DEVELOPMENT OF NOISE REMOVAL ALGORITHMS FOR IMAGES

Transcription

1 DEVELOPMENT OF NOISE REMOVAL ALGORITHMS FOR IMAGES A thesis submitted to the Sambalpur University for the degree of Doctor of Philosophy in Computer Science & Engineering by Punyaban Patel ( Registration No: 347 / 2010 / Computer Science & Engineering ) Sambalpur University Jyoti Vihar, Burla Odisha, India December, 2013

2 Development of Noise Removal Algorithms for Images A thesis submitted to Sambalpur University in partial fulfilment of the requirements for the degreeof Doctor of Philosophy in Computer Science & Engineering By Punyaban Patel ( Registration No: 347 / 2010 / Computer Science & Engineering ) Under the supervision of Dr. Chita Ranjan Tripathy, Co-Supervisor Professor, Department of CSE, VSSUT, Burla , India Prof. (Dr.) Banshidhar Majhi, Supervisor Professor, Department of CSE, NIT Rourkela, Rourkela , India Sambalpur University Jyoti Vihar, Burla Odisha, India December, 2013

3 December 30, 2013 Certificate This is to certify that the thesis entitled DEVELOPMENT OF NOISE REMOVAL ALGORITHMS FOR IMAGES being submitted by Punyaban Patel, presently working as an Assistant Professor in the Department of Compute Science and Engineering, Purushottam Institute of Engineering and Technology, Rourkela for the award of the degree of Doctor of Philosophy in Computer Science and Engineering under Sambalpur University, is a record of original research work carried out by him under our guidance and supervision. Mr. Patel has worked for more than three years. In our opinion, the thesis has fulfilled the requirement according to the regulation and has reached the standard necessary for submission. To our knowledge, the results envisaged in the thesis have not been submitted elsewhere for the award of any other degree or diploma. Prof.(Dr.) Chita Ranjan Tripathy, Co-Supervisor Professor, Department of CSE, VSSUT, Burla , India Prof.(Dr.) Banshidhar Majhi, Supervisor Professor, Department of CSE, NIT Rourkela, Rourkela , India ii

4 Dedicated to my parents iii

5 Abstract Image denoising has been a well-studied problem and a highly demanded area of research in the field of image processing. Images are generally degraded due to faulty sensor, channel error, camera miss-focus, atmospheric turbulence, relative camera motion, image acquisition and or transmission etc. Such conditions are inevitable while capturing a scene through a camera. As degraded images are of little scientific values, restorations of such images are utmost essential. As camera manufacturers continue to pack increasing numbers of pixels per unit area, an increase in noise sensitivity manifests itself in the form of a noisier image. Yet researchers continue to focus attention on it to better the current state-of-the-art. Recently proposed methods take different approaches to the problem and yet their denoising performances are comparable. Impulsive noise is common in images which arise at the time of image acquisition and or transmission of images. Impulsive noise can be classified into two categories, namely Salt & Pepper Noise (SPN) and Random Valued Impulsive Noise (RVIN). Removal SPN is easier as compared to RVIN due to its characteristics. In this thesis, investigations have been made to recover images from their degraded observations; mainly concentrate on removal of SPN and RVIN from images. Most of the nonlinear filters used in removal of impulsive noise work in two phases, i.e. detection followed by filtering only the corrupted pixels keeping uncorrupted ones intact. Performance of such filters is dependent on the performance of detection schemes. In this work, thrust has been put to devise an accurate detection scheme and applied the novel mean and median filtering mechanism. Four algorithms are proposed to detect and removal of SPN from the contaminated images. These schemes are: (i) New Adaptive Median Filter (NAMF), (ii) Dynamic Adaptive Median Filter (DAMF), (iii) Fuzzy Based Adaptive Mean Filter (FBAMF), and (iv) Efficient Adaptive Mean Filter (EAMF). The performance of the proposed schemes have been studied in isolation and compared with relevant standard techniques to derive an overall inference about the performance of the schemes with respect to Mean Absolute Error (MAE), Mean Square Error (MSE), Peak Signal-to-Noise Ratio (PSNR), Improve Peak Signal-to-Noise Ratio (ISNR), Structural Similarity Index Measure (SSIM), Image Quality Index (IQI). The comparative analysis shows that the performance metrics of proposed schemes are good and the restored images are also visually good as compared to relevant standard schemes mentioned in their respective chapters. Among all the proposed schemes in SPN, it is observed that DAMF and FBAMF show superior performance over others in low density noise. EAMF performs better in both medium and high density SPN. iv

6 An algorithm is proposed for detection and removal of RVIN which uses back propagation neural network. The neural network is trained on Lena image with RVIN with 20% noise density using two input statistical parameters. These statistics are called robust outlyingness ratio (ROR) and the similarity measure(s), which are used for generating a pattern for each pixel to find how much a pixel looks like an impulse noise. The identified pixels are then filtered using a novel filtering mechanism, which is based on spatial property. The trained detector is used for detecting RVIN on other images like Bridge, Boat, Pepper and Goldhill. It is observed from the simulated results the proposed scheme performs better as compared to their competent schemes with respect to both visual as well as quantitative parameters. v

7 Acknowledgement The Ph.D. thesis is the result of a challenging journey, upon which many people have contributed and given their support. I would like to thank them who have helped me sail through an arduous task of completing this thesis. First and foremost, I am deeply indebted to my supervisor Prof.(Dr.) Banshidhar Majhi, Professor, Department of Computer Science and Engineering, NIT Rourkela for his critical role in the completion of my doctoral work. The completion of my dissertation is an uphill task needed to undergo a long journey. Without the constant help and assistance of my supervisor, this thesis could have never seen the light of the day. Prof. Majhi is a man of valuable guidance, scholarly inputs, academic expertise, consistent encouragement and as a whole an inexhaustible source of inspiration that I received throughout the research work. He treats me with a sense of love and meticulous care that boosts the unbreakable bondage between the scholar and the guide. Although a professor of wide acclaim and profound knowledge, I find a friend in him who keeps his door open for me round the clock. I owe a debt of sincere gratitude to my other supervisor Prof.(Dr.) C.R.Tripathy, Professor, Department of Computer Science and Engineering, VSSUT, Burla, Sambalpur for his unstinting support and valuable suggestion which was of utmost importance to translate my dream into reality. A teaching personality of sheer talent and academic excellence, Professor C.R.Tripathy comes forward, almost any time, to offer suggestions and clear my doubts. I would like to thank Prof.(Dr.) Smaran Kumar Sanyal, former Professor of the Department of Electrical Engineering & Principal of VSSUT, Burla and presently professor in the Department of Electrical Engineering, Siksha O Anusandhan University, Bhubaneswar for his considerable influence on my research. Since long he has been a guiding force and an inspiring figure for me. I feel fortunate to have a friend like Prof Bibhudatta Sahoo, Department of CSE, NIT Rourkela, whose fruitful cooperation and valuable support; and good suggestions in my personal and professional life, encourage me all the times to proceed with this task. I am glad to mention the encouragement, guidance and friendly cooperation of Prof. S.K Rath, Prof. S.K. Jena, Dr. Ashok Kumar Turuk, Dr. Ratnakar Dash, Dr. Durga Prasad Mohapatra, Prof Rameswar Baliarsingh, Prof Pankaj Kumar Sa, Prof. Korra Sathya Babu, Prof. Pabitra Mohan Khilar, and Prof.(Mrs.) Suchismita Chinara, Dept. of CSE, NIT Rourkela and Prof. G. Panda, IIT Bhubaneswar. Heartfelt thanks to all of them for their valuable support and motivation in pursuit of this research. Completing this work would have been all the more difficult, without the generous support of my colleagues Prof. Bibeka Nanda Jena, Dept. of E & TC, PIET, Rourkela. Despite his rigorous schedule, he offered generous support and true friendship in hour of need. I am truly thankful to him as most of the time he is the co-author of my papers. vi

8 I expresses heartfelt gratitude to my cousin brother Prof Satis Kumar Patel & his colleague Prof (Dr.) Prasna Kumar Mishra, from the department of Physics, G.M.College, Sambalpur, for their active and memorable role in my research. They have provided invaluable outsiders perspectives to my research when most needed. I would like to thank Prof K.M.Purohit, Director, and my colleagues of CSE / IT department, Purushottam Institute of Engineering and Technology for their valuable support. I cannot forget to offer my sincere and hearty thanks to my friends Prof. Sukumar Mishra, IIT Delhi and Prof Ashok Kumar Pradhan, IIT Kharagpur, Prof. Sudipta Mohapatra, IIT Kharagpur, Prof. Saroj Kumar Meher, ISI Bangalore, and Prof Ruplal Choudhary, University of Illinois (USA) for their encouragement. I would also like to thank my brother-in-law, Dr. Ramdayal Patel, physician and my friend Mr. Rabindra Kumar Nayak for giving me stimulating and overwhelming remark as needed. I offer my gratitude to my wife Sheela for her love and care that keeps me in good spirit through thick and thin. It was her incessant encouragements that help me work actively for this thesis over the past few months getting the better of some sleepless nights. My little son Riyam is always an impetus and a jewel like personality who makes me shine through the darkest hour of difficult journey. Above and beyond all, my heartfelt gratitude goes to all my brothers Mr. Satyaban Patel, Mr. Bhagyaban Patel and Mr. Gyanaban Patel and special thanks to Prince, Pritam and our whole family who have been a constant source of inspiration for my research work. The last but not the least, this is the word of acknowledgment I have saved for my dear parents Mr. Bimaleswar Patel and Smt. Bishnupriya Patel, for their invaluable blessings, love, encouragement, support, and unwavering belief in me. Without them, I would not be the person I am today. I owe them everything. I dedicate this thesis to my parents, family, and teachers for their constant support and unconditional love. I love you all dearly. Punyaban Patel vii

9 Contents Certificate Abstract Acknowledgement List of Figures List of Tables Abbreviations ii iv vi xi xv xviii Chapter Introduction Impulse noise models Performance Measures used Literature survey...11 A. Filtering without Detection...11 B. Detection followed by Filtering...12 C. Hybrid Filtering Motivation Objectives Layout of the thesis...25 Chapter Adaptive Median Filtering Technique for Removal of Impulse Noise from Images Median Filtering Technique Proposed Scheme Simulation Results Summary...43 viii

10 Chapter Dynamic Adaptive Median Filter (DAMF) for Removal of High Density Impulse Noise from Images Proposed Scheme Simulation Results and Discussion Summary...65 Chapter Fuzzy Based Adaptive Switching Mean Filtering Technique for Removal of Impulse Noise from Images Preliminaries on Fuzzy Logic Proposed Method...68 A. Fuzzy noise measure of pixels in the test window...69 B. Adaptive Mean Filtering Simulation Results Summary...89 Chapter An Efficient Adaptive Mean Filtering Technique for Removal of Salt and Pepper Noise from Images Proposed Method Simulation Results Summary Chapter Back Propagation Neural Network based Impulsive Noise Suppression Related works Computation of robust outlyingness ratio (ROR) and similarity measure (S) Proposed scheme Simulation and results Summary ix

11 Chapter Comparative Study of Proposed Techniques Results and discussion Summary Chapter Conclusion Bibliography 130 Dissemination 140 x

12 List of Figures Figure No. Figure Name Figure 1.1 Model of the general image degradation / restoration process.. 5 Figure 1.2 Model of the image degradation / restoration process due to noise 5 Figure 1.3 Figure 1.4 Figure 1.5 Figure 1.6 Figure 1.7 Figure 1.8 Representation of (a) Salt & Pepper Noise (b) Random Valued Impulsive Noise... 7 Performance comparison of different filtering schemes without detection on SPN(Lena image) 20 Performance comparison of different filtering schemes where detection followed by filtering on SPN(Lena image) Performance comparison of different filtering schemes where detection followed by filtering on SPN(Lena image) Comparative analysis of (a) PSNR (db) and (b) ISNR (db) at various noise densities of Lena image. 22 Comparative analysis of (a) SSIM and (b) IQI at various noise densities of Lena image Figure 2.1 Illustration of Median Filtering scheme. 27 Figure 2.2 Flow Chart of NAMF Algorithm Figure 2.3 Illustration of NAMF for Case I. 31 Figure 2.4 Illustration of NAMF for Case II Figure 2.5 Illustration of NAMF for Case III.. 33 Figure 2.6 Illustration of NAMF for Case IV.. 33 Figure 2.7 PSNR(dB) vs. Threshold value (T) of Lena image 34 Figure 2.8 Restored images of Lena and Boat images using NAMF scheme. 35 Figure 2.9 Performance comparison of filters at different noise densities of Lena image Figure 2.10 Performance comparison of filters at different noise densities of Boat image Page No. Figure 2.11 Figure 2.12 Comparative analysis of (a) PSNR(dB) and (b) ISNR(dB) at various noise densities of Boat image Comparative analysis of (a)ssim and (b)iqi at various noise densities of Boat image xi

13 Figure 3.1 Flow chart of DAMF algorithm Figure 3.2 An image segment for illustrating DAMF scheme. 48 Figure 3.3 Illustration of DAMF for Case I Figure 3.4 Illustration of DAMF for Case II Figure 3.5 Illustration of DAMF for Case III Figure 3.6 Illustration of DAMF for Case IV Figure 3.7 Figure 3.8 Figure 3.9 Figure 3.10 Figure 3.11 Figure 3.12 Figure 3.13 Figure 3.14 Figure 3.15 Restored Lena images of various filters corrupted by 30%, 60% and 90% noise density. Comparative analysis of restored images and image quality map at various noise densities of Lena image. Comparative analysis of restored images and image quality map at various noise densities of Boat image. Comparative analysis of (a) PSNR and (b) MSE at various noise density(%) of Lena image.. Comparative analysis of (a) MAE and (b) ISNR at various noise density(%) of Lena image.. Comparative analysis of (a) SSIM and (b) IQI at various noise density (%) of Lena image.. Comparative analysis of (a) PSNR and (b) MSE at various noise density (%) of Boat image. Comparative analysis of (a) MAE and (b) ISNR at various noise density (%) of Boat image. Comparative analysis of (a) SSIM and (b) IQI at various noise density (%) of Boat image Figure 4.1 Figure 4.2 Figure 4.3 Figure 4.4 Figure 4.5 Figure 4.6 An example of Γ-function MFs... Fuzzy set used for noise detection... Flow chart of FBAMF algorithm Illustration of FBAMF Restored Lena images of various filters.. Performance comparison of filters at different noise densities of Lena image.. xii

14 Figure 4.7 Figure 4.8 Figure 4.9 Figure 4.10 Figure 4.11 Figure 4.12 Figure 4.13 Performance comparison of filters at different noise densities of Boat image... Comparative analysis of (a) PSNR and (b) MSE at various noise density(%) of Lena image Comparative analysis of (a) MAE and (b) ISNR at various noise density(%) of Lena image. Comparative analysis of (a) SSIM and (b) IQI at various noise density(%) of Lena image... Comparative analysis of (a) PSNR and (b) MSE at various noise density(%) of Boat image... Comparative analysis of (a) MAE and (b) ISNR at various noise density(%) of Boat image... Comparative analysis of (a) SSIM and (b) IQI at various noise density(%) of Boat image Figure 5.1 A window of size 3 3 square kernel.. 90 Figure 5.2 Illustration of Mean filtering scheme. 90 Figure 5.3 Flow chart of EAMF algorithm. 93 Figure 5.4 Performance comparison of filters at different noise densities of Lena image Figure 5.5 Performance comparison of filters at different noise densities of Boat image 100 Figure 5.6 Figure 5.7 Comparative analysis of (a) PSNR(dB) and (b) ISNR at various noise densities of Boat image... Comparative analysis of (a) SSIM and (b) IQI at various noise densities of Boat image Figure 6.1 Figure 6.2 Figure 6.3 Figure 6.4 Original and noisy Lena image with SPN and RVIN.. A 5 5 window divided into four directions. BPNN Structure for noise detection... Structure of NNDF filter Figure 6.5 Convergence characteristic of the neural network xiii

