapter. The proposed detection scheme involves
second order difference of pixels, which is described in Section 2.1. Threshold values are selected for impulse detection using different image statistics and neural
models. The need for adaptive threshold is described in Section 2.2. Multilayer
Perceptron based Adaptive Thresholding (MLPAT) for impulse detection is discussed in Section 2.3. In Section 2.4, a Functional Link Artificial neural Network
is used to determine the adaptive threshold named, Image Statistics based Adaptive
Thresholding (ISAT) is presented. Radial Basis Functional Network based adaptive thresholding (RBFNAT) for impulse detection is the second noise detection
scheme presented in Section 2.5. Section 2.6 presents a comparative analysis of
the proposed schemes with some of the well accepted schemes. Finally, Section 2.7
provides a complete summary of the chapter.
42
2.1 Second Order Difference of Pixels
2.1
Second Order Difference of Pixels
First and second order derivative must be considered in a digital context before
using it for impulse detection. The behavior of these derivatives in the areas
of constant gray level, at the onset and end of discontinuities, and along gray
level ramps of an image is required to be studied. On the basis of this study we
can say the discontinuities in an image can be used to model noise points, lines
and edges. The behavior of derivatives during transitions into and out of these
image features also is of interest. So for the sake of simplified explanation, onedimensional derivative is focused initially in a digital context. The derivatives of
a digital function are defined in terms of differences. Any definition we use for
first derivative that must be:
i. zero in the areas of constant gray level values i.e. flat segment,
ii. nonzero at the onset of a gray level step or ramp and along the ramp.
Similarly in that context, the second difference must be:
i. zero in the flat areas and along ramps of constant slopes,
ii. nonzero at the onset and end of a gray level step or ramp.
Since derivatives are found for digital quantities whose values are finite, the maximum possible gray level change is also is finite, and the shortest distance over
which that change can occur is between adjacent pixels. First-order derivative of
a one-dimensional function f (x) may be defined as:
∂f
= f (x + 1) − f (x)
∂x
(2.1)
Similarly, second-order derivative may be defined as:
∂2f
= f (x + 1) + f (x − 1) − 2f (x)
∂x2
(2.2)
Figure 2.1 shows a horizontal gray level profile of the edge between two regions.
Also the first and second difference of the gray level profile are shown in the figure.
From left to right along the profile, the first difference is positive at the points of
43
2.1 Second Order Difference of Pixels
Gray Level Profile
First−Order Derivative
Second−Order Derivative
Figure 2.1: Gray level profile, first-order and second-order derivative of an image
transition into and out of the ramp; and is zero in the flat segment. The second
derivative is zero except at the transition points [3].
This behavior of second difference is exploited in the proposed schemes to
determine the sanctity of a pixel. An impulse is nothing but the change in gray
level profile of an image. The second difference of an impulse will result in a spike.
Also there will be a spike for an edge. In order to differentiate between these two
spikes a second order difference based impulse detection mechanism is employed
at location of the test pixel. Once a test pixel is identified as an impulse it is
immediately filtered by replacing it with the median of the surrounding pixels.
This filtered pixel also takes part in the noise detection phase of the next test
pixel and subsequent filtering, if needed. The detection (and filtration)is done
twice, once in the horizontal direction and again in the vertical direction, thus
each test pixel is compared with its neighbors in both directions. Hence selective
filtering helps in achieving superb visual quality and remove the noise completely
at all noise conditions.
44
2.1 Second Order Difference of Pixels
The noise detection algorithm is applied in both horizontal and vertical passes
as described in Section 2.1.1 in detail.
Selection of noise threshold is an important task in the noise detection algorithm and is described in Section 2.2. It should be noticed that the threshold used
in both the directions are different and is obtained using a neural detector.
2.1.1
Algorithm
The proposed algorithm consists of two passes and is described below:
Pass One
i. Choose a window X (t) of size 3 × 5 located at the top-left corner of the
observed image X.
⎛
Xi−1,j−1 Xi−1,j Xi−1,j+1 Xi−1,j+2
X
⎜ i−1,j−2
⎜
X (t) = ⎜ Xi,j−2
Xi,j−1
Xi,j
Xi,j+1
Xi,j+2
⎝
Xi+1,j−2 Xi+1,j−1 Xi+1,j Xi+1,j+1 Xi+1,j+2
Consider a 3 × 3 sub-window X (w) from X as:
⎛
Xi−1,j Xi−1,j+1
X
⎜ i−1,j−1
⎜
X (w) = ⎜ Xi,j−1
Xi,j
Xi,j+1
⎝
Xi+1,j−1 Xi+1,j Xi+1,j+1
ii. Compute the first order 3 × 4 difference
⎛
(d)
(d)
f
f
⎜ i−1,j−1 i−1,j
⎜ (d)
(d)
f (d) = ⎜ fi,j−1
fi,j
⎝
(d)
(d)
fi+1,j−1 fi+1,j
(d)
(t)
⎞
⎟
⎟
⎟
⎠
(2.3)
⎞
⎟
⎟
⎟
⎠
matrix f (d) from X (t) as:
⎞
(d)
(d)
fi−1,j+1 fi−1,j+2
⎟
⎟
(d)
(d)
fi,j+1
fi,j+2 ⎟
⎠
(d)
(d)
fi+1,j+1 fi+1,j+2
(2.4)
(2.5)
(t)
where fi+k,j+l = Xi+k,j+l − Xi+k,j+l−1, k = −1, 0, 1 and l = −1, 0, 1, 2.
iii. Compute the second order 3 × 3 difference matrix s(d) from f (d) as:
⎛
⎞
(d)
(d)
(d)
s
s
s
⎜ i−1,j−1 i−1,j i−1,j+1 ⎟
⎜ (d)
⎟
(d)
(d)
(d)
s = ⎜ si,j−1
si,j
si,j+1 ⎟
⎝
⎠
(d)
(d)
(d)
si+1,j−1 si+1,j si+1,j+1
45
(2.6)
2.2 Adaptive Threshold Selection
(d)
(d)
(d)
where si+p,j+q = fi+p,j+q+1 − fi+p,j+q , p = −1, 0, 1 and q = −1, 0, 1.
iv. The decision index di,j at (i, j) is then computed as:
⎧
⎨ 0 if s(d) > θ1
i,j
di,j =
⎩ 1 otherwise
(2.7)
Select threshold θ1 as described in Sections 2.2– 2.5.
v. Use median filter on the noisy pixels only to remove noise from the pixel
(i, j) with the sub-window as in (2.4).
vi. Shift the window X (t) one by one column from left to right and top to bottom
(as shown in Figure 2.2(a)) and for all windows repeat the steps (ii) through
(vi).
Pass Two
i. Repeat steps (i) through (vi) of Pass One (as shown in Figure 2.2(b)) with
X (t) order as 5 × 3, f (d) order as 4 × 3, and the threshold value as θ2 in place
of θ1 .
2.2
Adaptive Threshold Selection
The sanctity of a pixel is decided solely by the threshold. If a predefined parameter of a test pixel exceeds the threshold value, it is termed as contaminated.
Solution to image restoration problem depends very much on the type of image,
characteristics and density of noise. It is observed from the following experiment
that a single threshold value does not serve the purpose as well as in different
noise conditions. The steps are described as follows:
i. An image (say Lena) is corrupted with impulsive noise of densities 1%, 5%,
10%, 15%, 20%, 25%, and 30%.
ii. The first noisy image Lena1 (the subscript is for 1% of noise) is subjected
to the proposed algorithm outlined in Section 2.1.1 by varying the threshold
value θ between 0 and 1.
46
2.2 Adaptive Threshold Selection
X1,1
X1,2
X1,3
X1,4
X1,5
X1,N−4 X1,N−3 X1,N−2 X1,N−1 X1,N
X2,1
X2,2
X2,3
X2,4
X2,5
X2,N−4 X2,N−3 X2,N−2 X2,N−1 X2,N
X3,1
X3,2
X3,3
X3,4
X3,5
X3,N−4 X3,N−3 X3,N−2 X3,N−1 X3,N
XM−2,1 XM−2,2 XM−2,3 XM−2,4 XM−2,5
XM−2,N−4 XM−2,N−3 XM−2,N−2 XM−2,N−1 XM−2,N
XM−1,1 XM−1,2 XM−1,3 XM−1,4 XM−1,5
XM−1,N−4 XM−1,N−3 XM−1,N−2 XM−1,N−1 XM−1,N
XM,1
XM,2
XM,3
XM,4
XM,5
XM,N−4
XM,N−3
XM,N−2
XM,N−1
XM,N
(a) Horizontal Direction
X1,1
X1,2
X1,3
X1,N−2 X1,N−1 X1,N
X2,1
X2,2
X2,3
X2,N−2 X2,N−1 X2,N
X3,1
X3,2
X3,3
X3,N−2 X3,N−1 X3,N
X4,1
X4,2
X4,3
X4,N−2 X4,N−1 X4,N
X5,1
X5,2
X5,3
X5,N−2 X5,N−1 X5,N
XM−4,1 XM−4,2 XM−4,3
XN−4,N−2 XN−4,N−1 XN−4,N
XM−3,1 XM−3,2 XM−3,3
XN−3,N−2 XN−3,N−1 XN−3,N
XM−2,1 XM−2,2 XM−2,3
XN−2,N−2 XN−2,N−1 XN−2,N
XM−1,1 XM−1,2 XM−1,3
XN−1,N−2 XN−1,N−1 XN−1,N
XM,1
XN,N−2
XM,2
XM,3
XN,N−1
XN,N
(b) Vertical Direction
Figure 2.2: Window Selection for an M × N Image
iii. The MSE(dB) for each threshold is computed and plotted as shown in Figure 2.3. The plot shows that the image achieves minimum MSE for 1% noise,
(1)
(1)
denoted as MSEmin at θ = 0.29 and let this threshold be denoted as θopt .