15 Figure 6.6 Figure 6.7 Figure 6.8 Figure 6.9 Figure 6.10 Comparative analysis of restored images and image quality map at various noise densities of Boat image.. Restored image of Boat and Bridge images at 20%, 30% and 40% noise density applied by proposed (NNDF) approach.. Restored image of Pepper and Goldhill images at 20%, 30% and 40% noise density applied by proposed (NNDF) approach. Comparative analysis of (a) PSNR(dB) and (b) IQI for various filters in Bridge image Comparative analysis of (a) PSNR(dB) and (b) IQI for various filters in Pepper image Figure 7.1 Figure 7.2 Performance comparison of filters at different noise densities of Lena image Performance comparison of filters at different noise densities of Boat image xiv

16 List of Tables Table No. Table 1.1 Table 1.2 Table 1.3 Table 1.4 Table Name Comparative analysis of PSNR(dB) of different filters for Lena image corrupted with salt and pepper noise of varying strength Comparative analysis of ISNR(dB) of different filters for Lena image corrupted with SPN of varying strength. Comparative analysis of IQI of different filters for Lena image corrupted with SPN of varying strength Comparative analysis of SSIM of different filters for Lena image corrupted with SPN of varying strength Page No Table 2.1 Comparative analysis of PSNR (db) for various filters in Lena image.. 35 Table 2.2 Comparative analysis of ISNR (db) for various filters in Lena image 36 Table 2.3 Comparative analysis of SSIM for various filters in Lena image 36 Table 2.4 Comparative analysis of IQI for various filters in Lena image 37 Table 2.5 Comparative analysis of PSNR (db) for various filters in Boat image.. 37 Table 2.6 Observations of the comparative analysis of PSNR(dB) in Table Table 3.1 Comparative analysis of MAE For various filters in Lena image 51 Table 3.2 Comparative analysis of PSNR(dB) for various filters in Lena image 51 Table 3.3 Comparative analysis of ISNR(dB) for various filters in Lena image. 52 Table 3.4 Comparative analysis of SSIM for various filters in Lena image 52 Table 3.5 Comparative analysis of IQI for various filters in Lena image 53 Table 3.6 Comparative analysis of MAE for various filters in Boat image. 53 Table 3.7 Comparative analysis of PSNR(dB) for various filters in Boat image. 54 Table 3.8 Comparative analysis of ISNR(dB) for various filters in Boat image.. 54 Table 3.9 Comparative analysis of SSIM for various filters in Boat image xv

17 Table 3.10 Comparative analysis of IQI for various filters in Boat image. 55 Table 4.1 Comparative analysis of MAE For various filters in Lena image 75 Table 4.2 Comparative analysis of PSNR(dB) for various filters in Lena image 75 Table 4.3 Comparative analysis of ISNR(dB) for various filters in Lena image. 76 Table 4.4 Comparative analysis of SSIM for various filters in Lena image 76 Table 4.5 Comparative analysis of IQI for various filters in Lena image 77 Table 4.6 Comparative analysis of MAE For various filters in Boat image 77 Table 4.7 Comparative analysis of PSNR(dB) for various filters in Boat image. 78 Table 4.8 Comparative analysis of ISNR(dB) for various filters in Boat image.. 78 Table 4.9 Comparative analysis of SSIM for various filters in Boat image. 79 Table 4.10 Comparative analysis of IQI for various filters in Boat image. 79 Table 5.1 Comparative analysis of PSNR (db) for various filters in Lena image 95 Table 5.2 Comparative analysis of ISNR(dB) for various filters in Lena image. 95 Table 5.3 Comparative analysis of SSIM for various filters in Lena image 96 Table 5.4 Comparative analysis of IQI for various filters in Lena image 96 Table 5.5 Comparative analysis of PSNR(dB) for various filters in Boat image 97 Table 5.6 Comparative analysis of ISNR(dB) for various filters in Boat image. 97 Table 5.7 Comparative analysis of SSIM for various filters in Boat image. 98 Table 5.8 Comparative analysis of IQI for various filters in Boat image. 98 Table 6.1 Comparative analysis of PSNR(dB) for various filters in Bridge image. 116 Table 6.2 Comparative analysis of IQI for various filters in Bridge image 116 xvi

18 Table 6.3 Comparative analysis of PSNR(dB) for various filters in Pepper image 117 Table 6.4 Comparative analysis of IQI for various filters in Pepper image 117 Table 7.1 Classification of noise on the basis of noise density level 121 Table 7.2 Comparative analysis of MAE for various filters in Lena image. 123 Table 7.3 Comparative analysis of MSE for various filters in Lena image Table 7.4 Comparative analysis of PSNR(dB) for various filters in Lena image. 123 Table 7.5 Comparative analysis of ISNR(dB) for various filters in Lena image. 123 Table 7.6 Comparative analysis of SSIM for various filters in Lena image 124 Table 7.7 Comparative analysis of IQI for various filters in Lena image 124 Table 7.8 Comparative analysis of MAE for various filters in Boat image. 124 Table 7.9 Comparative analysis of MSE for various filters in Boat image Table 7.10 Comparative analysis of PSNR(dB) for various filters in Boat image. 125 Table 7.11 Comparative analysis of ISNR(dB) for various filters in Boat image. 125 Table 7.12 Comparative analysis of SSIM for various filters in Boat image. 125 Table 7.13 Comparative analysis of IQI for various filters in Boat image. 125 xvii

19 List of Abbreviations SPN Salt and Pepper Noise RVIN Random Valued Impulse Noise MSE Mean Square Error MAE Mean Absolute Error PSNR Peak Signal to Noise Ratio ISNR Improve Peak Signal to Noise Ratio SSIM Structural Similarity Index Measure IQI Image Quality Index NAMF New Adaptive Median Filter DAMF Dynamic Adaptive Median Filter FBAMF Fuzzy Based Adaptive Mean Filter EAMF Efficient Adaptive Mean Filter ANN Artificial Neural Network NNDF Neural Network Detection based Filter ROR Robust Outlyingness Ratio S Similarity measure BPNN Back Propagation Neural Network MAD Median of the Absolute Deviations PWMAD Pixel-Wise MAD FL Fuzzy Logic MF Membership Function xviii

20 Chapter 1: Introduction 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 depend solely on the sense of vision. Vision allows humans to perceive and understand the world surrounding them in a better manner. Processing visual information by the computer has been drawing significant attention of 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, 7, 10 ]. A monochrome image I, is described as a two-dimensional function can be defined as, ( ) ( ) where, and are spatial coordinates. Amplitude of at any pair of coordinates ( ) is called intensity I or gray value of the image. When spatial coordinates 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 band (R,G,B) in a color image. The digital images are called bit-maps or raster-scan images, and are composed of an array (grid or matrix) of smaller units called pixels (picture elements). Each pixel in the digital image is a uniform patch of colour but on the display screen is made up of a red, green and blue phosphor dot or stripe. A pixel is the smallest digital image element manipulated by image processing software. Thus, bit maps often show blocky areas or jagged lines under close examination. The main objectives of image processing are [4]: to recover good quality of images from their degraded observations due to noise, blur which may affect during the process of acquisition, transmission, storage etc. to reduce the size (bytes) of the image so that it can be easily stored in small memory and transmitting very fast over a long distance in wired or wireless medium as in Fax, mobile phone, internet etc. to extract meaningful information such as features and structure of an image. to make images more beautiful or understandable by Human Perception and Automatic Machine Perception. to have very good visual display in applications like television, video, photo-phone etc, The acquired image signal must be noise-free and blurring-free for useful processing. 1

21 Development of Noise Removal Algorithms for Images to process an existing image in a desired manner and obtaining an image in a readable format. to release the image manipulator from the tyranny of the darkroom, its time scales and its noxious chemicals. to provide a flexible environment for successive experimental attempts to achieve some desired effect. Image processing has become a pre-cursor for various vision applications. Few such applications are discussed below in nutshell [1, 7, 9]. (a) Biometrics: It is a way of identifying human beings based on certain physiological characteristics i.e. fingerprint, face, DNA, iris, & behavioural characteristics i.e. gait, voice, signature analysis, signature verification etc. (b) Food quality monitoring: It can be applied in the food processing industry for inspecting the surface of fruits and vegetables to detect their condition and quality for better preservation and utilization. (c) Medical imaging: There are many imaging modalities such as X-rays, CT, MRI, PET, Ultrasound and telesurgical applications where robots are controlled to perform surgical operations. It is used for heart disease identification, lung disease identification and digital mammogram (breast tumour detection). (d) Factory automation: Machine vision system based on image processing and many automation systems are deployed by industries for applications such as visual inspection, surface defect testing, measurements of belt width and edges of blade and knife of surgical instruments, surface quality inspection and fibre analysis. The faulty components can be identified by analyzing the infra-red images. (e) Remote sensing: The role of image processing in remote sensing applications is quite immense. The sensors capture the pictures of the earth s surface in remote sensing satellites or multi-spectral scanner which is mounted on the aircraft. These pictures are processed by transmitting it to the earth station. Imaging applications include meteorological applications such as weather forecasting and prediction of atmospheric changes; resource mobilization and locating natural resources. (f) Document image processing: It aims to create a paperless office by capturing the documents in the form of an image. Image archival and retrieval systems effectively archive and help in retrieving the documents such as content-based retrieval systems, image search engines and scripts recognition systems. (g) Defense / Military Surveillance: Aerial surveillance methods are used to continuously keep an eye on the land and oceans. Thermal images have the ability to acquire useful images 2

22 Chapter 1: Introduction at night and under atmospheric conditions such as fog and smoke. This helps target acquisition and reconnaissance systems. (h) Photography: Image processing is helpful in creating special effects such as warping, blending, animation and other visual techniques. The book publishers can enhance and lay out digital images for publication. It is also used in video for creating special effects. (i) Entertainment: Photography is an excellent example of image processing. With the availability of low-cost cameras and the Internet, many applications such as facsimile image transmission, video conferencing, video phones, video editing, animation and image morphing are quite useful for personal as well as commercial purposes. (j) Communications: With the growth of multimedia technology, information can be easily transmitted through the Internet. Video conferencing helps the people in different locations for live interaction and communication. (k) Automotive: The latest development in the automotive sector is night vision system. Night vision system through infrared cameras helps to identify obstacles during night time to avoid accidents. (l) Moving Object Tracking: It enables to measure motion parameters and acquired visual record of the moving object like motion based tracking and recognition based tracking. (m) Intelligent Transportation Systems: This technique can be used in automatic number plate recognition and traffic sign recognition. The overall image processing activities are classified into various areas as given below: [7, 10] (1) Image enhancement: The quality of the image is enhanced by eliminating / reducing the factors such as noise, poor brightness, contrast, blur, artifacts, including dust and scratch on the image. Enhancement techniques basically are heuristic procedures designed to manipulate an image in order to take advantage of the psychological aspects of the human visual system. (2) Image restoration: Image restoration is the objective way of improving the quality of the image. Restoration attempts to recover an image that has been degraded by using apriori knowledge of the degradation phenomenon. If the causes of degradation are not known, then the degradations are estimated approximately by blind deconvolution to restore the original image. (3) Image compression: Multimedia objects occupy a lot of space. Hence, it creates problem for storage and transmission. Image compression algorithms such as lossless and lossy 3

23 Development of Noise Removal Algorithms for Images compression are used to reduce the data that are needed to describe the object by eliminating the redundancies that are present in the image. (4) Image segmentation: It is the process of partitioning a digital image into multiple regions and extracting a meaningful region of interest (ROI). The segmentation algorithms are either based on user interaction or based on the pixel relationships. (5) Image analysis: Often, machine vision system requires image measurement which includes measurement of shape, size, texture, and colour of the objects that are present in the image. The image analysis algorithms takes images as input and produces numerical and graphical information based on the characteristics of the image data. Image analysis comprises classification of objects, performing statistical tasks, and providing extraction and description of the scene for ultimate interpretation. (6) Image synthesis: It deals with the creation of images from other images or non-image data. It is used to create images that are not available physically or cannot be acquired using any imaging procedure using image registration and visualization. For example, computer tomography (CT) in medical imaging, benchmark and test images. (7) Features extraction and object description: Feature extraction is a process of extraction and generation of features to assist the task of object classification. The features may be (i) natural features (visual appearance) of the image that are natural to the object, and (ii) Artificial features (derived features) that are obtained using image manipulation. These image features are used to describe the object in a meaningful manner so as to aid the recognition process and to help in the discrimination of these objects. (8) Image morphology: It is the study of shapes of the objects present in the image and extraction of image features. The Decomposition of compressed image data, Reconstruction of image slices from CT or MRI raw data, Computer Graphics, Animation and Visual Reality (Synthetic Objects) belong to this class. Image processing is characterized by specific solution; hence the technique that works well in one area can be inadequate in another. The actual solution of a specific problem still requires significant research and development [4, 12]. Among the broad spectrum of applications, remote sensing, medical imaging, image morphing and warping are important. Image restoration is one of the prime areas of image processing and it is very much objective. The restoration techniques are based on mathematical and statistical models of image degradation. Denoising and deblurring tasks come under this category. Its objective is to recover the images from degraded observations. The techniques involved in image restoration are oriented towards modeling the degradations and then applying an inverse procedure to 4

24 Chapter 1: Introduction obtain an approximation of the original image. Hence, it may be treated as a deconvolution operation. The degraded image ( ) is obtained by applying the degradation operator ( ) onto the image ( ) along with the additive noise ( ). The degradation phenomenon is mathematically expressed as, ( ), ( )- ( ) ( ) The objective of image restoration is to estimate ( ) from the observed image ( ) using the known value of [7, 8]. The general image degradation and subsequent restoration model is shown in the Figure 1.1. f(x y) g(x y) f(x y) Degradation Restoration True image Function(H) + Filter(S) Restored Image Noise η(x y) Figure 1.1: Model of the general image degradation / restoration process f(x y) g(x y) f(x y) True Image + Restoration Filter(s) Restored image Impulse Noise η(x y) Figure 1.2: Model of the image degradation / restoration process due to noise In this thesis, we have concentrated on restoration of images from their degraded observations due to impulse noise. The block diagram is shown in Figure 1.2. In common use, the word noise refers to any unwanted sound. Noise, on a circuit, can be caused by voltage spikes in equipment, voltage changes on adjacent pairs in a copper cable, tones generated for network signaling, maintenance and test procedures, lightening flashes during thunderstorms, and a wide variety of other phenomena. 5

25 Development of Noise Removal Algorithms for Images Noise can block, distort, change or interfere with the meaning of a message in both human and electronic communication. In signal processing or computing it can be considered unwanted data without meaning; that is, data that is not being used to transmit a signal, but is simply produced as an unwanted by-product of other activities. Images taken with both digital cameras and conventional film cameras will record noise from a variety of sources. Many further uses of these images require that the noise will be (partially) removed for aesthetic purposes as in artistic work or marketing, or for practical purposes such as computer vision. The possible classification takes into consideration the way the noise affects the image, resulting in additive noise and multiplicative noise. There are different types of noise encounter in image processing [10, 11]. These are; (a) Impulsive noise As impulse noise is short in duration ( 1 / 100 of a second, or so); it has little effect on voice communications, but can cause bit errors in a data transmission. Impulsive noise can be classified as salt-and-pepper noise (SPN) and random-valued impulse noise (RVIN)[4, 5, 6]. In salt-and-pepper noise (SPN), the noisy pixel value is either 0 or 255. In random-valued impulse noise (RVIN), the noisy pixels value takes any value within the range 0 and 255. (b) Gaussian noise Gaussian noise is statistical noise that has a probability density function of the normal distribution (also known as Gaussian distribution). In other words, the values that the noise can take on are Gaussian-distributed. It is most commonly used as additive white noise to yield additive white Gaussian noise (AWGN). (c) Mixed noise When more than one type of noise is present in the image, it is called mixed noise. In this type of noise, the image contains dark and white dots and looks soft and slightly blurry, where each pixel in the image is changed from its original value by a (usually) small amount [7]. (e) Speckle noise Speckle noise is a granular noise that inherently exists in and degrades the quality of images. It is a multiplicative noise, i.e. it is in direct proportion to the local grey level in any area. The signal and the noise are statistically independent of each other [7]. Speckle noise occurs in almost all coherent imaging systems such as laser, acoustics and SAR (Synthetic Aperture Radar) imagery and because of this noise the image resolution and contrast become reduced, thereby reducing the diagnostic value of this imaging modality. So, speckle noise reduction is an important prerequisite, whenever ultrasound imaging is used for tissue characterization. Since we thrust on impulse noise, the details on impulse noise models are given below. Accordingly, this chapter is organized as follows. The Section 1.1 deals with impulse noise models. Section 1.2 discusses the performance measures used. Section 1.3 gives the detail 6

26 Chapter 1: Introduction literature survey on impulse noise filters. Section 1.4 outlines the motivation for the work. In Section 1.5 the objectives are given. Section 1.6 gives the layout of the thesis. 1.1 Impulse noise models Depending on the model used to characterize the noise, we can encounter impulse noise, Gaussian noise and many others. In this thesis we are giving more importance on impulse noise [1, 7, 8, 10, 22, 43]. Impulse noises can be described by the following model: ( ) { ( ) ( ) ( ) where, ( ) denotes a noisy image pixel, ( ) denotes a noise free image pixel and ( ) denotes a noisy impulse at the location( ). Impulsive noise can be classified as salt-andpepper noise (SPN) and random-valued impulse noise (RVIN)[4, 5, 6]. In salt-and-pepper noise, noisy pixels take either minimal or maximal values i.e. ( ) * +, and for random-valued impulse noise, noisy pixels take any value within the range minimal to maximal value i.e. ( ), - where, denote the lowest and the highest pixel luminance values within the dynamic range respectively so that it is a little bit difficult to remove random valued impulse noise rather than salt and pepper noise [3]. The preservation of image details faces difficulties due to the attenuation of noise. Figure 1.3 may best describe the difference between SPN and RVIN. In the case of SPN the pixel substitute in the form of noise may be either or. Whereas in RVIN situation it may range from. Cleaning such noise is far more difficult than cleaning fixedvalued impulse noise; the differences in gray levels between a noisy pixel and its noise-free neighbors are significant most of the time. In this thesis, we focus on impulse noise and schemes that are proposed to suppress them. * + (a) Salt & Pepper Noise with ( ) * +, - (b) Random Valued Impulsive Noise with ( ), - Figure 1.3: Types of impulse noise in images 7

27 Development of Noise Removal Algorithms for Images 1.2 Performance Measures used One of the issues of denoising is the measure of the reconstruction error. In order to separate the noise and image components from a single observation of a degraded image, it is necessary to assume or have knowledge about the statistical properties of the noise. The metrics used for performance comparison of different filters (both existing and proposed) are defined below. There are basically two classes through which we can measure the performance and quality of an image. These are objective quality and the subjective or qualitative or distortion measure. The metrics used for performance comparison among different filters are defined below: A. Objective Quality: 1) Mean Square Error (MSE) and Mean Absolute Error (MAE) In statistics, the mean square error (MSE) of an estimator is one of many ways to quantify the amount by which an estimator differs from the true value of the quantity being estimated. Given an original image of size ( ) pixels and as reconstructed image, the error can MSE be denoted as, ( ) ( 4) Similarly, the mean absolute error (MAE) is defined as, ( 5) The goal of de-noising is to find an estimate image such that both MSE and MAE should be as minimum as possible. 2) Peak Signal to Noise Ratio (PSNR) PSNR [7, 10] 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. Reconstructed images with higher PSNR are judged as of better quality. PSNR is the ratio between the maximum possible power of a signal and the power of noise. PSNR is usually expressed in terms of the logarithmic decibel and defined as, ( ). / ( 6) 8

28 Chapter 1: Introduction where, 255 is the maximum possible amplitude for an 8-bit image. An improvement in the PSNR magnitude will increase the visual appearance of the image. PSNR is typically expressed in decibels (db). For comparison with the noisy image, the greater the ratio, the easier it is to identify and subsequently isolate and eliminate the source of noise. A PSNR of zero indicates that the desired signal is virtually indistinguishable from the unwanted noise. PSNR is a good measure for comparing restoration results for the same image, but between-image comparisons of PSNR are meaningless. One image with 20 db PSNR may look much better than another image with 30 db PSNR. 3) Improve Peak Signal to Noise Ratio (ISNR) For the purpose of objectively testing the performance of the restored image, Improvement in signal to noise ratio (ISNR) is used as the criteria, which is defined by [17]. [ ] [ ] ( 7) where, and are the total number of pixels in the horizontal and vertical dimensions of the images, and are the original, degraded and the restored image respectively. 4) Structural Similarity Index Measure (SSIM) SSIM is a novel method for measuring the similarity between two images [20, 21]. It is computed from three image measurement comparisons: luminance, contrast, and structure. Each of these measures is calculated over an (8 8) local square window which moves pixelby-pixel over the entire image. At each step, the local statistics and SSIM index are calculated within the local window. Because the resulting SSIM index map often exhibits undesirable blocking artifacts, each window of size ( pixels) is filtered with a Gaussian weighting function. In practice, one usually requires a single overall quality measure of the entire image and thus, the mean SSIM index is computed to evaluate the overall image quality. The SSIM can be viewed as a quality measure of one of the images being compared while the other image is regarded as perfect quality. It can give results between 0 and 1, where 1 means excellent quality and 0 means poor quality. The Structural Similarity Index Measure (SSIM) [19] between the original image and restored image can be defined by, ( ) ( ) ( ) ( 8) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 9

29 Development of Noise Removal Algorithms for Images ( ) ( ) where, is the original Image, is the restored image, is the corrupted image, M N is the size of the image, L is the luminance comparison, C is the contrast comparison, S is the structure comparison, μ is the mean and σ is the standard deviation. B. Subjective or Qualitative or Distortion Measure Along with the above performance measure, subjective assessment is also required to measure the image quality. In a subjective assessment measure, 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. The qualitative measurement approach does not depend on the image being tested, the viewing conditions or the individual observer. (1) Image Quality Index (IQI) IQI was proposed by Wang and Bovik [18], Madhu, Nair and G. Raju [19], which is easy to calculate and applicable to various image processing applications. IQI models any distortion as a combination of three different factors: loss of correlation, luminance distortion, and contrast distortion. IQI is defined as, ( ) ( ) ( ) ( 9) where, ( ) ( ) ( ) ( ) ( ) IQI is first applied to local regions using a sliding window approach with size. The represents the sliding window of original and restored images respectively. Here, we have taken. At the j th step, the local quality index is computed within the sliding window using the formula given above. If there are a total of M steps, then the overall image quality index is given by, ( ) ( 0) where, j varies from 1 to M. The dynamic range of IQI is, -], and the best value 1 is achieved if and only if restored image R is equal to the original image O. 10

30 Chapter 1: Introduction 1.3 Literature survey Noise removal from a contaminated image signal is a prominent field of research and many researchers have suggested a large number of algorithms and compared their results [65]. The main thrust on all such algorithms is to remove impulsive noise while preserving image details. These schemes differ in their basic methodologies 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, attempts have been made for detailed literature reviews of impulse noise removal on the reported articles and a study of their performance through computer simulation. The various schemes for image denoising are broadly classified based on the characteristics of the filtering schemes [7]. These are (A) Filtering without detection, (B) Detection followed by filtering, (C) Hybrid filtering. Some of these filtering schemes are described as follows; A. Filtering without Detection In this type of filtering a window mask is moved across the observed image. The mask is usually of size ( ), where 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. This technique does not detect contaminated pixels. It applies the filtering mechanism throughout the subject without discriminating any pixel. The Moving Average (MA) [23] is a simple linear filter. The average of all pixels of a sliding window is replaced with the pixel of interest. ( ) ( 1) Where, is the noisy image, is the restored image and is the sliding window of size centered around( ). Its performance both in subjective as well as objective way is very poor. In traditional median filtering called Standard Median filter (SMF) [7], the filtering operation is performed across each pixel without considering whether it is corrupted or not. So, the image details contributed by the uncorrupted pixels are also subjected to filtering and as a result, the image details are lost in the restored version. To alleviate this problem, an impulse noise detection mechanism is applied prior to the image filtering. In switching median filters [24, 25], a noise detection mechanism has been incorporated so that only those pixels identified as corrupted would undergo the filtering process while those identified as uncorrupted would remain intact[ 40, 41, 42, 64 ]. 11

31 Development of Noise Removal Algorithms for Images Weighted median filter is the extension of median filter. In weighted median filter, its specified pixels within a local neighbourhood are repeated a given number of times in the computation of the median value. The basic idea is to give weight to each pixel. Each pixel is given a weight according to its spatial position in the window. The Centered Weighted Median (CWMF) [26] filter is giving more weight only to the central value of each window. B. Detection followed by Filtering This type of filtering involves two steps. In the first step, it identifies noisy pixels and in the second step, it filters those pixels. Here also a mask is moved across the image and some arithmetical operations are 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. 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. The Progressive Switching Median Filter (PSMF) [27] was proposed which achieves the detection and removal of impulse noise in two separate stages. In the first stage, it applies impulse detector and then the noise filter is applied progressively in an iterative manner in the second stage. In this method, impulse pixels located in the middle of large noise blotches can also be properly detected and filtered. The performance of this method is not good for very highly corrupted image [14]. Nonlinear filters such as Adaptive Median Filter (AMF) [28] can be used for discriminating corrupted and uncorrupted pixels and then apply the filtering technique. Noisy pixels will be replaced by the median value and uncorrupted pixels will be left unchanged. AMF performs well at low noise densities but at higher noise densities, window size has to be increased to get better noise removal which will lead to less correlation between corrupted pixel values and replaced median pixel values [15, 16]. A Minimum-Maximum Exclusive Mean (MMEM) [29] filter to remove impulse noise from highly corrupted images is proposed. 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 the average of all the pixels of that particular range is more than a certain value then that pixel is replaced with the average, otherwise it is left intact. This is one of the good schemes filters like SMF [7], rank-ordered mean (ROM) [38] because of its simplicity and easy implementation. An efficient Decision-Based Algorithm (DBA) [30] was proposed using a fixed window size of 3 3. First it detects the noisy and noisy free pixels, by checking whether the value of a 12

32 Chapter 1: Introduction processed pixel element lies between the maximum and minimum values that occur inside the selected window. This is because the impulse noise pixels can take the maximum and minimum values in the dynamic range (0, 255) [39]. If the value of the pixel processed is within the range, then it is an uncorrupted pixel and left unchanged. If the value does not lie within this range, then it is a noisy pixel and is replaced by the median value of the window or by its neighborhood values. It shows promising results and a smooth transition between the pixels is lost with lower processing time which degrades the visual quality of the image. To overcome the problem in DBA, an Improved Decision-Based Algorithm (IDBA) [31] is proposed where the corrupted and uncorrupted pixels in the image are detected by checking the pixel element value against the maximum and minimum values in the window selected. The maximum and minimum values that the impulse noise takes will be in the dynamic range (0, 255) [39]. If the pixel being currently processed has a value within the minimum and maximum values in the window of processing, then it is an uncorrupted pixel and no modification is made to that pixel. If the value doesn t lie within the range, then the corrupted pixels can be replaced either by the median pixel or by the mean of processed pixels in the neighborhood. It results in a smooth transition between the pixels with edge preservation and better visual quality for low-density impulse noise. The limitation of this method is that in the case of high-density impulse noise, the fixed window size of 3 3 will result in image quality degradation due to the presence of corrupted pixels in the neighborhood. The Robust Estimation Based Filter (REBF) [32] is proposed for Removal of High Density Impulse Noise from images. The function of the proposed filter is to detect the outlier pixels and restore the original value using robust estimation. In this proposed approach, impulses are first detected based on the minimum, median and maximum value in the selected window. If the median pixel and the current pixel lie inside the dynamic range [0,255] then it is considered as noise free pixel. Otherwise it is considered as a noisy pixel and replaced by an estimated value. The visual quality results show that the proposed filter removes impulse noise completely without any blurring and sinking effect. A novel improved median filtering (NIMF) [17] algorithm is proposed for the removal of highly corrupted with salt-and-pepper noise from images. Firstly all the pixels are classified into signal pixels and noisy pixels by using the Max-Min noise detector. The noisy pixels are then separated into three classes, which are low-density, moderate-density, and high-density noises based on the local statistic information. Finally, the weighted 8-neighborhood similarity function filter, the 5 5 median filter and the 4-neighborhood mean filter are adopted to remove the noises for the low, moderate and high level cases respectively. In experiment, the proposed algorithm is compared with three typical methods, named Standard Median filter, Extremum Median filter and Adaptive Median filter respectively. The validation results show that the proposed algorithm has better performance for capabilities of noise removal, adaptivity and detail preservation, especially effective for the cases when the images are very highly corrupted. 13