(i)
(i)
iv. Similarly, θopt are obtained by recording the minimum MSE MSEmin for
i ∈ {5, 10, 15, 20, 25, 30} percentage of noise densities.
v. The relationship between optimum threshold versus the noise densities is
shown in Figure ??. This clearly reveals that threshold needs to be different
at different at different noise densities to minimise the error and hence to
maximise the PSNR (dB) in restored images.
vi. The overall relationshipsbetween MSE(dB) and its corresponding optimum
threshold for different noise conditions for Lena image is shown in Figure 2.4.
47
2.2 Adaptive Threshold Selection
vi. Similar steps are repeated for other standard images like Lisa, House, Peppers etc.
The observations are plotted in Figures 2.5(a), 2.5(b), 2.5(c)
and 2.5(d).
305
300
295
MSE dB
290
285
280
275
270
Optimum Threshold
265
0
0.1
0.2
0.29
0.4
0.5
0.6
0.7
0.8
0.9
1
Threshold
Figure 2.3: Variation of MSE for different threshold values for 1% RVIN noise for
Lena image.
It is in general observed that, there exists an optimum threshold for every
image and for a particular noise density. Even these values differ from image to
image for the same noise density. In addition, the plots reveals clearly that there
exists nonlinear relationship between optimum threshold and noise densities as
well as MSE.
0.4
Optimum Threshold
0.35
0.3
0.25
0.2
1
5
10
15
20
25
30
Noise Density
Figure 2.4: Variation of Optimum threshold for different noise % for Lena image.
The experimental results gives a direction that if an optimum threshold can be
derived adaptively from a given noisy image, the noise detection becomes efficient
48
2.2 Adaptive Threshold Selection
0.9
0.9
30%
0.8
0.7
0.7
0.6
Minimum MSE
Minimum MSE
30%
0.8
25%
0.5
0.4
20%
0.3
0.6
0.5
0.4
25%
0.3
20%
15%
0.2
0.2
10%
05%
0.1
0
0.1
0.15
0.2
0.25
0.3
0.35
Optimum Threshold
0.4
15%
10%
0.1
01%
0
0.45
0.2
0.25
0.6
0.6
Minimum MSE
Minimum MSE
0.4
0.45
0.5
0.8
30%
0.7
25%
0.4
0.3
01%
0.35
(b) Lisa
0.7
0.5
0.3
Optimum Threshold
(a) Lena
0.8
05%
20%
30%
0.5
25%
0.4
0.3
20%
0.2
0.2
15%
15%
0.1
10%
10%
0.1
05%
05%
01%
0
0.2
0.25
0.3
0
0.1
0.35
Optimum Threshold
0.15
0.2
0.25
01%
0.3
Optimum Threshold
(c) House
(d) Peppers
Figure 2.5: Variation of Minimum MSE at different Threshold values
49
0.35
2.3 Adaptive Thresholding for Impulse Detection using MLP
and in turn will affect the filtering performance. But to predict the threshold,
neither the parameters like the noise percentage nor MSE will be a help in real
time image processing as both need the knowledge of original image which is not
available. Hence, a parameter which can be derived from the given noisy image
will be of great help to handle real life situations. For the purpose, a statistical
parameter called Coefficient of Variance (CV) for a noisy image is defined as:
CV =
σ
µ
(2.8)
where, σ and µ are the standard deviation and mean of the noisy image respectively. To further extend the experiment we compute the CVs for all noisy images
for Lena i.e CV(i) , for i ∈ {5, 10, 15, 20, 25, 30}. The relation between CVs and the
optimum threshold is shown in Figure 2.6. This figure also gives the additional
information regarding the existence of a non linear relationship between these two
parameters. Hence, it is decided to utilise the computable parameters, µ, σ 2 , CV
from a noisy image to predict optimum threshold. Neural network being the candidate for a non linear predictor, various neural architectures have been exploited
for the purpose.
0.4
30%
Theta Optimum
0.35
25%
0.3
0.25
20%
0.2
15%
10%
0.45
0.5
0.55
0.6
05%
0.65
01%
0.7
Coefficient of Variance (CV)
Figure 2.6: Variation of Optimum threshold with CV at different noise density for
Lena image.
2.3
Adaptive Thresholding for Impulse Detection using MLP
Over the past few years, a view has emerged that computing based on the structure
and function of the biological neural networks may hold the key to the success
50
2.3 Adaptive Thresholding for Impulse Detection using MLP
of solving intelligent tasks. The new field is called Artificial Neural Networks
(ANN), although it is more appropriate to describe it as parallel and distributed
processing [59]. An ANN consists of interconnected processing units and has a
natural tendency to store knowledge for further use. ANN serves as a potential tool
for numerous nonlinear problems. The ANN based signal detection and filtering
schemes are robust, accurate and work well under nonlinear situations [4].
An ANN consists of interconnected processing units. Typically each processing
unit consists of a summing part followed by an output part. Each summing part
receives a number of input values from a group of other neurons or from external
stimulus. It weights each value, and computes a weighted sum. This weighted sum
is called activation value and constitutes the arguments to a nonlinear activation
function. The resulting value of the activation function is the output of the neuron.
This output gets distributed along weighted connections to other neurons. The
actual manner in which these connections are made defines the flow of information
in the network and called architecture of the ANN.
A neural network has to be configured such that the application of a set of
inputs produces the desired set of outputs. This is achieved by updating the
weights and the process of training the network are called learning paradigms. The
learning paradigms may be supervised, unsupervised or reinforced [11]. Typically
neural networks consists of at least two layers of neurons—a hidden layer and an
output layer. The hidden layer neurons should have nonlinear and differentiable
activation functions. The nonlinear activation functions enable a neural network
to be a universal approximator. The problem of representation is solved by the
nonlinear activation functions [60].
Multilayer perceptron (MLP) networks is an important class of neural networks. MLP network consists of a set of simple sensory units called perceptrons.
These sensory unit constitute the input layer and one or more hidden layer of the
network. The input signal passes through the network in the forward direction
making it a feed forward neural network. MLP is the most widely used neural
classifier for which many learning paradigms have been developed and it belongs to
51
2.3 Adaptive Thresholding for Impulse Detection using MLP
bias
µ
bias
bias
Threshold
σ
2
bias
Input Layer
Hidden Layer
Figure 2.7: Multi-Layer Perceptron Structure of Threshold (θ1 ) Estimator.
the class of supervised neural networks [11]. In MLP networks there exists a nonlinear activation function. The hidden layers along with the connected synaptic
weights make the MLP network active for highly complex tasks.
Here in this section a simple 2–3–1 multi layer perceptron (MLP) (Figure 2.7) is
used to adapt the image environment and to provide an optimal threshold value for
impulsive noise detection. Both the noisy image characteristics (Section 2.2) mean
(µ) and variance (σ 2 ) of Lisa, House, Gatlin and Peppers images are obtained.
These two statistical parameters along with corresponding θopt of these four images
are used here to prepare the training dataset. The suggested neural network is
trained with the available training dataset using the conventional back propagation
algorithm [61]. The Back propagation Algorithm trains the MLP for a given set of
input patterns with known classifications. µ and σ 2 of the noisy image are used as
the two inputs parameters to the perceptron network and θopt is used as the target
output of the network. The training convergence characteristics of the network is
obtained and is shown in Figure 2.8.
The neural network with trained weights are used to obtained threshold subsequently. It is observed that the neural network can predict accurate threshold
for images that are not at all used for training.
First pass of the noise detection algorithm( 2.1.1) uses the threshold value
52
2.4 Image Statistics based Adaptive Thresholding using FLANN
−14
−16
MSE(dB)
−18
−20
−22
−24
−26
0
1000
2000
3000
Iterations
4000
5000
6000
Figure 2.8: Convergence Characteristics of Multilayer Perceptron Network
obtained using the MLP. The output image of the first pass is then subjected to
second pass of the algorithm. In the second pass a different θ is used. Mean and
variance of the output image of the first pass is fed to the network to get the new
threshold value to be used in the second pass.
2.4
Image Statistics based Adaptive Thresholding using FLANN
The Functional Link Artificial Neural Network (FLANN) has been developed as
an alternative architecture to the well–known Multi-Layer Perceptron (MLP) net
with application to both function approximation and pattern recognition [62]. The
main advantage of using FLANN is reduced computational cost in the training
stage, while maintaining the approximation performance of the MLP network. It
is basically a flat net and the need of the hidden layer is removed. The functional
expansion effectively increases the dimensionality of the input vector and hence the
hyperplanes generated by the FLANN provides greater discrimination capability
in the input pattern space [62, 63].