33 Development of Noise Removal Algorithms for Images A Modified Decision Based Unsymmetrical Trimmed Median Filter (MDBUTMF) [34] algorithm is proposed for the restoration of gray scale and color images that are highly corrupted by salt and pepper noise. The proposed algorithm replaces the noisy pixel by trimmed median value when other pixel values, 0 s and 255 s are present in the selected window and when all the pixel values are 0 s and 255 s then the noise pixel is replaced by mean value of all the elements present in the selected window. When this algorithm is tested against different gray scale and color images, it gives better Peak Signal-to-Noise Ratio (PSNR) and Image Enhancement Factor (IEF). A Tolerance based Selective Arithmetic Mean Filtering Technique (TSAMFT) [35] is proposed to remove salt and pepper noise from corrupted images. Arithmetic Mean filtering technique is modified by the introduction of two additional features. In the first phase, to calculate the Arithmetic Mean, only the unaffected pixels are considered. In the second phase, a Tolerance value has been used for the replacement of the pixels. This proposed technique provides much better results than that of the existing mean and median filtering techniques. The Peak Signal to Noise Ratio (PSNR) of the filtered image using the proposed technique is much higher than that of the filtered images obtained by the existing mean filtering techniques. The FBDA [19] is an improved fuzzy-based switching median filter in which the filtering is applied only to corrupted pixels in the image while the uncorrupted pixels are left unchanged. During the time of filtering process, FBDA selects only uncorrupted pixels in the selected window based on a fuzzy distance membership value. The positive impulsive noise may be caused by electron radiation in the photo-electronic imaging system [44]. A novel nonlinear filter based on row and column filtering (RCF) was presented and its denoised and detail preservation properties were analyzed. According to the statistical behaviors of each row and column of an image, the pixel value is determined by its neighborhood. Each row is operated firstly. Then each column processing gives the final result. The given filter was compared with median filter, recursive median filter, adaptive filter and robust statistical adaptive filter through the computer simulations. It is shown that the filter is of a high performance for positive impulsive noise removal and detail preservation. This is another nonlinear technique which also works in two stages [45]. The authors have suggested to identifying noisy pixels 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 values which are analyzed using the median. It is a good filter in low noise conditions but the performance is slightly degrades beyond of 20% noise. This method [46] is a modified version of Median of Absolute Deviation from median (MAD) statistic. MAD has been used to estimate the presence of image details. An iterative Pixel Wise MAD, i.e. PWMAD has been proposed by the authors that provides a reliable 14

34 Chapter 1: Introduction removal of impulses. Its performance is more than average and fails when the edge density is more. The Rank Order Absolute Difference (ROAD) [47] scheme presents efficient measures to determine the closeness of a test pixel to its surrounding pixels. This measured has been used to detect impulsive noise in an image. It quantifies how different in intensity the test pixels are from their neighbours. The original switching median filter cannot detect the noise pixel whose value is close to its neighbors if the threshold is designed for emphasizing the detail preservation. Therefore, it is difficult differentiate between noisy and a noise-free pixel in the sliding window. A switching median filter is proposed [48] which modified by adding one more noise detector to improve the capability of impulse noise removal. Here, the impulse noise detector is established based on the rank order arrangement of the pixels in the sliding window. The research work by Abreu et al [49, 38], an adaptive approach has been suggested to solve the restoration problem where the authors have conditioned the filtering on the current state of the algorithm. The state variable has been defined as the output of a classifier that act on the difference between the current pixel value and the remaining ordered pixel values inside a window centered on the pixel of interest. This scheme is undoubtedly one of the robust and simple but it fails in preserving the finer details of the image. A novel technique [51] has been proposed for denoising the images which are corrupted by random valued impulse noise. The detection of noisy pixels is done using variable weights of all neighbor directional pixels through (5 x 5) mask. The proposed operator performs arithmetic absolute differences along with some other arithmetic operations on the pixels aligned in the four main directions with the center pixel to classify test pixel. It shows better denoising capability along with preservation of fine image textures and details for the images corrupted with random valued impulses. A novel Modified Directional Weighted Median Based (MDWM) [52] filter has been proposed, this is based on the differences between the current pixel and its neighbors aligned with four main directions. A direction index is used for each edge aligned with a given direction. Then, the minimum of these four direction indexes is used for impulse detection. It tend to work well for restoring the images corrupted by random-valued impulse noise with low noise level but poorly for highly corrupted images. The DWM filter provides better performances of suppressing impulse with high noise level which may enhance the performance in terms of removal of random-valued impulse noise compared to the DWM filter. A new technique [53] has been proposed for restoring images distorted by random-valued impulse noise. The detection process is based on finding the optimum direction, by calculating the standard deviation in different directions in the filtering window. The tested pixel is deemed original if it is similar to the pixels in the optimum direction. The proposed 15

35 Development of Noise Removal Algorithms for Images technique has superior performance, when compared to other existing methods, especially at high noise rates. A new nonlinear filter [54] has been proposed called detail preserving median based filter for removing salt and pepper noise and random valued impulse noise with edge and detail preservation is presented. The proposed method first detects the impulse pixel based on threshold values and then the corrupted pixels are replaced by the median value of the uncorrupted pixels in the filtering window. This method outperforms many of the existing methods. An efficient algorithm [55] has been proposed for the removal of random-valued impulse noise from a corrupted image which uses a statistic of rank-ordered relative differences to identify pixels which are likely to be corrupted by impulse noise. Once a noisy pixel is identified, its value is restored by a simple weighted mean filter. Simulation results indicate that this algorithm provides a significant improvement over many other existing techniques. A new filtering scheme [56] has been proposed based on contrast enhancement within the filtering window for removing the random valued impulse noise. The application of a nonlinear function for increasing the difference between a noise-free and noisy pixels results in efficient detection of noisy pixels. As the performance of a filtering system, in general, depends on the number of iterations used, an effective stopping criterion based on noisy image characteristics to determine the number of iterations is also proposed. Extensive simulation results exhibit that the proposed method significantly outperforms many other well-known techniques. An approach has been proposed for removal of impulse noise using two phases where as in the first phase detects contaminated pixels and the second phase filters only those pixels keeping others intact. The detection scheme utilizes second order difference of pixels in a test window and the filtering scheme is a variation median filter based on the edge information. This scheme outperforms them in terms of Peak Signal-to-Noise Ratio (PSNR), number of false detection and miss detection, also good at preserving finer details. 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. A novel and effective median filter, called tri-state median (TSM) [37] filter, is proposed where noise detection is realized by an impulse detector which takes the outputs from the standard median (SM) filters and centre weighted median (CWM) filters and compares them with the origin or center pixel value in order to make a tri-state decision. An attractive merit of this filtering scheme is that it provides an adaptive decision to detect local noise simply 16

36 Chapter 1: Introduction based on the outputs of these filters. Given a specified threshold T, the output of our proposed TSM filter may correspond to one of three possible states, namely the origin pixel value (i.e., the pixel is noise-free), the SM filtered output (i.e., the pixel is corrupted) or the CWM filtered output (i.e., the pixel is probably uncorrupted with ). As a result, impulse noise can be removed for those corrupted pixels through SM or CWM filtering. For those uncorrupted pixels identified, they remain unchanged in order to preserve the local image details. Consequently, the trade off between suppressing noise and preserving detail is well balanced over a wide variety of images. The schemes are studied in detail and to have an in depth performance analysis of various schemes have been made through simulation in MATLAB. The comparative results in terms of PSNR(dB), ISNR(dB), IQI and SSIM of restored Lena image are shown in Tables respectively. The restored images of Lena image corrupted with various impulse noise densities are shown in Figures For better visual analysis a graphical representation of PSNR (db), ISNR (db), IQI and SSIM at various noise densities are shown in Figure 1.7 and Figure 1.8 for Lena image. 17

37 Development of Noise Removal Algorithms for Images Filters Table 1.1: Comparative analysis of PSNR(dB) of different filters for Lena image corrupted with salt and pepper noise of varying strength % of noise MA SMF CWMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF TSAMFT FBDA TSM Filters Table 1.2: Comparative analysis of ISNR(dB) of different filters for Lena image corrupted with salt and pepper noise of varying strength % of noise MA SMF CWMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF TSAMFT FBDA TSM

38 Chapter 1: Introduction Table 1.3: Comparative analysis of IQI of different filters for Lena image corrupted with salt and pepper noise of varying strength Filters % of noise MA SMF CWMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF TSAMFT FBDA TSM Filters Table 1.4: Comparative analysis of SSIM of different filters for Lena image corrupted with salt and pepper noise of varying strength % of noise MA SMF CWMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF TSAMFT FBDA TSM

39 Development of Noise Removal Algorithms for Images % of noise Restored image Filters 30% (a) 50% (b) 70% (c) 90% (d) Restored image of (a) Restored image of (b) Restored image of (c) Restored image of (d) MA SMF CWMF Figure 1.4 : Performance comparison of different filtering schemes where filtering without detection at different salt and pepper noise densities of Lena image. % of noise Restored image Filters 30% (a) 50% (b) 70% (c) 90% (d) Restored image of (a) Restored image of (b) Restored image of (c) Restored image of (d) PSMF AMF MMEM DBA IDBA Figure 1.5 : Performance comparison of different filtering schemes where detection followed by filtering at different salt and pepper noise densities of Lena image. 20

40 Chapter 1: Introduction % of noise Restored image Filters 30% (a) 50% (b) 70% (c) 90% (d) Restored image of (a) Restored image of (b) Restored image of (c) Restored image of (d) REBF NIMF MDBUT MF TSAMF T FBDA TSM Figure 1.6: Performance comparison of different filtering schemes where detection followed by filtering at different salt and pepper noise densities of Lena image. 21

41 ISNR (db) PSNR (db) Development of Noise Removal Algorithms for Images MA SMF CWMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF TSAMFT FBDA TSM Noise Density (%) (a) MA SMF CWMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF TSAMFT FBDA TSM Noise Density (%) Figure 1.7: Comparative analysis of (a) PSNR(dB) and (b) ISNR (db) at various noise densities of Lena image. (b) 22

42 IQI SSIM Chapter 1: Introduction MA SMF CWMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF TSAMFT FBDA TSM Noise Density (%) (a) MA SMF CWMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF TSAMFT FBDA TSM Noise Density (%) Figure 1.8: Comparative analysis of (a)ssim and (b) IQI at various noise densities of Lena image. (b) 23

43 Development of Noise Removal Algorithms for Images 1.4 Motivation From the literature survey, it is observed that the performance of any filtering scheme is dependent on the detection mechanism. The better 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 a precomputed numerical value. Mostly the reported schemes use a fixed threshold which does not serve the purpose at various noise conditions as well as in different images. Hence, to improve the detector performance, the need for an adaptive threshold is of utmost necessity which can be automatically determined from the characteristics of an image and the noise present in it. In this thesis, attempts have been made to determine a threshold from an observed noisy image. This problem has been formulated as a prediction problem and various models have been chosen to determine a threshold for the input noisy images. Also, it shows from the literature survey that the linear filters are often used for the removal of impulse noise which is not efficient. On the other hand, non-linear filters are generally efficient for the removal of impulse noise. However, there exists further scope to improve the performance of these filters. 1.5 Objectives The thesis objectives are, 1. to work towards improved and efficient detectors(including fuzzy and ANN) for identifying contaminated pixels. 2. to use better image statistics for identifying contaminated pixels. 3. to devise adaptive window size and thresholding techniques so that noise detection would be more efficient. 4. to explore the utility of selective filtering for image sharpening to produce high quality images with preserved image details. 5. to work towards improvement of filters for removing impulse noise using different soft computing techniques. 24

44 Chapter 1: Introduction 1.6 Layout of the thesis The rest of the thesis is organized as follows: Chapter 2: New Adaptive Median Filter (NAMF): In this chapter, an improved adaptive median filtering technique called New Adaptive Median Filter is proposed to overcome the shortcomings of standard median filter and Adaptive Median Filters (AMFs) that removes salt-and-pepper noise while preserving edges. This filter is designed to reconfigure itself and provide real-time noise reduction. Chapter 3: Dynamic Adaptive Median Filter (DAMF): A new algorithm is proposed namely, Dynamic Adaptive Median Filter (DAMF) where corrupted pixels can either be replaced by the median pixel or with the mean of the neighborhood processed pixels which results in a smooth transition between the pixels with edge preservation and better visual quality. Chapter 4: Fuzzy Based Adaptive Mean Filter (FBAMF): In this chapter we proposed a fuzzy based adaptive mean filtering (FBAMF) scheme which works on two stages. The first stage deals with noise detection followed by the application of adaptive mean filtering to remove the salt and pepper noise. Chapter 5: Efficient Adaptive Mean Filter (EAMF): A new algorithm called an efficient adaptive mean filtering (EAMF) scheme is proposed in this chapter. This filter replaces the noisy pixels with the mean value of non-noisy neighbouring pixels selected from a window dynamically. If the number of non-noisy pixels in the selected window is not sufficient, a window of next higher size is chosen and the size of the window is automatically adapted based on the density of noise in the image as well as the density of corruption local to a window. Chapter 6: Neural Network Detection based Filter (NNDF): In this chapter, a noise detection scheme is proposed to classify the noisy pixels of an image contaminated by RVIN. Subsequently, a good filtering scheme for these noisy pixels is proposed. Here, a back propagation neural network is trained on a standard image using two input statistical parameters called robust outlyingness ratio (ROR) and the similarity measure(s) to generate a pattern. Then, the identified pixels are filtered using a novel filtering scheme. Chapter 7: Comparative Study of Proposed Techniques: In this chapter, we have compared our proposed schemes to derive an overall inference about the performance of the schemes with respect to performance measured used as described in Section 1.2. The restored images are also visually compared among the schemes. Chapter 8: Conclusion: This chapter provides the concluding remarks with a stress on achievements and limitations of the proposed schemes and the scope of the further research are outlined at the end. 25

45 Chapter 2: New Adaptive Median Filtering Technique Chapter 2 New Adaptive Median Filtering Technique for Removal of Impulse Noise Images very often get contaminated by salt-and-pepper noise either due to malfunctioning of camera sensors during acquisition or during transmission due to channel noise. As a result, it affects further processing of images. Hence, before dealing with high level image processing, it is of vital importance to restore the image through filtration process. The linear filter has poor performance as compared to non-linear ones in denoising [33, 36, 58]. Hence non-linear filters are mostly used to remove salt-and-pepper noise from images. Many schemes have been developed to deal with salt-and-pepper noise. Median filtering is one of the successful scheme used by many researchers [33, 62, 63] and various variations of median filter like adaptive median filter, the multistate median filter, or the median filter based on homogeneity information, Improved Progressive Switching Median Filter etc. have been found in literature [50, 58, 59, 60, 61, 42, 44]. In this chapter, we have proposed a similar such variant of median filter based on adaptive window selection scheme and its performance has been compared with standard filters in terms of PSNR, ISNR, SSIM and IQI for Lena and Boat images. The chapter is organized as follows. Section 2.1 explains the standard median filtering technique. Section 2.2 presents the proposed technique for noise removal. Section 2.3 outlines the simulation and results. Finally, Section 2.4 deals with the summary of the chapter. 2.1 Median Filtering Technique The median filter has the capability to reduce impulse noise; however, for larger window size it produces severe smoothing. The median filter has two main advantages over the mean filter: (a) The median is a more robust than the mean and so an outlier pixel in a neighborhood will not affect the median value significantly. (b) Unlike the mean, the median value represents one of the pixels in the neighborhood; the median filter does not create new unrealistic pixel value when the filter straddles an edge. For this reason, the median filter is much better at preserving sharp edges than the mean filter. 26

46 Development of Noise Removal Algorithms for Images The median filter is a sliding-window spatial filter which replaces the center value in the window with the median of all the pixel values in the window. The working principle of a median filter in an image is explained in Figure 2.1. Consider a segment of an image is considered in Figure 2.1(a). let the centre pixel considered for filtration is the highlighted pixel (value 255). The 3 3 and 5 5 window corresponding to the test pixel is shown in Figs. 2.1 (b) & (c) respectively (b) 3 3 window (a) Segment of an image (c) 5 5 window Figure 2.1: Illustration of Median Filtering scheme To apply the median filter the neighbourhood values after ascending order and the middle value is selected for replacement. In case of 3 3 window the sorted values are 214, 214, 214, 214, 214, 214, 215, 215, and 255. The median value, 214 replaces the centre pixel 255. Similarly, in case of 5 5 window the median value obtained is 215. The standard median filter can successfully remove salt-and-pepper noise with a smaller window size when the noise density is low in images. For high density impulse noise, a higher window size is necessary to combat the impulse noise. However, as the window size increases the filtered image suffers from blurring. Further, the median filter is applied across the image pixels without irrespective of its contamination and becomes computationally expensive. Since Salt & Pepper noise affects only selected pixels with some probability, median filter sometimes introduces unnecessary distortions in the restored images. Further, median filter does not have the capability to distinguish between noise pixel and an edge pixel. As a result, filtered image loses the edge properties. 27

47 Chapter 2: New Adaptive Median Filtering Technique To overcome these shortcomings, Adaptive Median Filters (AMFs) have been applied widely [28]. These filters perform a pre-processing to identify the pixels in an image affected by impulse noise. It compares the pixel value of the test pixel with its surrounding neighbour pixels. Both the size of the neighbourhood as well as the threshold value is adjusted during comparison. A pixel that is different from majority of its neighbours and structurally misaligned with the neighbour pixels is labelled as an impulse noise. These noise pixels are then replaced by the median pixel value of the pixels in the neighbourhood [28]. The proposed scheme uses an improved adaptive median filtering technique that removes salt-and-pepper noise while preserving edges. This filter is designed to reconfigure itself and provide real-time noise reduction. The proposed filter solves the dual purpose of removing noise as well as distortion from the images and is capable of removing high density impulse noise (up to 70%). The details of the suggested scheme are given below Proposed Scheme The suggested scheme namely, new adaptive median filter (NAMF) works in two phases for each pixel. In the first phase, we decide whether the test pixel is corrupted or not, using a simple algorithm from a given window in the neighborhood of test pixel. For corrupted pixel, the pixels with minimum and maximum values are eliminated from the window. If the total remaining pixels are less than the window size, the window size is increases and the overall process is repeated for the test pixel on the new window. If for any pixel, the window size is increased more than the predefined maximum window size (W max ) then the test pixel is replaced with average of the window. The overall steps followed are listed in Algorithm 2.1. A flowchart is also given in Figure 2.2 for better readability. 28

48 Development of Noise Removal Algorithms for Images Algorithm 2.1: New Adaptive Median Filter ( NAMF ) Input : The noisy image Y Output: The filtered image Step1 : Initialize a sub-window size, W s = 3 and maximum window size, W max = 11 Step 2: Select a sub-window W s W s with center pixel Y i,j. Step 3: Find the maximum (Y max ) and minimum (Y min ) grey values within the window Step 4: If the Y max -Y min Threshold (T), then go to step 9. Step 5: If the Y min < Y i,j. < Y max then go to step 9. Step 6: Collect the set of pixels ( ) from the sub-window where, Y min < S i,j. < Y max Step 7: If the size of, then replace Y i,j with median of pixels in. Go to step 9. Step 8: W s W s + 2, If W s W max,then go to Step 2. else replace the center pixel by mean of the pixels in sub-window of size W max Step 9: Shift the test pixel. Go to Step 1 Step 10: Repeat Steps 1 through 9 for image pixels. 29

49 Chapter 2: New Adaptive Median Filtering Technique Read an image (Y), Initialize W s =3 and W max =11 A Select a 2-D window of size W s W s with centre pixel Y i,j B Choose Y max and Y min values of the pixels in the window& calculate the difference between them Yes Difference value > threshold? No No Is Y min < Y i,j. < Y max? Yes Noise free pixel Eliminate the pixels with value equal to Min or Max value of the window Yes Whether all the pixels are processed? No Yes If the remaining pixels in the window W s? No Shift the window to next pixel Replace the centre pixel by median value of the remaining pixels in the window Increase the window size, W s W s + 2 A Filtered pixel B Shift the window to next pixel A Stop Figure 2.2: Flow Chart of NAMF Algorithm 30

50 Development of Noise Removal Algorithms for Images For completeness, the working principles of NAMF are illustrated below through an example. Four different cases are considered to demonstrate different conditions along with action taken during filtering process. Case I: Consider the segment of an image Figure 2.3(a) and a 3 3 window is selected from the image segment as given in Figure 2.3(b) with centre pixel as 255. Here Y min = 214, Y max = 255 and the difference between Y max and Y min is 41. As the difference is greater than the chosen threshold, 30 and since Y min < Y i,j. < Y max, the centre pixel Y i,j is detected as noisy and the proposed filter (NAMF) is applied for the pixel. The noise removal process starts by collecting the set of pixels ( ) from the sub-window, where Y min < S i,j. < Y max i.e. S= {215, 215}. As the cardinality of set S, S less than W s, the window size W is increased by 2, i.e. W s W s +2. The modified window size is shown in Figure2.3(c) (a) Segment of an image (b) 3 3 window (c) 5 5 window Figure 2.3: Illustration of NAMF for Case I Considering window size 5 5, Y min, and Y max are found to be 214 and 255 respectively. In the similar way the difference (Y max - Y min ) is greater than the selected threshold 30 and Y min <Y i,j. <Y max implies the pixel Y i,j is noisy. The set of pixels S is obtained from 5 5 window as S ={215, 215, 215, 216, 215, 215, 215, 215, 215, 215, 215, 215}. As the cardinality of set S, S greater than, the centre pixel Y i,j is replaced by the median value as

51 Chapter 2: New Adaptive Median Filtering Technique Case II: Consider the segment of an image Figure 2.4(a) and a 3 3 window is selected from the image segment as given in Figure 2.4(b) with centre pixel as 0. Here Y min = 0, Y max = 255 and the difference between Y max and Y min is 255. As the difference is greater than the chosen threshold, 30 and since Y min < Y i,j. < Y max, the centre pixel Y i,j is detected as noisy and the proposed filter (NAMF) is applied for the pixel. The noise removal process starts by collecting the set of pixels S from the sub-window, where Y min < S i,j. < Y max i.e. S= { }. As the cardinality of set S, S less than W s, the window size W s is increased by 2, i.e. W s W s +2. The modified window size is shown in Figure2.4(c). Considering window size 5 5, Y min, and Y max are found to be 0 and 255 respectively. In the similar way, the difference (Y max - Y min ) is greater than the selected threshold 30 and Y min <Y i,j. <Y max implies the pixel Y i,j is noisy. The set of pixels S is obtained from 5 5 window as S ={216, 217, 214, 214, 215, 213, 214, 215, 216, 217, 218, 216, 215, 214}. As S greater than, the centre pixel Y i,j is replaced by the median value as (a) Segment of an image (b) 3 3 window (c) 5 5 window Figure 2.4: Illustration of NAMF for Case II Case III: Consider the segment of an image as in Figure 2.5(a) and a 3 3 window is selected from the image segment as given in Figure 2.5(b) with centre pixel as 0. Here Y min = 0, Y max = 28 and the difference between Y max and Y min is 28. As the difference is less than the chosen threshold, 30, the centre pixel Y i,j is detected as non-noisy although it is 0. 32

52 Development of Noise Removal Algorithms for Images (a) Segment of an image (b) 3 3window Figure 2.5: Illustration of NAMF for Case III Case IV: Consider the segment of an image Figure 2.6(a) and a 3 3 window is selected from the image segment as given in Figure 2.6(b) with centre pixel as 29. Here Y min = 25, Y max = 29 and the difference between Y max and Y min is 4. As the difference is less than the chosen threshold, 30, the centre pixel Y i,j is detected as non-noisy (b) 3 3window (a) Segment of an image 2.3 Simulation Results Figure 2.6: Illustration of NAMF for Case IV To validate the efficacy of the proposed NAMF scheme, simulation has been carried out on MATLAB R2008a on standard images like Lena, Boat etc. along with other standard schemes such as SMF [7], PSMF [27], AMF [28], MMEM [29], DBA [30], IDBA [31], REBF [32], NIMF [33], and MDBUTMF [34]. Comparative analysis has been made with respect to both qualitative and quantitative measures. The threshold, T plays a major role in the performance of noise detection, which in turn has impact on the performance of the filter. 33

53 Chapter 2: New Adaptive Median Filtering Technique To select a threshold, we vary the threshold from 5 to 60 in a step of 5 for four different Lena noisy images. The PSNR (db) is computed by applying NAMF scheme in recovered images and plotted the threshold vs. PSNR (db) as shown in Figure 2.7. It may be observed that the optimum PSNR (db) is obtained in threshold value 30 in all the four noise cases. Hence, this value is used as threshold for all noisy images during simulation. Figure 2.7: PSNR(dB) vs. Threshold(T) of Lena image Results obtained through simulations are presented in the Table 2.1, Table 2.2, Table 2.3, and Table 2.4 for performance metrics PSNR (db), ISNR (db), SSIM, and IQI respectively. Performance of these filtering schemes has been studied by varying noise density 10% to 90%. The visual performance of NAMF scheme has been shown in Figure 2.8 for Lena and boat image at 70% noise case. Further, the visual comparative analysis at 30%, 60%, and 90% noise in Lena and Boat image are shown Figure 2.9 and Figure 2.10 respectively. For better readability, the comparative analyses of PSNR, ISNR, SSIM, and IQI with respect to noise densities (%) are shown in Figures for Boat image. It is in general observed from the results that the proposed scheme NAMF shows comparable performance with the existing schemes up to 20% noise density and shows improved performance between 30% -70% noise densities. The observations of PSNR(dB) obtained from different schemes for Lena image is summarized in Table 2.6 for better understanding. However, the performance of the scheme degrades severely as compared to existing schemes beyond 70% noise. 34

54 Development of Noise Removal Algorithms for Images Original image Noisy image (70%) Restored image using NAMF Original image Noisy image (70%) Restored image using NAMF Figure 2.8: Restored images of Lena and Boat images using NAMF scheme % of noise Table 2.1: Comparative analysis of PSNR (db) for various filters in Lena image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUT MF NAMF

55 Chapter 2: New Adaptive Median Filtering Technique % of noise Table 2.2: Comparative analysis of ISNR (db) for various filters in Lena image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUT MF NAMF % of noise Table 2.3: Comparative analysis of SSIM for various filters in Lena image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUT MF NAMF

56 Development of Noise Removal Algorithms for Images % of noise Table 2.4: Comparative analysis of IQI for various filters in Lena image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBU TMF NAMF % of noise Table 2. 5 : Comparative analysis of PSNR (db) for various filters in Boat image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBU TMF NAMF

57 Chapter 2: New Adaptive Median Filtering Technique Table 2.6 : Observations on the comparative analysis of PSNR(dB) in Lena image (of Table 2.1) % of noise PSNR(dB) value of NAMF is lower than: PSNR(dB) value of NAMF is almost equal with: PSNR(dB) value of NAMF is better than: 10 MDBUTMF SMF, PSMF, AMF, MMEM, DBA, IDBA, REBF, NIMF 20 MDBUTMF SMF, PSMF, AMF, MMEM, DBA, IDBA, REBF, NIMF 30 MDBUTMF SMF, PSMF, AMF, MMEM, DBA, IDBA, REBF, NIMF 40 REBF SMF, PSMF, AMF, MMEM, DBA,IDBA, NIMF, MDBUTMF 50 REBF SMF, PSMF, AMF, MMEM, DBA, IDBA, NIMF, MDBUTMF 60 REBF, NIMF SMF, PSMF, AMF, MMEM, DBA, IDBA, MDBUTMF 70 REBF, NIMF SMF, PSMF, AMF, MMEM, DBA, IDBA, MDBUTMF 80 REBF, NIMF SMF, PSMF, AMF, MMEM, DBA, IDBA, MDBUTMF 90 Performance of NAMF is degrading 38

58 Development of Noise Removal Algorithms for Images Original image 30% noise 60% noise 90% noise Filters SMF Restored Images From 30% From 60% From 90% Image Quality Map of Restored Images From 30% From 60% From 90% PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF NAMF Figure 2.9: Performance comparison of filters at different noise densities of Lena image. 39

59 Chapter 2: New Adaptive Median Filtering Technique Filters Original image 30% noise 60% noise 90% noise Restored Images From 30% From 60% From 90% Image Quality Map of Restored Images From 30% From 60% From 90% SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF NAMF Figure 2.10: Performance comparison of filters at different noise densities of Boat image. 40

60 Development of Noise Removal Algorithms for Images (a) (b) Figure 2.11: Comparative analysis of (a) PSNR(dB) and (b) ISNR(dB) at various noise densities of Boat image 41

61 Chapter 2: New Adaptive Median Filtering Technique (a) (b) Figure 2.12: Comparative analysis of (a) SSIM and (b) IQI at various noise densities of Boat image 42

62 Development of Noise Removal Algorithms for Images 2.4 Summary In this chapter, we have developed a new filtering technique and compared both visually as well as through quantitative parameters with the existing schemes. It is observed that, this scheme performs at par with some schemes at low noise densities, however, outperforms all of them between 40% - 70 % noise densities. But the scheme performs poorly beyond 70% noise in images. 43

63 Chapter 3: Dynamic Adaptive Median Filter Chapter 3 Dynamic Adaptive Median Filter (DAMF) for Removal of High Density Impulse Noise Standard Median Filter (SMF) is the most popular non-linear filter used to remove salt-andpepper noise due to its good denoising power and computational efficiency [67]. However, the major drawback of the SMF is that, the filter is effective only for low noise densities, and additionally, exhibits blurring if the window size is large and leads to insufficient noise suppression if the window size is small [41]. When the noise level is over 50%, the edge details of the original image will not be preserved by the median filter [39]. Nevertheless, it is important that during the filtering (restoration) process the edge details have to be preserved without losing the high frequency components of the image edges [13,41]. The ideal approach is to apply the filtering technique only to noisy pixels, without changing the uncorrupted pixel values. Non-linear filters such as Adaptive Median Filter (AMF), decision based or switching median filters [36,68,69,70] can be used for discriminating corrupted and uncorrupted pixels, and then apply the filtering technique. Noisy pixels will be replaced by the median value and uncorrupted pixels will be left unchanged. AMF performs well at low noise densities since the corrupted pixels which are replaced by the median values are very few. At higher noise densities, window size has to be increased to get better noise removal which will lead to less correlation between corrupted pixel values and replaced median pixel values. In decision-based or switching median filter the decision is based on a pre-defined threshold value. The major drawback of this method is that defining a robust decision measure is difficult. Also these filters will not take into account the local features as a result of which details and edges may not be recovered satisfactorily, especially when the noise level is high. Chan et al. [39] proposed an algorithm to overcome this problem, which consists of two stages. The first stage is to classify the corrupted and uncorrupted pixels by using AMF and in the second stage, regularization method is applied to the corrupted pixels to preserve edges and suppress noise. The drawback of this method is that for high impulse noise, it requires large window size of 39 39, and additionally requires complex circuitry for the implementation and determination of smoothing factor β to get good results [39]. Srinivasan and Ebenezer [66] proposed an algorithm in which the corrupted pixels are replaced by either the median pixel or neighborhood pixel by using a fixed window size of 3 3 resulting in lower processing time and good edge preservation. Although the recent technique [66] showed promising results, we discovered that a smooth transition between the pixels is lost leading to degradation in the visual quality of the image, since it only considers the left neighborhood from the last processed value. To overcome this problem we propose a new algorithm namely, Dynamic Adaptive Median Filter (DAMF) where corrupted pixels can either be replaced by the median pixel or with the 44