A Functional Link Artificial Neural Network has a feedforward architecture
with a number of non-linear enhancement hidden nodes, referred to as functional
53
2.4 Image Statistics based Adaptive Thresholding using FLANN
links. This proposed detector (FLANN) is shown in Figure 2.9. It is a two layers
structure. The parameters used in the training are same as that of previous
section and are derived from the input noisy image. Mean and variance are the
two statistical inputs which are functionally expanded in the input layer with the
trigonometric polynomial basis functions given by:
{1, µ, sin(πµ), · · · , sin(Nπµ), cos(πµ), · · · , cos(Nπµ),
σ 2 , sin(πσ 2 ), · · · , sin(Nπσ 2 ), cos(πσ 2 ), · · · , cos(Nπσ 2 )}
In order to calculate the error, the actual output on the output layer is compared
with the desired output. Depending on this error value, the weight matrix between
the input–output layers is updated using back propagation learning algorithm.
The training convergence characteristics of the network is shown in Fig. 2.10.
w0
bias b=1
µ
Functional Expansion
sin ( πµ)
µ
σ2
sin ( 50πµ)
cos ( πµ)
w1
w2
..
..
.
w 51
w 52
..
..
.
w 101
cos ( 50πµ)
Actual
Output
w 102
σ2
w 103
sin (π σ 2 )
..
..
.
w 152
sin (50 π σ 2)
w 153
cos ( π σ 2)
w 202
cos ( 50π σ 2)
..
..
.
Error
Σ
+
Target
Output
Figure 2.9: Functional Link Artificial Neural Network (FLANN) Structure for
Threshold Estimation
This threshold value is used in the first pass of the algorithm to detect impulses
in the horizontal direction. The filtered image obtained after the first pass is then
subjected to second pass of the algorithm, where impulses are detected in vertical
fashion. In the second pass a different θ is used. Using the mean and variance
of the output image of the first pass new threshold value for the second pass is
computed.
54
2.5 RBFN based Adaptive Threshold Selection
for Detecting Impulsive Noise in Images
10
5
0
MSE(dB)
−5
−10
−15
−20
−25
−30
−35
0
200
400
600
800
1000
Iterations
Figure 2.10: Convergence Characteristics of FLANN structure
2.5
RBFN based Adaptive Threshold Selection
for Detecting Impulsive Noise in Images
Radial Basis Functional Network (RBFN) have gained considerable attention as
an alternate to multilayer perceptrons trained by the back propagation algorithm.
The basis function are embedded in a two layer neural network, where each hidden
unit implements a radial activated function. There are no weights connected
between the input layer and hidden layer. The output units implement a weighted
sum of hidden unit outputs. The input into an RBF network is nonlinear while the
output is linear. The RBF’s are characterized by there localization (center) and
by an activation hyperspace(activation function). The activation function used in
a RBFN is usually a localized Gaussian basis function. In this detection scheme
we use the standard Gaussian nonlinearity basis function as defined in ( 2.9).
φi (x) = exp(−
(x − ci )2
)
2σ 2
(2.9)
Each gaussian basis function consists of a center (ci ) and a variance σ 2 as its input
parameters. The spread σ of all the Gaussian basis function has been taken fixed
55
2.5 RBFN based Adaptive Threshold Selection
for Detecting Impulsive Noise in Images
and a standard value of 0.1 is used. Basis function centers can be randomly sampled among the input instances or obtained by Orthogonal Least Square Learning
Algorithm or found by clustering the samples and choosing the cluster means as
the centers. Since our training data set is limited so the centers are randomly selected from the training sample and are used to compute φi . The distance metric
employed to calculate the distance of the inputs from the basis center is Euclidean
distance.
The proposed neural detector is a two layers structure and is shown in Figure 2.11. Finding the appropriate RBF weights is called network training and
φ(•)
w
µ
φ(•)
w
w
w
φ(•)
1
2
3
Σ
Actual
Output
4
σ2
φ(•)
Error
Σ
Target
Output
Figure 2.11: Radial Basis Functional Network (RBFN) Structure for Threshold
Estimation
Least Mean Square(LMS) learning algorithm is applied. The parameters used for
training are same as that of previous section ( 2.3). Mean and variance of the
noisy image are the two input parameters to the input layer of the network used
to obtain the noise threshold. Using a set of input–output pair (training data
set) we optimize the network parameters using LMS. In order to determine the
error, the actual output on the output layer is compared with the desired output.
Depending on this error value, the weight matrix between the input–output layers
is updated. The training convergence characteristics of the network is shown in
Figure 2.12.
The threshold value obtained using RBFN is used in the first pass of the algo56
2.6 Simulations and Results
0
−5
MSE(dB)
−10
−15
−20
−25
−30
0
100
200
300
Iterations
400
500
600
Figure 2.12: Convergence Characteristics of Radial Basis Functional Network
rithm to detect impulses in the horizontal direction. The filtered image obtained
after the first pass is then subjected to second pass of the algorithm, where impulses are detected in vertical fashion. In the second pass a different threshold
is used. Using the mean and variance of the output image of the first pass new
threshold value for the second pass is computed. All the steps of first iteration is
repeated in the second iteration with the new threshold.
2.6
Simulations and Results
The three proposed schemes (MLPAT, ISAT, RBFNAT) are simulated with some
of the best performing schemes reviewed in Section 1.6. Adaptive Two-Pass Median filter (2-Pass) [57], Adaptive Center Weighted Median Filter (ACWMF) [29],
Signal Dependent-Rank Ordered Mean (SD-ROM) [41], Tri-State Median (TSM) [42],
Pixel Wise MAD (PWMAD) [37] and Second Order Differential Impulse Detector
(SODID) [64] are used for comparison. Lena image is corrupted with Random
Valued Impulsive Noise of 1% to 30% noise densities. These noisy images are
subjected to filtering by the proposed schemes (MLPAT, ISAT, RBFNAT) along
57
2.6 Simulations and Results
with the above six existing schemes. The PSNR (in dB) and PSP (in percentage)
thus obtained are plotted in Figures 2.13 and 2.14 respectively.
Similarly, simulations are conducted with other standard images like Lisa,Girl,
Clown, Gatlin, Bridge, Boat and Peppers. Table 2.1 lists the PSNR obtained at
15% and 20% of RVIN. Another listing is shown in Table 2.2 for PSP at the same
noise densities.
Two subjective comparisons are also made in Figures 2.15 and 2.16. The former
figure shows the restored images of Lena corrupted with 15% of noise density and
the later one shows restored images of Peppers corrupted with 20% noise density.
The performance of the proposed schemes in terms of P SNR(dB) are better
than most of the schemes except SDROM and TSM. However, both the proposed schemes are computationally better than the above two techniques (listed
in Table 2.3). This is verified by simulating the schemes in Matlab 7.0, Microsoft
Windows XP (SP2) Operating System and Intel Pentium D–2.80 GHz with 1GB
of RAM.
44
2Pass
ACWMF
PWMAD
SD−ROM
TSM
SODID
MLPAT
ISAT
RBFNAT
42
40
PSNR(dB)
38
36
34
32
30
28
26
24
0
5
10
15
20
25
30
Noise Percentage
Figure 2.13: PSNR (dB) variations of Restored Lena image corrupted with RVIN
of varying strengths by different adaptive threshold schemes
58
2.7 Summary
Table 2.1: PSNR (dB) of different adaptive schemes at 15% and 20% of noise on
different images
15%
RVIN
20%
RVIN
2.7
Lisa
Girl
Clown
Gatlin
Bridge
Boat
Peppers
2Pass
31.34
29.62
22.84
31.59
25.77
29.33
31.55
ACWMF
31.78
30.04
22.56
31.62
25.36
28.87
32.98
PWMAD
30.50
29.28
23.02
30.66
26.07
29.25
31.29
SD-ROM
31.98
31.31
24.33
32.77
27.48
30.75
32.00
TSM
32.05
31.05
23.88
32.46
27.08
30.51
33.04
SODID
30.71
30.19
24.52
31.71
26.76
29.59
31.87
MLPAT
29.86
30.20
22.97
31.67
26.68
29.98
32.04
ISAT
31.79
30.17
23.59
31.83
17.42
28.93
32.15
RBFNAT
32.46
29.39
26.20
32.77
26.13
29.67
34.34
2Pass
30.46
28.41
22.25
30.45
25.09
28.32
30.14
ACWMF
30.97
29.92
23.56
31.34
24.82
28.10
31.50
PWMAD
28.26
27.73
22.16
28.77
24.99
27.57
29.04
SD-ROM
30.86
29.92
23.59
31.51
26.55
29.50
31.40
TSM
30.95
29.69
23.28
31.30
26.28
29.35
31.41
SODID
28.89
28.66
22.82
30.14
25.82
28.41
30.24
MLPAT
29.90
29.11
22.38
30.67
25.83
28.81
30.55
ISAT
30.37
28.14
21.69
29.49
16.64
28.18
30.48
RBFNAT
31.73
28.47
26.16
31.34
25.55
28.88
33.16
Summary
This chapter proposes an improved filtering scheme for suppressing impulsive noise
of varying strengths from corrupted images. The threshold value used for detection
of impulsive noise is suggested to be an adaptive one. This leads to reliable
detection of corrupted pixels. The filtration is thus performed selectively only on
the detected noisy pixels. Hence undue distortion is eliminated in the restored
images. In this chapter two different ways of determining the threshold values are
presented. Along with MLP, various neural architecture i.e FLANN, RBFN was
used to determine the threshold. The proposed scheme’s performances are poor
for some images when compared with existing schemes. However, computationally
the proposed schemes are well off.