64 Development of Noise Removal Algorithms for Images mean of the neighborhood processed pixels which results in a smooth transition between the pixels with edge preservation and better visual quality. In addition, our proposed algorithm DAMFstarts with an initial window size of 3 3, resulting in lower processing time compared with AMF and other algorithms. It gives better Peak Signal-to- Noise Ratio (PSNR) and Structural Similarity (SSIM) index values compared to the algorithm proposed by Srinivasan and Ebenezer [66], AMF and other existing algorithms. DAMF replaces the corrupted test pixel with the median or mean of non-corrupted neighboring pixels selected from a window dynamically. If the number of non-corrupted pixels in the selected window is not sufficient, a window of next higher size is chosen. Thus, window size is automatically adapted based on the density of noise in the image as well as the density of corruption local to a window. As a result, window size may vary pixel to pixel while filtering. The scheme is simple to implement and does not require multiple iterations. The efficacy of the proposed scheme is evaluated with respect to subjective as well as objective parameters on standard images on various noise densities. Comparative analysis reveals that the proposed scheme has improved performance over other schemes, preferably in high density impulse noise cases. It has been observed that most of the schemes use a fixed size window for filtering of corrupted pixels. The size of window is larger in high density impulse noise and smaller in low density noise. But no scheme addresses a selection of a dynamic window for a test pixel based on the density of corruption in its neighbor pixels. In this chapter, we propose a Dynamic Adaptive Median Filter (DAMF) for removing high density salt-and-pepper noise. The filter is dynamic in nature as it decides the window size for the test pixel locally before filtering during run time and is adaptive due to the selection of a proper window size. The exhaustive simulation along with comparative analysis with the existing schemes in low as well as high density impulse noise shows the strength of the proposed scheme. The present chapter is organized as follows; Section 3.1 deals with the proposed scheme. In Section 3.2, the simulation results along with comparative analysis are discussed in detail. Finally, Section 3.3 deals with the summary of the chapter. 45

65 Chapter 3: Dynamic Adaptive Median Filter 3.1 Proposed Scheme The proposed scheme works on two stages. The first stage detects the noisy pixels in the image, the second stage repairs those noisy pixels by applying DAMF. The details of DAMF scheme is presented as Algorithm 3.1. If the center pixel of the selected 3 x 3 window is either 0 or 255 then it is considered to be noisy. If the total number of non-noisy neighbors is greater or equals to 3 then the test pixel is replaced with median of healthy neighbors. Otherwise, the size of window in increased to 5 5 and the process is repeated till the window size reaches to a predefined maximum window size. In this proposed scheme, a maximum window size is selected to be 15. The action of DAMF for the Removal of High Density Impulse Noise is presented as flow chart in Figure3.1. Algorithm 3.1: Dynamic Adaptive Median Filter (DAMF) Input : The noisy image Y Output: The filtered image Step 1. Initialize a sub-window size, W=3 and maximum window size, W max = 15. Step 2. Select a sub-window W W with center pixel. Step 3. If is not equal to 0 or 255, shift the window and go to Step 1 (noise free pixel). Step 4. Collect the set of pixels ( ) from the sub-window ignoring the pixel with 0 or 255. Step 5. If the size of, (i) Replace with median of pixels in. (ii) Shift the window (iii) Go to Step 1 Step 6. Set W=W+2, Step 7. If W W max, go to Step 2.. Else replace the center pixel by mean of the pixels in sub-window of size W max Step 8. Repeat Step 2 through Step 7 for all pixels in the image. 46

66 Development of Noise Removal Algorithms for Images Read an image(y) Initialize W s =3 and W max =15 Select a window of size W W with centre pixel X i,j A No If X i,j 0 or 255 Yes Collect the set of pixels (S) from the window by ignoring 0 or 255 Noise free pixel No If size S 3 Yes Increase the window size, W s W s + 2 X i,j Median(S) Yes If W s W max No Shift the window to next pixel A X i,j Mean(W max ) A Filtered pixel Shift the window to next pixel A Figure 3.1: Flow chart of DAMF algorithm 47

67 Chapter 3: Dynamic Adaptive Median Filter The working of DAMF scheme is explained in the Example 3.1considering four different cases. Each and every pixel of the image is checked for the presence of salt-and-pepper noise. Example 3.1: Consider an image segment as shown in Figure Case I Figure 3.2: An image segment for illustrating DAMF scheme If the processing pixel ij is non-noisy (i.e. 122) and all other pixel values lies between 0 s and 255 s as illustrated in Figure Figure 3.3 Illustration of DAMF for Case I A 3 3window as in Figure 3.3 is selected from the image segment. The centre pixel, = 122 which is noise free pixel. Now, shift the window to next pixel. 48

68 Development of Noise Removal Algorithms for Images Case II If the processing pixel ij is noisy (i.e. 0) and all other pixel values lies between 0 s and 255 s as illustrated in Figure Figure 3.4: Illustration of DAMF for Case II A 3 3 window as in Figure 3.4 is selected from the image segment. The centre pixel, = 0 which is a noisy pixel. After ignoring the pixel with 0 or 255, the cardinality of set S of pixels in the window,, which is greater than 3 (i.e. > 3). Now, the centre pixel ij is replaced by the median value 117. Now, shift the window to next pixel. Case III If the processing pixel is noisy pixel that is noisy (i.e. 255) and the other pixels are 0, 255 or values between 0 and 255 as is illustrated in Figure Figure 3.5: Illustration of DAMF for Case III A 3 3 window as in Figure 3.5 is selected from the image segment. The centre pixel, = 255 which is a noisy pixel. After ignoring the pixel with 0 or 255, the cardinality of set S of pixels in the window,, which is greater than 3 (i.e. > 3). Now, the centre pixel ij is replaced by the median value 123. Now, shift the window to next pixel. Case IV If the processing pixel is noisy pixel and the other pixels are 0 and255 is illustrated in Figure 3.6. A 3 3window as in Figure 3.6(a) is selected from the image segment. The centre pixel, = 0 which is a noisy pixel. After ignoring the pixel with 0 or 255, the cardinality of set S of pixels in the window, which is less than 3 (i.e. < 3). 49

69 Chapter 3: Dynamic Adaptive Median Filter As S less than, the window size W is increased by 2, i.e. W W+2, is shown in Figure 3.6(b). The set of pixels S is obtained from 5 5 window as * +. As S greater than, the centre pixel (= 0) is replaced by the median value 119. Now, shift the window to next pixel (a) (b) Figure 3.6: Illustration of DAMF for Case IV 3.2 Simulation Results and Discussion To validate the efficacy of the proposed DAMF scheme, simulation has been carried out on standard images like Lena, Boat etc. in MATLAB R2008a. The images are subjected to as low as 10% to as high as 90% noise densities. The proposed scheme along with the well performing schemes like SMF, AMF, PSMF, EDBA, IDBA, REBF, MDBUTMF are applied to the noisy images. The window size is made variable at various noise densities. Subjective as well as objective evaluations have been made for each restored images. Comparative analysis of DAMF scheme with the aforesaid schemes has been made. Tables gives the performance comparisons of MAE, PSNR, ISNR, SSIM, and IQI for Lena image at various noise density respectively. The set of evaluations are made with Boat image and depicted in Tables The plots for PSNR, MSE, MAE, ISNR, SSIM and IQI against noise densities are shown in Figures for Lena image and in Figures for Boat image.. The restored Lena images from different schemes are shown in Figure3.7 at 30%, 60% and 90% noise cases. The image quality maps of different schemes as well as proposed scheme of restored Lena image and Boat image are also shown in Figure 3.8 and Figure 3.9 respectively. Brighter image quality map (IQI 1) indicates that the restored image is closer to the original image, and darker image quality map indicates that the restored image is more distant from the original image. By analyzing the different parameters, it is observed that the proposed scheme shows a superior restoration performance as compared to its competent schemes. Hence, in general the proposed scheme has a better say in combating high density impulse noise. 50

70 Development of Noise Removal Algorithms for Images % of Noise Table 3.1: Comparative analysis of MAE for various filters in Lena image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUT MF DAMF % of Noise Table 3.2: Comparative analysis of PSNR(dB) for various filters in Lena image SMF PSMF AMF MME M Filters DBA IDBA REBF NIMF MDBU TMF DAMF

71 Chapter 3: Dynamic Adaptive Median Filter % of Noise Table 3.3: Comparative analysis of ISNR(dB) for various filters in Lena image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBU TMF DAMF % of Noise Table 3.4: Comparative analysis of SSIM for various filters in Lena image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBU TMF DAMF

72 Development of Noise Removal Algorithms for Images % of Noise Table 3.5: Comparative analysis of IQI for various filters in Lena image SMF PSMF AMF MME M Filters DBA IDBA REBF NIMF MDBU TMF DAMF % of Noise Table 3.6: Comparative analysis of MAE for various filters in Boat image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MBD UTMF DAMF

73 Chapter 3: Dynamic Adaptive Median Filter % of Nois e Table 3.7: Comparative analysis of PSNR(dB) for various filters in Boat image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MBDU TMF DAMF % Noise Table 3.8: Comparative analysis of ISNR(dB) for various filters in Boat image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MBDU TMF DAMF

74 Development of Noise Removal Algorithms for Images % of Noise Table 3.9: Comparative analysis of SSIM for various filters in Boat image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MBDU TMF DAMF % of Noise Table 3.10: Comparative Analysis of IQI For Various Filters In Boat Image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MBDU TMF DAMF

75 Chapter 3: Dynamic Adaptive Median Filter Original Image(a) (a 1 ) Noisy Image (30%) of (a) Recovered of (a 1 ) by SMF Recovered of (a 1 ) by PSMF Recovered of (a 1 ) by AMF Recovered of (a 1 ) by MMEM Recovered of (a 1 ) by DBA Recovered of (a 1 ) by IDBA Recovered of (a 1 ) by REBF Recovered of (a 1 ) by NIMF Recovered of (a 1 ) by MDBUTMF Recovered of (a 1 ) by DAMF Original Image(b) (b 1 ) Noisy Image (60%) of (b) Recovered of (b 1 ) by SMF Recovered of (b 1 ) by AMF Recovered of (b 1 ) by PSMF Recovered of (b 1 ) by MMEM Recovered of (b 1 ) by DBA Recovered of (b 1 ) by IDBA Recovered of (b 1 ) by REBF Recovered of (b 1 ) by NIMF Recovered of (b 1 ) by MDBUTMF Recovered of (b 1 ) by DAMF Original Image(c) (c 1 ) Noisy Image (90%) of (c) Recovered of (c 1 ) by SMF Recovered of (c 1 ) by AMF Recovered of (c 1 ) by PSMF Recovered of (c 1 ) by MMEM Recovered of (c 1 ) by DBA Recovered of (c 1 ) by IDBA Recovered of (c 1 ) by REBF Recovered of (c 1 ) by NIMF Recovered of (c 1 ) by MDBUTMF Recovered of (c 1 ) by DAMF Figure 3.7: Restored Lena images of various filters corrupted by 30%, 60% and 90% noise density 56

76 Development of Noise Removal Algorithms for Images (i) Original image (ii) 30% (iii) 60% (iv) 90% Filters Restored Images From 30% From 60% From 90% Image Quality Map of Restored Images From30% From60% From90% SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF DAMF Figure 3.8: Comparative analysis of restored images and image quality map at various noise densities of Lena image. 57

77 Chapter 3: Dynamic Adaptive Median Filter (i) Original image (ii) 30% (iii) 60% (iv) 90% Filters Restored Images From 30% From 60% From 90% Image Quality Map of Restored Images From30% From60% From90% SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF DAMF Figure 3.9: Comparative analysis of restored images and image quality map at various noise densities of Boat image. 58

78 Development of Noise Removal Algorithms for Images (a) (b) Figure 3.10: Comparative analysis of (a) PSNR and (b) MSE at various noise densities of Lena image 59

79 Chapter 3: Dynamic Adaptive Median Filter (a) (b) Figure 3.11: Comparative analysis of (a) MAE and (b) ISNR at various noise densities of Lena image 60

80 Development of Noise Removal Algorithms for Images (a) (b) Figure 3.12: Comparative analysis of (a) SSIM and (b) IQI at various noise densities of Lena image 61

81 Chapter 3: Dynamic Adaptive Median Filter (a) (b) Figure 3.13: Comparative analysis of (a) PSNR and (b) MSE at various noise densities of Boat image. 62

82 Development of Noise Removal Algorithms for Images (a) (b) Figure 3.14: Comparative analysis of (a) MAE and (b) ISNR at various noise densities of Boat image. 63

83 Chapter 3: Dynamic Adaptive Median Filter (a) (b) Figure 3.15: Comparative analysis of (a) SSIM and (b) IQI at various noise densities of Boat image. 64

84 Development of Noise Removal Algorithms for Images 3.3 Summary In this chapter, we propose a dynamic adaptive filtering scheme, namely, DAMF to recover images corrupted with high density salt-and-pepper noise. The performance of the algorithm has been tested at low, medium and high noise densities on different gray-scale images. The filter works in two phases, namely, identification of corrupted locations followed by the filtering operation. The window size for any test pixel is selected dynamically utilizing the local information from its neighbors. Subsequently, it applies the median filter considering only the window of the non-corrupted neighbors. The proposed scheme is evaluated both qualitatively as well as quantitatively. The comparative performance analysis in general shows that the proposed scheme outperforms the existing schemes both in terms of noise reduction and retention of images details at high densities impulse noise. 65

85 Chapter 4: Fuzzy Based Adaptive Mean Filtering Technique Chapter 4 Fuzzy Based Adaptive Mean Filtering Technique for Removal of Impulse Noise Salt-and-pepper noise is a special case of impulse noise, where a certain percentage of individual pixels in digital image are randomly digitized into two extreme intensities i.e. minimum (0) and the maximum (255) for 8-bit image. The contamination of digital image by salt-and-pepper noise is largely caused by error in image acquisition and/or recording. For example, faulty memory locations or impaired pixel sensors can result in digital image being corrupted with salt-and-pepper noise [78,79]. Emergent techniques based on fuzzy logic have been successfully used to design nonlinear filters. A variety of methods have been recently proposed in the literature which are able to perform detail-preserving smoothing of noisy image data yielding better results than classical operators[82, 85, 86, 87]. Fuzzy techniques for image processing applications are most commonly used in high-level computer vision and pattern recognition [71, 77]. In this chapter we propose a fuzzy based adaptive mean filtering (FBAMF) scheme which is a non-recursive filter that works on two stages. The first stage deals with noise detection followed by the application of adaptive mean filtering to remove the salt and pepper noise. This chapter is organized as follows. Section 4.1 explained the preliminaries of fuzzy logic. Section 4.2 presents the proposed method. Section 4.3 discusses the simulation and results. Finally, Section 4.4 deals with summary of the chapter. 4.1 Preliminaries on Fuzzy Logic The basic assumption upon which classical logic (or two-valued logic) is based on, that every proposition is either true or false. As a consequence of the Heisenberg principle of uncertainty, it is known that truth values of certain propositions in quantum mechanics are inherently indeterminate due to fundamental limitations of measurement. In order to deal with such proposition, the classical two-valued logic is extended to three-valued logic. Then, it extended to n-valued logic. The set of truth values of an n-valued logic thus defined as, { ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) } ( ) These values can be interpreted as degrees of truth. There are two main characteristics of fuzzy systems that give them better performance for specific applications: 66