59
2.7 Summary
Table 2.2: PSP of different adaptive schemes at 15% and 20% of noise on different
images
15%
RVIN
20%
RVIN
Lisa
Girl
Clown
Gatlin
Bridge
Boat
Peppers
2Pass
35.23
51.76
51.95
31.75
54.73
67.30
67.41
ACWMF
6.93
13.29
38.68
5.57
27.98
15.27
0.55
PWMAD
7.35
11.05
24.85
4.00
15.83
13.95
10.53
SD-ROM
0.14
0.93
10.29
0.39
3.06
1.04
0.34
TSM
0.22
2.62
17.51
0.98
7.94
2.55
0.57
SODID
4.84
11.56
19.94
8.34
15.54
13.00
12.16
MLPAT
4.65
11.16
36.87
8.11
15.36
11.16
10.55
ISAT
11.82
62.63
54.04
13.11
0.01
73.98
23.65
RBFNAT
3.69
6.29
13.88
11.68
27.80
28.87
17.54
2Pass
35.67
58.10
52.98
33.24
55.71
67.50
67.45
ACWMF
0.60
0.43
12.60
0.41
28.69
15.80
0.57
PWMAD
7.06
7.82
22.78
5.03
15.10
13.18
10.05
SD-ROM
0.18
0.40
9.86
0.33
3.10
1.11
0.37
TSM
0.31
1.21
21.07
1.00
8.30
2.82
0.73
SODID
6.52
16.74
24.37
10.10
18.75
16.85
15.92
MLPAT
6.25
17.84
42.46
10.10
18.50
14.70
14.11
ISAT
40.17
65.59
56.85
12.38
0.06
74.21
55.98
RBFNAT
11.82
62.63
54.04
13.11
0.01
73.98
23.65
Table 2.3: Computational time for different Schemes for removing impulsive noise
from Lena image corrupted with 15% of RVIN
Scheme
Time (sec)
2-PASS
149.19
ACWMF
413.03
PWMAD
234.68
SDROM
11.60
TSM
74.34
SODID
10.72
MLPAT
11.97
ISAT
11.16
RBFNAT
4.09
60
2.7 Summary
70
60
2Pass
ACWMF
PWMAD
SD−ROM
TSM
SODID
MLPAT
ISAT
RBFNAT
50
PSP
40
30
20
10
0
0
5
10
15
20
25
30
Noise Percentage
Figure 2.14: PSP variations of Restored Lena image corrupted with RVIN of
varying strengths by different adaptive threshold schemes
61
2.7 Summary
(a) True Image
(b) 15% Noisy
(c) 2-Pass
(d) ACWMF
(e) PWMAD
(f) SDROM
(g) TSM
(h) SODID
(i) MLPAT
(j) ISAT
(k) RBFNAT
Figure 2.15: Impulsive Noise filtering of Lena image corrupted with 15% of RVIN
by different adaptive threshold schemes
62
2.7 Summary
(a) True Image
(b) 20% Noisy
(c) 2-Pass
(d) ACWMF
(e) PWMAD
(f) SDROM
(g) TSM
(h) SODID
(i) MLPAT
(j) ISAT
(k) RBFNAT
Figure 2.16: Impulsive Noise filtering of Peppers image corrupted with 20% of
RVIN by different adaptive threshold schemes
63
Chapter 3
CV based Adaptive Threshold for
Impulsive Noise Detection
In this chapter an improved threshold selection strategy to detect random valued
impulsive noise of varying strengths is proposed. The proposed method utilizes
another variation of neural network architecture. The method is adaptive in the
sense that, the threshold obtained is adaptable to different type of images and
noise conditions. The network tuned for one image works for other images as well
at different noise conditions. Emphasis is on the use of right kind of statistical
parameter to be used as input training pattern. Comparative analysis with other
standard techniques reveals that the proposed scheme outperforms its counterparts
in terms of noise suppression.
3.1
Methodology
Using the concepts and assumptions in Section 2.1 and 2.2 it can be visualized
that the performance of the detection scheme depends upon the threshold value.
Successively, threshold value determination depends upon the training parameters. In Chapter 2 two adaptive threshold detection scheme is discussed using
two statistical parameters (mean and variance) as the inputs to the neural detectors (MLP, FLANN and RBFN). This chapter introduces a single parameter
Coefficient of Variance(CV) which can replace the two input parameters (mean
and variance) as used in Chapter 2 as an input to the neural detector. Using CV
as the input training parameter is explained in the next section. A Functional
Link Artificial neural network is used for impulse detection using reduced training
64
3.2 CV based Adaptive Threshold Detection Algorithm (CVAT)
parameters in this chapter. The adaptive threshold detection using FLANN and
CV as input is described in Section 3.3. Decreasing the training parameters and
using an efficient detector i.e. FLANN makes the algorithm work much faster and
the network converges faster.
3.2
CV based Adaptive Threshold Detection Algorithm (CVAT)
Many different techniques are used to determine whether a given pixel is affected
with impulses or not. Some of these techniques are relatively simple, on other hand
some others are complex. Whatever may be the technique, they first determine a
threshold and on that basis apply some filtering mechanism. In Chapter 2 three
such threshold detection schemes based on neural network have been presented.
In this chapter a variation of the previous detection schemes (2.3, 2.5) is being
proposed with improved training parameters.
Second order difference ( 2.1) is utilized here to determine the sanctity of a
pixel. Each test pixel is compared with its neighbors in both horizontal and vertical
directions. The detected noisy pixel is replaced by the median of the neighboring
pixels. The noise detection algorithm of Section 2.1.1 is used here and the adaptive
noise threshold is determined as explained in Section 3.3. Since, there cannot be
one threshold value, which will be a panacea for different types of images. Hence
the threshold should be an adaptive one rather than fixed. Threshold for an image
depends on an image environment. Where environment of an image means, the
type of image, characteristic of noise and its density. For obtaining a correct
threshold some of the image parameters are required. Proper investigation must
be carried out to determine the image parameters which can represent it aptly.
Steps for selecting the parameters is described below.
Suppose for any image and at a particular noise condition the threshold value
θ is varied in a wide range to obtain a set of mean squared error (MSE) values
such that a relation can be established. For example:
i. An image (say Peppers) is corrupted with impulsive noise of densities 1%,
65
3.2 CV based Adaptive Threshold Detection Algorithm (CVAT)
5%, 10%, 15%, 20%, 25%, and 30%.
ii. The first noisy image P eppers1 (the subscript is for 1% of noise) is subjected
to the proposed algorithm outlined in Section 2.1.1 by varying the threshold
value θ between 0 and 1.
iii. Corresponding to each θ one mean squared error (MSE) is obtained. The
(P eppers1 )
minimum among those MSEs is recorded as MSEmin
. Also the corre-
sponding threshold value is recorded as optimal threshold value θopt .
iv. Steps (ii) and (iii) are repeated for other noisy Peppers, i.e. P eppersi , i ∈
{5, 10, 15, 20, 25, 30}.
v. Repeat steps (i) to (iv) for other standard images like Lena, Lisa, House,
etc.
0.9
0.9
30%
0.8
0.8
0.7
0.7
0.6
Minimum MSE
Minimum MSE
30%
25%
0.5
0.4
20%
0.3
0.6
0.5
0.4
25%
0.3
20%
15%
0.2
0.2
10%
05%
0.1
0
0.1
0.15
0.2
0.25
0.3
0.35
Optimum Threshold
0.4
15%
10%
0.1
01%
0
0.45
0.2
0.25
0.6
0.6
Minimum MSE
Minimum MSE
0.4
0.45
0.5
0.8
30%
0.7
25%
0.4
0.3
0.35
(b) Lisa
0.7
0.5
0.3
01%
Optimum Threshold
(a) Lena
0.8
05%
20%
30%
0.5
25%
0.4
0.3
20%
0.2
0.2
15%
15%
0.1
10%
10%
0.1
05%
05%
01%
0
0.2
0.25
0.3
0
0.1
0.35
Optimum Threshold
0.15
0.2
0.25
01%
0.3
Optimum Threshold
(c) House
(d) Peppers
Figure 3.1: Variation of Minimum MSE at different Threshold values
66
0.35
3.2 CV based Adaptive Threshold Detection Algorithm (CVAT)
Figures 3.1(a), 3.1(b), 3.1(c) and 3.1(d), show the relation between θopt and
MSEmin for Peppers, Lena, Lisa and House images respectively.
From these plots (Figure 3.1) it is, in general, observed that the minimum MSE
and the corresponding threshold bear an exponentially decaying relation. This is
true for all other images. In a practical situation, the use of MSE or noise ratio
to predict the threshold is ruled out as they need knowledge of the original image
for computation. However, to alleviate this problem analysis have been made as
follows. The minimum MSE is inversely proportional to optimal threshold value
i.e.