86 Development of Noise Removal Algorithms for Images (i) Fuzzy systems are suitable for uncertainty or approximate reasoning, especially for a system with a mathematical model that is difficult to derive. (ii) Fuzzy logic allows decision making with estimated values under incomplete or uncertain information. A fuzzy system is represented by fuzzy variables that are members of a fuzzy set. A fuzzy set is a generalization of a classical set based on the concept of partial membership [82]. Let be a fuzzy set defined on universe of discourse U. The fuzzy set is described by the Membership ( Function (MF) ) that maps x to the real interval [0,1] i.e. the membership varying from 0 to 1: a membership of value 0 signifying the fact that the element does not belong to the set ; a membership of value 1 signifying that the element belongs to the set with full certainty; a membership of any other value from 0 to 1 representing the element to be a partial member of theset. Mathematically [71,72, 82, 83], ( ) {. / } ( ) Fuzzy sets are identified by linguistic labels e.g. low, medium, high, very high, tall, very tall, cool, hot, very hot, etc. The knowledge of a human expert can very well be implemented, in an engineering system, by using fuzzy rules. The membership functions in fuzzy set theory broadly classify into two types i.e.one input MFs (or 1-dimentional MFs) and two input MFs (or 2-dimentional MFs) where each in a different universe of discourse [82, 83]. There are different types of membership functions available in fuzzy set theory, these are, Triangular MFs, Trapezoidal MFs, Bell shaped MFs, Γ-function MFs, L-function MFs, Zadeh s MFs, Π-function MFs, Hyperbolic MFs, Gaussian MFS, Convex and Non-convex MFs. In our scheme we have used Γ-function with increasing MFs with straight line are called Γ-functions, because the similarity of the functions with this character. The function, - has two parameters defined as, ( ) ( ) ( ) { ( ) The membership function for the Γ-function is shown in Figure

87 Chapter 4: Fuzzy Based Adaptive Mean Filtering Technique µ 1 0 T 1 T 2 x Figure 4.1: An example of Γ-function MFs 5 Fuzzy logic has been applied in different areas of research and image filters not the exceptions. Many researchers have proposed for suppressing various types of noises [73, 74, 75, 76, 80, 85, 86, 87]. Simple fuzzy moving average (FMAV) [79] filters is one such scheme that uses triangular membership function. It is observed that, most of the schemes uses (i) smaller window(3 3) at low density noise and larger window at high density impulse noise and (ii) median filtering for uncorrupted pixels in a window. But, in the real time environment, the percentage of noise density is not known apriori as the knowledge of original image is not available. Hence, choosing a fixed size window in real time is an unrealistic assumption. Further, even at high density noise, choosing a larger size window for a pixel for which its smaller window contains sufficient uncorrupted pixel with lead to distortion in restored images. To achieve these objectives, in this chapter, we have proposed a Fuzzy Based Adaptive Mean Filtering (FBAMF) scheme. Even though the detection of corrupted pixel is based on [81], the filter selects a window size adaptively based on the window corruption characteristics. Further, at higher noise density average filter performs better than the median filter [15], we apply average filter for corrupted pixels. The window size is allowed to grow maximum size (15 15) to reduce the distortion and computational complexity. Comparative analysis shows the superiority over the reported scheme. 4.2 Proposed Method The proposed scheme FBAMF is a non-recursive filter that works on two stages. The first stage deals with noise detection followed by the application of adaptive mean filtering to restore the corrupted pixel. The proposed filtering scheme is applied to the noisy pixels whereas the noise-free pixels retained their original value. The detection and filtering schemes are discussed below in detail. 68

88 Development of Noise Removal Algorithms for Images A. Fuzzy noise measure of pixels in the test window The fuzzy set used for noise detection is shown in Figure 4.2. Figure 4.2: Fuzzy set used for noise detection The role of fuzzy noise detection is to generate a fuzzy flag map which gives each pixel a fuzzy flag indicating how much it like an impulse pixel. If the centre (test) pixel in a (3 3) window is either 0 or 255 it is considered to be noisy. The maximum value of the difference measure for each pixel in the selected window based on the current pixel can be calculated as follows: { } ( ) The membership function of the fuzzy set used here indicates that how much the test pixel is corrupted. The is used as the fuzzy input variable and the two predefined thresholds T 1 =15 and T 2 =25 are defined beforehand (Figure-4.2). This fuzzy measure is further utilised during the filtering operation. B. Adaptive Mean Filtering Once the noise measure for each pixel is determined apply the linear combination between the current pixel and the mean of the non-noisy neighbours of the current window to restore the detected noisy pixel. If the selected window contains all the elements as noisy, the size of window in increased to next window size and the process is repeated till the window size reaches to a predefined maximum window size. The overall FBAMF steps followed are shown in Algorithm 4.1 and its flow chart is shown in Figure

89 Chapter 4: Fuzzy Based Adaptive Mean Filtering Technique Algorithm 4.1: Fuzzy Based Adaptive Mean Filter (FBAMF) Input :The noisy image Y Output: The filtered image Step 1: Initialize a sub-window size, W s =3 and maximum window size, W max =15 Step 2: Select a sub-window W s W s with center pixel X i,j and defined as s { i r, j s r, s.-, /} Step 3: If ( X ij 0 or 255 ) then pixel value is left unchanged and go to Step 7. Step 4: Collect all the pixels in W s as; { ij ij ij *, +} Step 5: If cardinality of set S, S > 0, then (i) Calculate { } (ii) Calculate fuzzy measure of corruption at as [ (iii) Replace the center pixel as, =( ) where, = mean of S. Go to Step 7. Step 6: W s W s + 2, If W s max, go to Step 2. Else replace the center pixel by mean of the pixels in sub-window of size W max. Step 7: Shift the window left to right and top to bottom till all the pixels are considered and repeat Steps 1 through 7. 70

90 Development of Noise Removal Algorithms for Images Read the image(y) Initialize W s =3 and W max =15 Select a window of size W s W s with centre pixel X i,j A B No If X i,j? or Yes Collect the set of pixels (S) from the window by ignoring 0 and 255 Noise free pixel No Is size (S )> 0? Yes Increase the window size, W s W s +2 Find { s s }, fuzzy measure ( f ij ) of corruption at x ij as M ij T 1 T 2 T 1 Replace the center pixel j ( - j )* j j* j where, m ij is the mean of S Yes Is s ze (W s )? No Yes All the pixels are processed? No B X i,j Mean( max) Filtered pixel Shift the window to next pixel row wise and then column wise A Shift the window to next pixel Stop A Figure 4.3: Flow chart of FBAMF algorithm 71

91 Chapter 4: Fuzzy Based Adaptive Mean Filtering Technique For completeness, the working principles of FBAMF are illustrated below through an example. Five different cases are considered to demonstrate different conditions along with action taken during filtering process. The value of T 1 and T 2 are chosen to be 15 and 25 respectively through experimentation (a) 3 3 window (b) 3 3 window (e)3 3 and 5 5 window (d)3 3 window (c) 3 3 window Figure 4.4: Illustration of FBAMF 72

92 Development of Noise Removal Algorithms for Images Case I Consider the segment of an image Figure 4.4 and a 3 3 window is selected from the image segment as given in Figure 4.4(a) with centre pixel as 141, which is not equal to 0 or 255. It is not a noisy pixel. So no filtering operation is performed. Case II Consider the segment of an image Figure 4.4 and a 3 3 window is selected from the image segment as given in Figure 4.4(b) with centre pixel as 255 which is a noisy one. After collecting the set of all pixels (S) except the pixel of value 0 or 255, the S =8. Since S >0, then j is calculated as j { j -s j s j } = 120. It is passed through the fuzzy membership and found out to be 1. The filtered value =( - j )* j j* j Case III Consider the segment of an image Figure 4.4 and a 3 3 window is selected from the image segment as given in Figure 4.4(c) with centre pixel as 0, which is a noisy one. In the similar manner j and are determined to be 236 and 1 respectively. The filtered value is obtained as =( ) = (1-1) = , which is replaced by centre pixel. Case IV Consider the segment of an image Figure 4.4 and a 3 3 window is selected from the image segment as given in Figure 4.4(d) with centre pixel as 0, which is a noisy one. The value of j and are as usual computed and found out to be 21 and 0.6 respectively. Subsequently, the filtered value for the centre pixel is 12. Case V Consider the segment of an image Figure 4.4 and a 3 3 window is selected from the image segment as given in Figure 4.4(e) with centre pixel as 0, which is a noisy one. After collecting the set of all pixels (S) except the pixel of value 0 or 255 is S = 0. Hence the window size increased to 5 x 5. The process is repeated with the new window and S becomes = 10. Proceeding in the same way we get the filtered value for the test pixel to be

93 Chapter 4: Fuzzy Based Adaptive Mean Filtering Technique 4.3 Simulation Results To validate the proposed FBAMF, simulation has been performed on standard images, like Lena, Boat of size The images are subjected to as low as 10% noise density to as high as 95% noise density. The proposed scheme as well as the recently suggested few well performing schemes like SMF [7], PSMF [27], AMF [28], MMEM [29], DBA [30], IDBA [31], REBF [32], NIMF [33], and MDBUTMF [34] are applied to the noisy images. The simulation is carried out using MATLAB R2008a. There are basically two classes of metrics as discussed in Chapter 1(Section 1.2) through which performance measures and quality of restored images are evaluated to show the efficacy of the proposed scheme as compared to other standard and recently proposed schemes. The performance measures discussed above are used to prove the superiority of the proposed method. The performance parameter values such as MAE, PSNR, ISNR, SSIM and IQI obtained after applying the various filters are compared by varying the noise density from 10% to 90% are shown in Table for Lena image and Table for Boat image respectively. From the quantitative values shown in the tables, it is observed that FBAMF algorithm outperforms all other noise removal schemes. The MAE, MSE, PSNR, ISNR, and IQI of the restored images obtained from different existing scheme mentioned above simulated along with the proposed method are plotted in Figures for Lena image and Figure for Boat image respectively.the restored Lena images of various filters at 30%, 60% and 90% noise density are shown in Figure 4.5. It has been observed that the proposed scheme at low as well as high noise density is superior to all other scheme. In addition to the IQI value & the image quality map of the restored image has also been generated to evaluate the performance of the filters applied on noisy images of 30%, 60% and 90% noise density as shown in Figure 4.6 for Lena image and Figure 4.7 for Boat images respectively. Brighter image quality map (IQI 1) indicates that the restored image is closer to the original image, and darker image quality map indicates that the restored image is more distant from the original image. It may be observed that the image quality map of the proposed method is brighter as compared to other for low as well as high density salt-and-pepper noise. 74

94 Development of Noise Removal Algorithms for Images Table 4.1: Comparative analysis of MAE for various filters in Lena image Filters % of MDBU FBAM Noise SMF PSMF AMF MMEM DBA IDBA REBF NIMF TMF F Table 4.2: Comparative analysis of PSNR(dB)for various filters in Lena image Filters % of MDBU Noise SMF PSMF AMF MMEM DBA IDBA REBF NIMF FBAMF TMF

95 Chapter 4: Fuzzy Based Adaptive Mean Filtering Technique Table 4.3: Comparative analysis of ISNR(dB) for various filters in Lena image % of Noise Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBU TMF FBAMF Table 4.4: Comparative analysis of SSIM for various filters in Lena image % of Filters Noise SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBU TMF FBAMF

96 Development of Noise Removal Algorithms for Images Table 4.5: Comparative analysis of IQI for various filters in Lena image % of Filters Nois MDBU SMF PSMF AMF MMEM DBA IDBA REBF NIMF e TMF FBAMF Table 4.6: Comparative analysis of MAE for various filters in Boat image % of Filters Noise SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUT MF FBAMF

97 Chapter 4: Fuzzy Based Adaptive Mean Filtering Technique Table 4.7: Comparative analysis of PSNR(dB) for various filters in Boat image % of Filters Noise SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBU TMF FBAMF Table 4.8: Comparative analysis of ISNR(dB) for various filters in Boat image % of Filters Noise SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBU TMF FBAMF

98 Development of Noise Removal Algorithms for Images Table 4.9: Comparative analysis of SSIM for various filters in Boat image % of Noise Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBU TMF FBAMF % of Noise Table 4.10: Comparative analysis of IQI for various filters in Boat image SMF PSMF AMF MME M Filters DBA IDBA REBF NIMF MDBU TMF FBAMF

99 Chapter 4: Fuzzy Based Adaptive Mean Filtering Technique Original Image(a) (a1) Noisy Image (30%) of (a) Recovered of (a1) by SMF Recovered of (a1)by PSMF Recovered of (a1) by AMF Recovered of (a1) by MMEM Recovered of (a1) by DBA Recovered of (a1) by IDBA Recovered of (a1) by REBF Recovered of (a1) by NIMF Recovered of (a1) by MTBUTMF Recovered of (a1) by FBAMF Original Image(b) (b1) Noisy Image (60%) of (b) Recovered of (b1) by SMF Recovered of (b1) by AMF Recovered of (b1) by PSMF Recovered of (b1) by MMEM Recovered of (b1) by DBA Recovered of (b1) by IDBA Recovered of (b1) by REBF Recovered of (b1)bynimf Recovered of (b1)by MTBUTMF Recovered of (b1) by FBAMF Original Image(c) (c1) Noisy Image (90%) of (c) Recovered of (c1) by SMF Recovered of (c1) by AMF Recovered of (c1) by PSMF Recovered of (c1) bymmem Recovered of (c1) by DBA Recovered of (c1) by IDBA Recovered of (c1) by REBF Recovered of (c1) by NIMF Recovered of(c1) by MTBUTMF Recovered of (c1) by FBAMF Figure 4.5: Restored Lena images of various filters 80

100 Development of Noise Removal Algorithms for Images Filters (i) Original image (ii) 30% (iii) 60% (iv) 90% Restored Images Image Quality Map of (v) Restored Images From 30% From 60% From 90% From30% From60% From90% SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF FBAMF Figure 4.6: Performance comparison of filters at different noise densities of Lena Image 81

101 Chapter 4: Fuzzy Based Adaptive Mean Filtering Technique (i) Original image (ii) 30% (iii) 60% (iv) 90% Filters Restored Images From 30% From 60% From 90% Image Quality Map of Restored Images From30% From60% From90% SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF FBAMF Figure 4.7: Performance comparison of filters at different noise densities of Boat image 82

102 Development of Noise Removal Algorithms for Images (a) (b) Figure 4.8: Comparative analysis of (a) PSNR and (b) MSE at various noise densities of Lena image 83

103 Chapter 4: Fuzzy Based Adaptive Mean Filtering Technique (a) (b) Figure 4.9: Comparative analysis of (a) MAE and (b) ISNR at various noise densities of Lena image 84

104 Development of Noise Removal Algorithms for Images (a) Figure 4.10: Comparative analysis of (a) SSIM and (b) IQI at various noise densities of Lena image (b) 85

105 Chapter 4: Fuzzy Based Adaptive Mean Filtering Technique (a) Figure 4.11: Comparative analysis of (a) PSNR and (b) MSE at various noise densities of Boat image (b) 86