1
MSEmin ∝
θopt
f
(3.1)
also the noise percentage is inversely proportional to optimal threshold value, given
as:
η∝
1
θopt
(3.2)
where, η is the noise percentage. Also it is known that:
η ∝ CV
(3.3)
σ
µ
(3.4)
where,
CV =
where, σ and µ are the standard deviation and mean of the noisy image respectively. It should be noticed here that we have used CV instead of mean and
variance. Hence the number of input to the neural detector is reduced. The reason
of using CV is it is a more useful measure of dispersion in contrast to mean and
variance as used in MLPAT, ISAT, RBFNAT as explained in Chapter 2.
From the above four equations( 3.1, 3.2, 3.3, 3.4) it may be established that
the CV of a noisy image are proportional to the MSEmin and hence it can be
concluded that CV can be used as an input parameter for threshold selection.
67
3.3 Improved Adaptive Threshold Selection using FLANN
3.3
Improved Adaptive Threshold Selection using FLANN
The proposed improved adaptive threshold selection scheme is based on using efficient input parameters to the neural detector. Functional link Artificial neural
Network (FLANN) is a single layer network in which the need of hidden layers is
removed and is used here for determining the adaptive threshold. In contrast to
the linear weighting of the input pattern produced by the linear links of an MLP,
the functional link acts on an element of a pattern or on the entire pattern itself
by generating a set of linearly independent functions, and then evaluating these
functions with the pattern as the argument [62]. Further, the FLANN structure
offers less computational complexity and higher convergence speed than those of
an MLP because of its single layer structure. The functional expansion effectively
increases the dimensionality of the input vector and hence the hyperplanes generated by the FLANN provides greater discrimination capability in the input pattern
space [62, 63]. Hence FLANN is used for applications like function approximation
and pattern recognition. The back propagation algorithm, which is used to train
the network, becomes very simple because of absence of any hidden layer.
From section 3.2 it was established that the CV can be used as an input
training parameter. Hence CV is used as an input to the FLANN in the proposed
scheme (CVAT). The proposed neural detector is shown in Figure 3.2. The input
CV is functionally expanded in the input layer of FLANN with the trigonometric
polynomial basis functions given by:
{1, µ, sin(πCV), · · · , sin(Nπµ), CV, cos(πCV), · · · , cos(NπCV)}
The actual output on the output layer is compared with the desired output to determine the error. The weight matrix between the input–output layers is updated
using back propagation learning algorithm on the basis of this error. The neural
network with trained weights are used to obtain the threshold subsequently. It is
observed that FLANN can predict an accurate threshold for images that are not
used for training as well.
The threshold value thus obtained is used in the first pass of the algorithm.
68
3.3 Improved Adaptive Threshold Selection using FLANN
w0
bias b=1
sin (π CV)
w1
Functional Expansion
sin (2π CV)
CV
..
..
.
w2
sin (25π CV)
w 25
CV
w 26
cos (27π CV)
Actual
Output
w 27
cos (28π CV)
w 28
w 52
cos (52π CV)
..
..
.
Error
Σ
+
Target
Output
Figure 3.2: Functional Link Artificial Neural Network (FLANN) Structure for
Threshold Estimation using CV
0
−5
−10
MSE(dB)
−15
−20
−25
−30
−35
−40
0
100
200
300
400
Iterations
500
600
700
800
Figure 3.3: Convergence Characteristics of the CV based FLANN
Image output of the first pass is subjected to second pass of the algorithm. A
different threshold θ is used in the second pass of the noise detection algorithm.
Coefficient of variance (CV) of the output image of the first pass is calculated. This
69
3.5 Summary
new CV is again used as input to fed the FLANN to obtain the new threshold
value.
3.4
Simulations and Results
The proposed scheme CVAT is simulated on some standard images like Lena,
Lisa, Girl, Clown, Gatlin, Bridge, Boat and Peppers etc. Lena image is corrupted
with Random Valued Impulsive Noise of 1–30% noise densities. It is observed
that using a single parameter CV results with faster convergence along with much
less computational complexity. This smaller network size because of single input
parameter provides better options for easier implementations without hampering
noise suppressing capabilities.
The seven noisy images thus generated are passed through the proposed scheme
CVAT along with Signal Dependent-Rank Ordered Mean (SD-ROM) [41], TriState Median (TSM) [42] and Pixel Wise MAD (PWMAD) [37]. These are the
few best performer in terms of noise suppression as discussed in Chapter 1. The
simulated result of PSNR (in dB) is plotted in Figure 3.4 and that of PSP (in
Percentage) in Figure 3.5.
The computational time required for restoring Lena image with each scheme
cited above are recorded and is shown in Table 3.3. It is observed that the proposed
scheme is computationally much faster with respect to all other few best noise
suppression schemes.
Few more comparisons are listed in the form of tables. Table 2.1 lists the PSNR
of various images corrupted with 15% and 20% of noise. Similar observations of
PSP are listed in Table 3.2.
The figures in 3.6 and 3.7 shows the images of restored Lena and restored
Peppers corrupted with 15% and 20% of noise densities respectively.
3.5
Summary
The proposed scheme is an improved filtering scheme for suppressing impulsive
noise of varying strengths from corrupted images. A variation of neural network and with a single parameter adaptive threshold is obtained. The proposed
70
3.5 Summary
Table 3.1: PSNR (dB) of different schemes at 15% and 20% of noise on different
images
15%
RVIN
20%
RVIN
Lisa
Girl
Clown
Gatlin
Bridge
Boat
Peppers
PWMAD
30.50
29.28
23.02
30.66
26.07
29.25
31.29
SD-ROM
31.98
31.31
24.33
32.77
27.48
30.75
32.00
TSM
32.05
31.05
23.88
32.46
27.08
30.51
33.04
CVAT
36.45
33.87
23.59
33.16
25.89
28.93
33.11
PWMAD
28.26
27.73
22.16
28.77
24.99
27.57
29.04
SD-ROM
30.86
29.92
23.59
31.51
26.55
29.50
31.40
TSM
30.95
29.69
23.28
31.30
26.28
29.35
31.41
CVAT
34.68
31.72
22.53
31.60
25.91
28.28
32.57
Table 3.2: PSP of different schemes at 15% and 20% of noise on different images
15%
RVIN
20%
RVIN
Lisa
Girl
Clown
Gatlin
Bridge
Boat
Peppers
PWMAD
7.35
11.05
24.85
4.00
15.83
13.95
10.53
SD-ROM
0.14
0.93
10.29
0.39
3.06
1.04
0.34
TSM
0.22
2.62
17.51
0.98
7.94
2.55
0.57
CVAT
10.5
16.15
57.82
9.05
36.37
73.61
35.08
PWMAD
7.06
7.82
22.77
5.03
15.10
13.18
10.05
SD-ROM
0.18
0.40
9.86
0.33
3.10
1.12
0.37
TSM
0.31
1.21
21.07
1.00
8.30
2.82
0.73
CVAT
10.50
16.15
57.82
9.05
0.06
74.21
55.98
Table 3.3: Computational time consumed by different Schemes for removing impulsive noise from Lena image corrupted with 15% of RVIN
Scheme
Time (sec)
PWMAD
244.68
SDROM
11.20
TSM
77.14
CVAT
9.32
71
3.5 Summary
44
PWMAD
SD−ROM
TSM
CVAT
42
40
PSNR (dB)
38
36
34
32
30
28
26
24
0
5
10
15
Noise Percentage
20
25
30
Figure 3.4: PSNR (dB) plot of Restored Lena image corrupted with RVIN of
varying strengths
schemes’ performances are poor when compared with some of the schemes. However, computationally the proposed schemes are well off.
72
3.5 Summary
40
PWMAD
SD−ROM
TSM
CVAT
35
30
PSP
25
20
15
10
5
0
0
5
10
15
Noise Percentage
20
25
30
Figure 3.5: PSP plot of Restored Lena image corrupted with RVIN of varying
strengths
(a) True Image
(b) 15% Noisy
(c) PWMAD
(d) SDROM
(e) TSM
(f) CVAT
Figure 3.6: Subjective comparison of impulsive noise removal of Lena image corrupted with 15% of RVIN by different filters
73
3.5 Summary
(a) True Image
(b) 20% Noisy
(c) PWMAD
(d) SDROM
(e) TSM
(f) CVAT
Figure 3.7: Subjective comparison of impulsive noise removal of Peppers image
corrupted with 20% of RVIN by different filters
74
Chapter 4
Comparative Study of Impulsive
Noise Suppression Schemes
To combat impulsive noise from images, several schemes have been suggested in the
literature as well as in this thesis. In each chapter of this thesis the performance of
the proposed method has been compared isolatedly with relevant standard techniques. However the relative performance comparison has not been made amongst
the different proposed methods vis-a-vis with the standard methods. The objective of this chapter is to critically study the comparative filtering performance
amongst the various methods proposed in this thesis. A conclusion has also been
drawn to choose a method for impulsive noise filtering under a particular noise
situation. Impulsive noise can be classified into three categories i.e. low, medium
and high according to Table 4.1. Studies have been made at different noise conditions. For comparison, all the methods in a particular chapter is selected here
and Table 4.2 shows the different filtering scheme chosen from different chapters.
Table 4.1: Noise classification as per noise ratio
Noise Level
Noise Classification
0–15%
Low
15%–30%
Medium
30% and above
High
75
4.1 Performance Evaluation based on detector capability
Table 4.2: Noise removal scheme chosen for comparison
Scheme
Neural Structure
Noise Condition
MLPAT
MLP
Low & Medium
ISAT
FLANN
High
RBFNAT
RBFN
High
CVAT
FLANN
High
In sequel the following analysis is made with regard to the performance evaluation as presented,
• Detector Capability
• Average Filtering performance
• Computational Overhead
4.1
Performance Evaluation based on detector
capability
Four different noise detectors i.e. MLPAT, FLANNAT, RBFNAT and CVAT
detector have been proposed to detect impulsive noise at a test pixel location
based on the gray level information of its neighbor pixels in a 3 × 3 window.
The detector capability for noise classification is performed on the basis of certain
performance metrics i.e. False Positive % (FP) and False Negative (FN%) as
defined below.
FP% =
number of False Positives
× 100
Total number of noise free pixels
(4.1)
number of False Negatives
× 100
Total number of noisy pixels
(4.2)
F N% =
Where, classification of noise free pixels as noisy is termed as False Positive and
classification of noisy pixels as noise free is termed as False Negative. The reported
detectors are subjected to this test to determine their noise classification efficiency.
The proposed detectors performance in terms of FP% and FN% is compared with
PWMAD [37] the best scheme of the literature. The present study has been made
76
4.2 Comparison of Filtering Performance
for low and medium noise conditions (less than 30 %). Simulation has been carried
out using standard image i.e. Lena at 15% noise condition and the computed
results are presented in Table 4.3. Comparative analysis of the proposed detectors
reveals that CVAT detector yields the best performance in terms of the defined
parameter i.e FP% and FN%.
Table 4.3: False Positive Percentage(FP%) and False Negative Percentage (FN%)
of proposed schemes for Lena (512 × 512) with 15% RVIN.
FP% FN%
PWMAD 1.69 4.51
MLPAT
1.60 2.18
ISAT
1.64 2.14
RBFNAT 1.42 1.69
CVAT
0.88 1.22
4.2
Comparison of Filtering Performance
Filtering performance of the proposed schemes is measured here with a suitable
restoration parameter i.e. PSNR (Section 1.5). The suggested schemes are simulated on standard Lena image with noise levels varied between 1 to 30%. Computed results are compared on the basis of an certain criteria as presented in Table
4.4.PSNR values are computed and used as performance indices for the proposed
schemes. The basis of comparison is provided in Table 4.4.
Table 4.4: Basis of comparison among the filtering schemes
P arameter
PSNR (dB)
Range
Remarks
0–15
Satisfactory (S)
15–30
Good (G)
30 and above
Excellent (E)
Based on the aforesaid criteria, comparison has been made in two groups:
(a) Low and medium noise conditions and (b) high noise conditions. Computed
PSNR results obtained from the simulation of different schemes are shown in
Table 4.5 and 4.6. The plot in Figure 4.1 shows the PSNR variations of the
proposed schemes.
77
4.3 Computational Overhead
Table 4.5: Comparison of schemes under low and medium noise conditions
Filters
PSNR
Remarks
MLPAT
E
G
ISAT
E
E
RBFNAT
E
E
CVAT
E
E
Table 4.6: Comparison of different schemes under high noise conditions
Filters
4.3
PSNR
Remarks
MLPAT
G
S
ISAT
E
E
RBFNAT
E
E
CVAT
E
E
Computational Overhead
In this section the computational overhead associated with each proposed filter
to restore a corrupted pixel is compared. It is evident from the Table 4.7 that
the CVAT filtering scheme is the most computationally efficient scheme. The
computational time required for restoring Lena image with each proposed scheme
44
PWMAD
MLPAT
ISAT
RBFNAT
CVAT
42
40
PSNR (dB)
38
36
34
32
30
28
26
24
0
5
10
15
Noise Percentage
20
25
30
Figure 4.1: Variation of PSNR (dB) at different RVIN percentage on Lena image.
78
4.3 Computational Overhead
along with PWMAD [37] is shown in Figure 4.2. All the results were obtained by
simulating the schemes in Matlab 7.0, Microsoft Windows XP (SP2) Operating
System and Intel Pentium D–2.80 GHz with 1GB of RAM.
Table 4.7: Computational overhead per pixel associated in filtering schemes
Filters
Addition
Multiplication
MLPAT
7
8
ISAT
4
207
RBFNAT
10
12
CVAT
4
57
250
Computational Time (secs)
200
150
100
50
0
PWMAD
MLPAT
ISAT
RBFNAT
CVAT
Filtering Schemes
Figure 4.2: Computational time of proposed schemes for Lena (512 × 512) with
15% RVIN.
79
4.4 Summary
4.4
Summary
From the results obtained (Table 4.5, 4.6), it is observed that CVAT, RBFNAT,
ISAT filtering schemes perform better than MLPAT. But since the CV based
FLANN detector used in CVAT filtering scheme outperforms the other schemes,
CVAT scheme is chosen to be the best among these methods at all the noise
conditions.
In the next chapter, CVAT and RBFNAT filtering schemes are used for image
sharpening under impulsive noise condition.
80
Chapter 5
Image Sharpening under
Impulsive Noise Conditions
One of the problems of a image sharpening in practice is the noise boost-up, which
limits the applications of the enhancement schemes in low contrast images under
noisy conditions. To resolve this issue, a novel approach is presented, which effectively prevents the visual amplification of a noise while the image details are
being enhanced. The proposed scheme incorporates noise reduction algorithm before applying contrast enhancement to achieve the objective. Only low contrast
images under impulsive noise condition is considered here. RBFNAT(Chapter 2)
and CVAT(Chapter 3) are used for reducing noise before enhancement. Image
Enhancement scheme used here is based on a technique called Unsharp Masking(UM), which is described in Section 5.1. Noise amplification in low contrast
noisy images is the major drawback of linear unsharp masking. Since sharpening
(enhancement) and smoothing (noise removal) are contradicting in nature proper
care must be taken to obtain high quality images. This chapter tries to express
how selective filtering (Chapter 2, 3) can be applied along with UM to improve
the quality of low contrast noisy images. With appropriate choice of impulse noise
removal schemes the noise amplification can be prevented, to be employed for UM.
Linear Unsharp Masking (UM) is presented in Section 5.1. Section 5.2 reports
an improved image sharpening scheme under impulsive noise condition. Last, the
proposed sharpening scheme is compared with some of the existing schemes and is
presented in Section 5.3. Finally, Section 5.4 provides the summary of the chapter.
81
5.2 Improved Image sharpening under Impulsive Noise Condition
5.1
Image Enhancement using Unsharp masking
Image enhancement seeks to improve the visual quality of images. However, an
inherent difficulty is to define a mathematical criterion for visual quality. As a
result, many algorithms remain to a large extent empirical and a final assessment
can only be performed by the human observer. Unsharp Masking (UM) [1] is
a classical simple enhancement scheme which yields pleasant results utilizing an
effect called simultaneous contrast. Simultaneous contrast describes the visual
phenomenon that the difference in the perceived brightness of neighboring regions
depends on the sharpness of the transition. Unsharp Masking is implemented by
adding a scaled version of the input image to the image itself to form the enhanced
image. The block diagram of Linear Unsharp Masking is illustrated in Figure 5.1.
X
Y’
i,j
i,j
Enhanced
Output
Image
Input
Image
High Pass
Filter
X
H
i,j
λ
Figure 5.1: Linear Unsharp Masking scheme
5.2
Improved Image sharpening under Impulsive Noise Condition
The proposed image sharpening scheme under noise condition consists of impulse
detection followed by simple unsharp masking as described in Section 5.1. The
schematic diagram of Improved Unsharp Masking (IUM) scheme is illustrated
in Figure 5.2 . To enhance a low contrast noisy image adaptive noise detection
schemes (Chapter 2) is used. Initially the noisy pixels are detected followed by
median filtering. This type of selective filtering prevents unnecessary blurring of
image details and hence image details are preserved even after noise removal. The
output of the selective filter is fed to an high pass filter to separate the high and
82
5.3 Simulations and Results
V
Y
Selective
Filtering
Y’
i,j
i,j
AHE
Enhanced
Output
Image
Y’’
i,j
Noise
Detection
High Pass
Filter
X
H
i,j
Input
Image
X
λ
i,j
Figure 5.2: Improved Unsharp Masking scheme
low frequency components. Output after selective filtering followed by UM can be
expressed using the following relation:
= Ŷi,j + λHi,j
Yi,j
(5.1)
λ is the positive gain factor that controls the level of enhancement. Where Hi,j is
the output of a linear high pass filter which is obtained using equation 5.2.
Hi,j = 4Ŷi,j − Ŷi−1,j − Ŷi+1,j − Ŷi,j−1 − Ŷi,j+1
(5.2)
Adaptive Histogram Equalization (AHE) [65] is further applied to redistribute the
gray level intensity values of the image uniformly at local level to provide a more
sensible image.
5.3
Simulations and Results
The two proposed threshold selection (Chapter 2) schemes were used independently for noise removal before enhancement. The resulting images of noise removal schemes were simulated independently applying UM followed by AHE. Enhanced results were compared with some of the best performing schemes reviewed
in Section 1.6.
Since there is no standard quantitative measure because of unavailability of an
ideal image, subjective comparison for Lena and Peppers is presented in Figures 5.3
and 5.4.
83
5.4 Summary
5.4
Summary
Problem of noise amplification in image enhancement process is discussed and suitable solution scheme is presented. Use of selective filtering before unsharp masking
gives visually accepted results with preserved image details. Two different ways
of filtering are used along with unsharp masking to compare the enhanced images.
The experimental results demonstrate that the proposed approach can enhance
low contrast images under impulse noise condition. Further improvement in the
overall enhancement scheme can be achieved by making the amplification factor adaptive.However proposed scheme is not computationally efficient and some
parallel processing schemes must be used for real time applications.
(a) Low Contrast Noisy
(c) Median Filtering
lowed by UM
(b) Linear Unsharp Masking
fol- (d) FLANN followed by UM (e) RBFN followed by UM
Figure 5.3: Comparison among different enhancement approaches for Lena image
84
5.4 Summary
(a) Low Contrast Noisy
(c) Median Filtering
lowed by UM
(b) Linear Unsharp Masking
fol- (d) FLANN followed by UM (e) RBFN followed by UM
Figure 5.4: Comparison among different enhancement approaches for Pepper image
85
Chapter 6
Conclusions
The work in this thesis, primarily focuses on impulsive noise suppression from
images. Schemes for adaptive threshold selection for noise detection have also
been devised. Along with the above work image sharpening under impulsive noisy
condition is also a part of this work.The work reported in this thesis is summarized
in this chapter. Section 6.1 lists the pros and cons of the work. Section 6.2 provides
some scope for further development.
6.1
Achievements and Limitations of the work
Random Valued Impulsive Noise (RVIN) model is considered in the thesis. Then
in subsequent chapters (Chapter 2–3) some novel schemes are proposed. Salient
points of the thesis, highlighting the contribution at each stage, are presented
below.
The four proposed schemes deal with RVIN removal and are based on second
order difference of pixels. These schemes primarily proposes different techniques
to select threshold in order to make noise detection process more reliable.
MLP based Adaptive Thresholding for Impulse Detection (MLPAT) is the first
contribution that uses a simple Multilayer Perceptron Network (MLP) to determine the threshold value. A variation of ANN i.e. Functional Link ANN (FLANN)
is used in another contribution namely Image Statiscs based Adaptive Threshold
Selection for Detecting Impulsive Noise in Images (ISAT). Radial basis Functional
Network (RBFN) is used in another contribution namely RBFN based Adaptive
Threshold Selection for Detecting Impulsive Noise in Images (RBFNAT). All the
86
6.2 Further Developments
three neural network approach use mean and variance of noisy image as input parameters to the network. Comparisons reveal that there are some better techniques
in terms of PSNR. However, the proposed schemes computationally efficient.
In Chapter 3, again the same Functional Link Artificial Neural Network (FLANN)
is used in another contribution for detecting impulsive Noise in Images (CVAT).
This contribution also deals with removal of RVIN from images. This technique
utilizes a more efficient statistical parameter called called coefficient of variance
(CV) for training the neural network and to predict the threshold value. In terms
of PSNR as well as computational time this scheme outperforms its counterparts.
The last contribution Image Sharpening under Impulse Noise Condition suggests an enhancement scheme under noisy conditions. The proposed scheme utilizes selective filtering in improving the pitfalls of an well accepted enhancement
allgorithm Unsharp Masking. Prevention of noise amplification along with image details preservation while sharpening the proposed scheme outperforms its
counterparts in terms of image quality.
6.2
Further Developments
To conclude this thesis, following are some points that may lead to some better
and interesting results.
In this thesis, noise detection is mostly covered and for noise filtration median
filter is used. Research may be undertaken to devise better filtration techniques.
This technique together with a best detection technique can result in optimal
restoration of degraded image.
As it has been stated that the existing as well as proposed techniques are computationally expensive, investigation may be carried out in this direction. Development of parallel algorithms can also be done to counter attack the computational
overhead.
87
Bibliography
[1] B. Chanda and D. Dutta Majumder. Digital Image Processing and Analysis.
Prentice-Hall of India, 1st edition, 2002.
[2] Maria Petrou and Panagiota Bosdogianni. Image Processing the Fundamentals. John Wiley and Sons, 1st edition, 1999.
[3] R. C. Gonzalez and R. E. Woods. Digital Image Processing. Addison Wesley,
2nd edition, 1992.
[4] Banshidhar Majhi. Soft Computing Techniques for Image Restoration. PhD
thesis, Sambalpur University, 2000.
[5] S. K. Mitra and T.H. Yu. Nonlinear Filters for Image Sharpening and Smoothing. In IEEE International Conference on Systems engineering, volume 4,
pages 241 – 244, August 1991.
[6] William K. Pratt. Digital Image Processing. John Wiley-Interscience Publication, 3rd edition, 2001.
[7] H. Zhu, F.H. Y. Chan, and F.K. Lam. Image Contrast Enhancement by
Constrained Local Histogram Equalisation. Computer Vision and image Understanding, 73(2):281 – 290, February 1999.
[8] R.H. Sherrier and GA Johnson. Regionally Adaptive Histogram Equalisation
of the Chest. IEEE Transaction on Medical Imaging, 6:1 – 7, 1987.
[9] E.P Amburn S.M Pizer. Adaptive Histogram Equalization and its Variations.
Computer Vision, Grpahics, and Image Processing, 39:355 – 368, 1987.
[10] The NASA Website. http://history.nasa.gov.
88
Bibliography
[11] The Wikipedia the Free Encylopedia Website. http://en.wikipedia.org.
[12] H. Soltanian-Zadeh, J.P. Windham, and A.E. Yagle. A Multidimensional
Nonlinear Edge-Preserving Filter for Magnetic Resonance Image Restoration.
IEEE Transactions on Image Processing, 4(2):147 – 161, February 1995.
[13] J. A. Goyette, G. D. Lapin, M. G. Kang, and A. K. Katsaggelos. Improving Autoradiograph Resolution Using Image Restoration Techniques. IEEE
Engineering in Medicine Biology, pages 571 – 574, August/September 1994.
[14] Chieh Ju Tu, Shuen Huei Guan, Yung Yu Chuang, Jiann Rong Wu, Bing Yu
Chen, and Ming Ouhyoungi. International Conference on Computer Graphics
and Interactive Techniques. SIGGRAPH-2007, San Diego California, 2007.
[15] The Walt Disney Company Website. http://disney.go.com.
[16] Mark R. Banham and Aggleos K. Katsaggelos. Digital Image Restoration.
IEEE Signal Processing Magazine, 14(2):24 – 41, March 1997.
[17] T.P. ORourke and R.L. Stevenson. Improved Image Decompression for Reduced Transform Coding Artifacts. IEEE Transactions on Circuits and Systems for Video Technology, 5(6):490 – 499, December 1995.
[18] T. Ozcelik, J.C. Brailean, and A.K. Katsaggelos. Image and Video Compression Algorithms Based on Recovery Techniques Using Mean Field Annealing.
In IEEE Proceedings, pages 304 – 316, February 1995.
[19] X. Lee, Y.Q. Zhang, and A. Leon-Garcia. Information Loss Recovery for
Block-Based Image Coding Techniques-A Fuzzy Logic Approach.
IEEE
Transactions on Image Processing, 4(3):259 – 273, March 1995.
[20] S. Iyer and S. V. Gogawale. Image Enhancement and Restoration Techniques
in Digital Image Processing. Computer Society of India Communications,
pages 6 – 14, June 1996.
[21] I.Pitas and A.N.Venetsanopoulos. Nonlinear Digital Filters: Principles and
Applications. Kluwer Academic Publishers, 1990.
89
Bibliography
[22] J. G. Proakis and D. G. Manolakis. Digital Signal Processing: Principles,
Algorithms and Applications. Prentice Hall of India, New Delhi, 3rd edition,
2002.
[23] J.Astola and P.Kuosmanen. Fundamentals of Nonlinear Filtering. CRC Press,
1997.
[24] R. Bose. Information Theory Coding and Cryptography. TATA Mc-Graw Hill,
India, 2003.
[25] O.A Ojo and T.G.K. Spassova. An Algorithm for Integrated Noise Reduction
and Sharpness Enhancement. IEEE Transaction on Consumer Electronics,
46(3):474 – 480, August 2000.
[26] M. Vehvilainen and J. Yrjanainen. Circuit Arrangement to Accentuate the
Sharpness and Attenuate the Noise of a Television Image. In European Patent
EP95101009, 11, February 1994.
[27] Marshall N.W. A comparison between objective and subjective image quality measurements for a full field digital mammography system. Physics in
Medicine and Biology, 51(10):2441 – 2463, 2006.
[28] S. J. Ko and Y. H. Lee. Center Weighted Median Filters and Their Applications to Image Enhancement. IEEE Transactions on Circuits and Systems,
38(9):984 – 993, September 1991.
[29] T. Chen and H. R. Wu. Adaptive Impulse Detection Using Center-Weighted
Median Filters. IEEE Signal Processing Letters, 8(1):1 – 3, January 2001.
[30] D. R. K. Brownrigg. The Weighted Median Filter. Communications ACM,
27:807 – 818, August 1984.
[31] B. I. Justusson. Median Filtering: Statistical Properties. Two-Dimensional
Signal Processing-II, T. S. Hwang Ed. New York: Springer Verlag, 1981.
90
Bibliography
[32] E. Abreu, M. Lightstone, S. K. Mitra, and K Arakawa. A New Efficient
Approach for the Removal of Impulse Noise from Highly Corrupted Images.
IEEE Transactions on Image Processing, 5(6):1012 – 1025, June 1996.
[33] Z. Wang and D. Zhang. Progressive Switching Median Filter for the Removal
of Impulse Noise from Highly Corrupted Images. IEEE Transactions on Circuits and Systems–II: Analog and Digital Signal Processing, 46(1):78 – 80,
January 1999.
[34] K. Kondo, M. Haseyama, and H. Kitajima. An Accurate Noise Detector
for Image Restoration. In Proceedings of International Conference on Image
Processing 2002, volume 1, pages I–321 – I–324, September 2002.
[35] S. Zhang and Md. A. Karim. A New Impulse Detector for Switching Median
Filters. IEEE Signal Processing Letters, 9(11):360 – 363, November 2002.
[36] C. Butakoff and I. Aizenberg. Effective Impulse Detector Based on RankOrder Criteria. IEEE Signal Processing Letters, 11(3):363 – 366, March 2004.
[37] V. Crnojevic, V. Senk, and Z. Trpovski. Advanced Impulse Detection Based
on Pixel-Wise MAD. IEEE Signal Processing Letters, 11(7):589 – 592, July
2004.
[38] W. Y. Han and J. C. Lin. Minimum-Maximum Exclusive Mean (MMEM)
Filter to Remove Impulse Noise from Highly Corrupted Images. Electronics
Letters, 33(2):124 – 125, January 1997.
[39] P. S. Windyga. Fast Impulsive Noise Removal. IEEE Transactions on Image
Processing, 10(1):173 – 179, January 2001.
[40] Naif Alajlan, Mohamed Kamel, and Ed Jernigan. Detail Preserving Impulsive
Noise Removal. Signal Processing: Image Communication, 19:993 – 1003,
2004.
[41] E. Abreu and S. K. Mitra. A Signal-Dependent Rank Ordered Mean (SDROM) filter-A new approach for removal of impulses from highly corrupted
91
Bibliography
images. In Proceedings of International Conference on Acoustics, Speech, and
Signal Processing, volume 4 of ICASSP-95, pages 2371 – 2374, May 1995.
[42] T. Chen, K. K. Ma, and L. H. Chen. Tri-State Median Filter for Image
Denoising. IEEE Transactions on Image Processing, 8(12):1834 – 1838, December 1999.
[43] F. Russo. Impulse Noise Cancellation in Image Data Using A Two-Output
Nonlinear Filter. Measurement, 36:205 – 213, 2004.
[44] L. Khriji and M. Gabbouj. Median-Rational Hybrid Filters. In Proceedings
of International Conference on Image Processing 1998, volume 2, pages 853 –
857, October 1998.
[45] Tuncer Can Aysal and Kenneth E. Barner. Generalized Mean Median Filtering for Robust Frequency Selective Applications. IEEE Transactions on
Signal Processing, 55(3):937 – 948, March 2007.
[46] P. Maragos and R.W. Schafer. Morphological Filters Part–i: Their Set Theoritic Analysis and Relations to Linear Shift Invariant Filters. IEEE Transactions on Accoustics, Speech, Signal process, 35(8):1152 – 1169, June 1987.
[47] A. Polesel, G.Ramponi, and V.J. Mathews. Adaptive Unsharp Masking for
Contrast Enhancement. IEEE Transactions on Consumer Electronics, 1:267 –
270, 1997.
[48] B. Picinbono. Quadratic Filters. IEEE Transactions on Accoustics, Speech
and Signal Processing IEEE International Conference on ICASSP, 7(8):298 –
301, May 1982.
[49] S. Thurnhofer and S. K. Mitra. A general framework for quadratic volterra
filters. IEEE Transactions on Image Processing, 5(6):950 – 963, June 1996.
[50] M.A. Badamchizadeh and A. Aghagolzadeh.
92
Bibliography
[51] A. Polesel, G.Ramponi, and V.J. Mathews. Adaptive Unsharp Masking for
Contrast Enhancement. IEEE Transactions on Consumer Electronics, 1:267 –
270, 1997.
[52] M.Vehvilainen and J.Yrjanainen. Circuit Arrangement to Accentuate the
Sharpness and Attentuanate the Noise of Television Image, February 1994.
[53] G.A Mastin. Adaptive filters for digital image noise smoothing. Computer
Vision, Grpahics, and Image Processing, 31:103 – 121, 1985.
[54] R. M. Haralick and L.G Shapiro. Digital Image Processing. Addison Wesley,
1992.
[55] Marco Fischer, Jose L. Paredes, and Gonzalo R. Arce. Weighted median
image sharpeners for the world wide webl. IEEE Transactions on Image
Processing, 11(7):717 – 727, July 2002.
[56] T.C. Ayasal and K.E. Barner. Quadratic Weighted Median Filters for Edge
Enhancement of Noisy Images. IEEE Transactions on Image Processing,
15(11):3294 – 3301, November 2006.
[57] X. Xu and E. L. Miller. Adaptive Two-Pass Median Filter to Remove Impulsive Noise. In Proceedings of International Conference on Image Processing
2002, pages I–808 – I–811, September 2002.
[58] F. Russo and G. Ramponi. A Fuzzy Filter for Images Corrupted by Impulse
Noise. IEEE Signal Processing Letters, 3(6):168 – 170, June 1996.
[59] B.Yegnanarayana. Artificial Neural Networks. Prentice-Hall of India, 2003.
[60] V. Kecman. Learning and Soft Computing. Pearson Education India, 1st
edition, 2004.
[61] Simon Haykin. Neural Networks. Prentice Hall, 2nd edition, 1999.
[62] J. C. Patra, R. N. Pal, B. N. Chatterji, and G. Panda. Identification of Nonlinear Dynamic Systems Using Functional Link Artificial Neural Networks.
93
Bibliography
IEEE Transaction on Systems, Man, and Cybernatics, 29(2):254 – 262, April
1999.
[63] J. C. Patra, G. Panda, and R. Baliarsingh. Artificial Neural Network-Based
Nonlinearity Estimation of Pressure Sensors. IEEE Transaction on Instrumentation and Measurement, 43(6):874 – 881, December 1994.
[64] Banshidhar Majhi, Pankaj Kumar Sa, and Ganapati Panda. Second Order
Differential Impulse Detector. In IEE International Conference on Intelligent
Systems, ICIS-2005, Malaysia, December 2005.
[65] G.D Hann. Memory Integrated Noise Reduction for Television. IEEE Transactions on Consumer Electronics, 42(2):175 – 181, May 1996.
94
Dissemination of Work
Published
1. S. Mohapatra, R. Dash, P. K. Sa and B. Majhi, ̏Improved enhancement
scheme using a RBFN detector for impulse noise.˝, In IEEE International
Conference on Emerging Trends in Engineering and Technology (ICETET2008), pp 294 - 297, 16 - 18 July, 2008, Nagpur, India.
2. S. Mohapatra, R. Dash, P. K. Sa and B. Majhi, ̏RBFN based Impulsive
Noise Removal Image Enhancement Technique˝, IEEE Conference on Computational Intelligence, Control And Computer Vision in Robotics and Automation, (CICCVRA-2008), pp 130 - 135, 10 - 11 March, 2008, Rourkela,
India.
3. S. Mohapatra, P. K. Sa and B. Majhi,, ̏Impulsive Noise Removal Image Enhancement Technique˝, 6th WSEAS International Conference on Circuits,
Systems, Electronics, Control and Signal Processing,, (CSECS-2007), pp
317 - 322, 29 - 31 December, 2007, Cairo, Egypt.
4. S. Mohapatra, P. K. Sa and B. Majhi,, ̏An Improved Image Enhancement
Technique Combining Sharpening and Impulse Noise Reduction.˝, International Conference on Soft Computing and Intelligent Systems, (ICSCIS2007), pp 317 - 322, 27 - 29 December, 2007, Jabalpur, India.
5. S. Mohapatra, P. K. Sa and B. Majhi,, ̏CV based adaptive threshold selection for impulsive noise removal from images.˝, 2nd International conference on Advanced Computing and Communication Technologies, (ICACCT2007), pp 307 - 312, 03 - 04 November, 2007, Panipat, India.
95
Bibliography
Communicated
1. S. Mohapatra, R. Dash, P. K. Sa and B. Majhi, ̏Adaptive threshold selection for impulse noise detection in images using coefficient of variance˝,
International Journal of Neural Computing and Applications.
96
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Related manuals

Download PDF

advertisement