106 Development of Noise Removal Algorithms for Images (a) (b) Figure 4.12: Comparative analysis of (a) MAE and (b) ISNR at various noise densities of Boat image 87

107 Chapter 4: Fuzzy Based Adaptive Mean Filtering Technique (a) (b) Figure 4.13: Comparative analysis of (a) SSIM and (b) IQI at various noise densities of Boat image. 88

108 Development of Noise Removal Algorithms for Images 4.4 ummary In this chapter, we propose a fuzzy based adaptive mean filtering scheme, namely, FBAMF to recover images corrupted with high density salt-and-pepper noise. The filter works in two phases, namely, identification of corrupted locations followed by the filtering operation. The identification of noisy pixels from a selected window is made based on a fuzzy decision. The window size for any test pixel is selected adaptively utilizing the local information from its neighbours. Subsequently, it applies the mean filter considering only the non-corrupted neighbours in the window. The linear combination of the center pixel and the mean value is used to replace the noisy pixel value. The performance of the algorithm has been tested at low, medium and high noise densities on different standard grey scale images.the proposed scheme is evaluated both qualitatively as well as quantitatively. The comparative performance analysis in general shows that the proposed scheme outperforms the existing schemes both in terms of noise reduction and retention of images details at high densities impulse noise. 89

109 Chapter 5: An Efficient Adaptive Mean Filtering Technique Chapter 5 An Efficient Adaptive Mean Filtering Technique for Removal of Salt and Pepper Noise from Images Mean filtering is a simple, intuitive, and easy to implement method of smoothing images, i.e. reducing the amount of intensity variation between one pixel and the next. Mean filtering is most commonly used as a simple method for reducing noise in an image. There are different types of mean filtering techniques already have been proposed [1, 7, 81, 84]. The idea of mean filtering is simple to replace each pixel value in an image with the mean (average) value of its neighbors, including itself [1, 7]. This has the effect of eliminating pixel values which are unrepresentative of their surroundings. Mean filtering is usually thought of as a convolution filter. Like other convolutions it is based around a kernel, which represents the shape and size of the neighborhood to be sampled when calculating the mean. Often a 3 3 square kernel is used, as shown in Figure 5.1, although larger kernels (e.g. 5 5 squares) can be used for more severe smoothing. (Note that a small kernel can be applied more than once in order to produce a similar but not identical effect as a single pass with a large kernel). An example of mean filtering is shown Figure Figure 5.1: A window of size 3 3 square kernel Unfiltered values Mean filtered Figure 5.2: Illustration of Mean filtering scheme 90

110 Development of Noise Removal Algorithms for Images There are two main problems with mean filtering, namely, A single pixel with a very unrepresentative value can significantly affect the mean value of all the pixels in its neighborhood. When the filter neighborhood straddles an edge, the filter will interpolate new values for pixels on the edge and so will blur that edge. This may be a problem if sharp edges are required in the output. Most of the literature uses median filter for removing salt and pepper noise from digital images. However, we have proposed an efficient adaptive mean filtering (EAMF) scheme in this chapter that uses mean value of a dynamic window size for filtering of high density noisy images without blurring. This filter replaces the noisy pixels with the mean value of nonnoisy neighbouring pixels selected from a window dynamically. If the number of non-noisy pixels in the selected window is not sufficient, a window of next higher size is chosen. Thus window size is automatically adapted based on the density of noise in the image as well as the density of corruption local to a window. As a result window size may vary pixel to pixel while filtering. The efficacy of the proposed scheme is evaluated with respect to subjective as well as objective parameters on standard images on various noise densities. Comparative studies proves that the proposed method removes the salt and pepper noise effectively with better image quality compared with conventional methods and recently proposed methods. The visual and quantitative results show that the performance of the proposed filter in the preservation of edges and details is better even at noise level as high as 90%. The present chapter is organized as follows. Section 5.1 presents the proposed method. Section 5.2 discusses the simulation and results, and finally, the Section 5.3 briefs the summary of the chapter. 5.1 Proposed Method The proposed EAMF is an adaptive non-recursive mean filter removes impulse noise even for higher noise densities without much blurring and retains the edges and fine details. It contains a simple noise detection stage at the beginning of the filtering operation by inspecting the pixel value. If it is lies within the minimum (0) and maximum (255) gray level value, it is considered as a noise free pixel and kept unaltered. If the pixel matches with any of the minimum or maximum value, it is considered as a noisy pixel and processed by the proposed filtering method. The filtering stage starts with a (3 x 3) window which is applied on the noisy pixel only. Once a pixel identified as noisy then the mean of the non-noisy neighbours of the current window is used to restore the detected noisy pixel. If the selected window contains all the elements as noisy, the size of window is increased to (5 x 5) and the process is repeated till the window size reaches to a predefined maximum window size. The algorithm automatically chooses the optimal window size. The maximum window size is not allowed to exceed (13 13). The EAMF scheme is computationally efficient and preserves the 91

111 Chapter 5: An Efficient Adaptive Mean Filtering Technique edge details in the case of high-density impulse. The detail steps followed in EAMF is listed in Algorithm 5.1 followed by a flow chart in Figure 5.3. Algorithm 5.1 : Efficient Adaptive Mean Filter (EAMF ) Input : Output: The noisy image Y The filtered image Step 1. Initialize a sub-window size, W=3 and maximum window size, W max =13 Step 2. Select a sub-window W W with center pixel. Step 3. If is not equal to 0 or 255, shift the window and go to Step 1 Step 4. Collect the set of pixels (S) from the sub-window ignoring the pixels of intensity value 0 or 255. Step 5. If the cardinality of set S, S 1, do. (i) Replace with mean of pixels in S. (ii) Shift the window (iii) Go to Step -1 Else go to step -6 Step 6. W=W+2; Step 7. If W W max, go to Step 2, else replace the center pixel by mean of all the pixels in the sub-window of size W max Step 8. Repeat Step 2 through Step 7 for all pixels in the image. 92

112 Development of Noise Removal Algorithms for Images Read noisy image X, Initialize W=3 and W max =13 Select a window of size W W with centre pixel X i,j A No If X i,j 0 or 255 Yes Collect the set of pixels (S) from the window by ignoring 0 and 255 Noise free pixel No Increase the window size, W W+2 If size S 1? Yes X i,j Mean(S) Yes Are all the pixels are processed? No Yes If W W max No Shift the window to next pixel A X i,j Mean(W max ) Stop A Filtered pixel Shift the window to next pixel A Figure 5.3: Flow chart of EAMF algorithm 93

113 Chapter 5: An Efficient Adaptive Mean Filtering Technique 5.2 Simulation Results To validate the proposed scheme EAMFT, simulation has been performed on standard images. The images are subjected to as low as 10% noise density to as high as 90% noise density. The proposed scheme as well as the recently suggested few well performing schemes like SMF [7], PSMF [27], AMF [28], MMEM [29], DBA [30], IDBA [31], REBF [32], NIMF [33], and MDBUTMF [34]are applied to the noisy images. The simulation is carried out using MATLAB R2008a. Performance comparisons have been made both through visual results and objective parameters. PSNR, ISNR, SSIM, and IQI parameter comparisons are shown in Tables for Lena, and Tables for Boat image respectively. In addition to the IQI, the image quality maps of restored images of Lena and Boat have also been generated to evaluate the performance of the different algorithms. The restored images and its corresponding image quality maps at noise level 30%, 60% and 90% are shown in Figures 5.4 and 5.5 for Lena and Boat image respectively. Figures 5.6 and 5.7 depicts the graphical comparisons of various parameters of Boat image. From the simulations results, it is in general observed that EAMF algorithm outperforms all other noise removal filters in low as well as high density impulse noise. 94

114 Development of Noise Removal Algorithms for Images Table 5.1: Comparative analysis of PSNR (db) for various filters in Lena image % of Noise SMF PSMF AMF MME M Filters DBA IDBA REBF NIMF MDBU TMF EAMF Table 5.2: Comparative analysis of ISNR(dB) for various filters in Lena image % of Noise SMF PSMF AMF MME M Filters DBA IDBA REBF NIMF MDBU TMF EAMF

115 Chapter 5: An Efficient Adaptive Mean Filtering Technique % of Noise Table 5.3: Comparative analysis of SSIM for various filters in Lena image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBU TMF EAMF % of Noise Table 5.4: Comparative analysis of IQI for various filters in Lena image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBU TMF EAMF

116 Development of Noise Removal Algorithms for Images % of Noise Table 5.5: Comparative analysis of PSNR(dB) for various filters in Boat image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MBDU TMF EAMF % of Noise Table 5.6: Comparative analysis of ISNR(dB) for various filters in Boat image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MBDU TMF EAMF

117 Chapter 5: An Efficient Adaptive Mean Filtering Technique % of Noise Table 5.7: Comparative analysis of SSIM for various filters in Boat image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MBDU TMF EAMF % of Noise Table 5.8: Comparative analysis of IQI for various filters in Boat image Filters SMF PSMF AMF MMEM DBA IDBA REBF NIMF MBDU TMF EAMF

118 Development of Noise Removal Algorithms for Images Filters (i) Original image (ii) 30% (iii) 60% (iv) 90% Restored Images Image Quality Map of Restored Images From 30% From 60% From 90% From 30% From 60% From 90% SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF EAMF Figure 5.4: Performance comparison of filters at different noise densities of Lena image 99

119 Chapter 5: An Efficient Adaptive Mean Filtering Technique Filters (i) Original image (ii) 30% (iii) 60% (iv) 90% Restored Images Image Quality Map of Restored Images From 30% From 60% From 90% From 30% From 60% From 90% SMF PSMF AMF MMEM DBA IDBA REBF NIMF MDBUTMF EAMF Figure 5.5: Performance comparison of filters at different noise densities of Boat image 100

120 Development of Noise Removal Algorithms for Images (a) (b) Figure 5.6: Comparative analysis of (a) PSNR(dB) and (b) ISNR at various noise densities of Boat image 101

121 Chapter 5: An Efficient Adaptive Mean Filtering Technique (a) Figure 5.7: Comparative analysis of (a) SSIM and (b) IQI at various noise densities of Boat image (b) 102

122 Development of Noise Removal Algorithms for Images 5.3 Summary In this chapter, we propose a mean filtering scheme, namely, EAMFT to recover images corrupted with high density salt and pepper noise. The filter works in two phases, namely, identification of corrupted locations followed by the filtering operation. The window size for any test pixel is selected adaptively utilizing the local information from its neighbours. Subsequently, it applies the mean filter considering only the non-corrupted neighbours in the window. The linear combination of the centre pixel and the mean value is used to replace the noisy pixel value. The performance of the algorithm has been tested at low, medium and high noise densities on different standard grey scale images. The proposed scheme is evaluated both qualitatively as well as quantitatively. The comparative performance analysis in general shows that the proposed scheme outperforms the existing schemes both in terms of noise reduction and retention of images details at high densities impulse noise. 103

123 Development of Noise Removal Algorithms for Images Chapter 6 Neural Network based Random Valued Impulsive Noise Suppression Scheme Automatic recognition, classification, and grouping of patterns into meaningful categories helps in critical decision making [88, 89, 90, 91]. One such classification problem is counting impulsive noise in images. This has been widely studied by the researchers and a great amount of literature is also available. These schemes generally used a threshold value or a set of values for the segregation of noisy pattern. The accuracy of noise detection mostly depends on these thresholds. If a predefined parameter of a test pixel exceeds the threshold value, it is termed as noisy. On the contrary, the solution to image restoration problems depends very much on the type of image, characteristic of noise and its density[7]. Most of the reported schemes work very well under salt & pepper noise (SPN), whereas under random valued impulse noise (RVIN) their performance is quite miserable. Figure 6.1 shows how an image corrupted by RVIN is different from an image corrupted by salt and pepper noise. It is clearly observed that in salt and pepper noise the pixels of the original image are replaced by a value 0 or 255, whereas in RVIN the corrupted pixels can have any value in the available dynamic range, i.e. in between 0 and 255 for 8-bit images. Hence, there cannot be one threshold value, which will serve like a panacea to all adverse situations. The selection of the line to separate the noisy and noise-free pixels needs to be chosen carefully. Preferably, the selection process should dynamically adapt to its environment and produce an optimal value. The artificial neural network has been used to classify noises in images [57, 102, 103]. In this chapter, we propose a neural network detection based filter (NNDF) to combat RVIN in images. The NNDF scheme aims at efficient classification of pixels as noisy or noise free. The input parameters, to the neural network are derived from two different statistical parameters namely, robust outlyingness ratio (ROR) and similarity measure (S). Subsequently, the identified noisy pixels are filtered with a median filter. [22] The overall chapter is organized as follows. Section 6.1 deals with the related works on RVIN schemes. Section 6.2 explains the computation of robust outlyingness ratio (ROR) and similarity measure (S). Section 6.3 presents the proposed scheme. Section 6.4 discusses the simulation and results. Finally, Section 6.5 deals with summary of the chapter. 104

124 Chapter 6: Neural Network based Random Valued Impulsive Noise Suppression Scheme Original Lena image Noisy Lena image by 20% SPN Noisy Lena image by 20% RVIN Figure 6.1: Original and noisy Lena image with SPN and RVIN 6.1 Related works A novel adaptive impulse detection using center-weighted median filter (ACWMF) [92] is proposed, which employs the switching scheme based on the impulse detection mechanism. It utilizes the center-weighted median (CWM) [26] filters that have varied center weights to define a more general operator, which realizes the impulse detection by using the differences defined between the outputs of CWM filters and the current pixel of concern. The ultimate output is switched between the median and the current pixel itself. As it is using a simple thresholding operation, the proposed filter yields superior results to other switching schemes in suppressing both types of impulses with different noise ratios. 105

125 Development of Noise Removal Algorithms for Images An impulse noise filter with adaptive mad-based threshold (ADMAD) [93], an extension to the switching scheme introduced in [94] is presented, where threshold T is varying from pixel to pixel. Its value is modified in accordance with the local variance, estimated by using median of the absolute deviations (MAD). Most of the contemporary impulse noise filters perform well on the traditional model of impulse noise (salt & pepper), where the new impulse detection concept removes any kind of impulse noise efficiently, while preserving image details. A new adaptive switching median (ASWMF) [95] filter is proposed, where no a priori threshold is to be given, instead, it is automatically computed from image pixels and based on the weighted mean value and the weighted variance or standard deviation in a selected sliding window. The weights are the inverse of the difference between each pixel of the considered window and the mean value of the window. Hence, the impulse noise does not corrupt too much the determination of the local adaptive threshold. The ASWM filter removes any kind of impulse noise efficiently. A new efficient algorithm called An Efficient Detail-Preserving Approach for Removing Impulse Noise in Images (ATBMF) is proposed [96] to remove impulse noise from corrupted images while preserving image details. It is based on alpha-trimmed means [97] used only in impulse noise detection instead of pixel value estimation.once a noisy pixel is identified, its value is replaced by a linear combination of its original value and the median of its local window. This algorithm consists of three steps: impulse noise detection, refinement, and impulse noise cancellation, which replaces the values of identified noisy pixels with estimated ones. A generalized framework of median based switching schemes, called multi-state median (MSM) [98] filter is proposed which uses a simple thresholding logic. The output of the MSM filter is adaptively switched among those of a group of center weighted median (CWM) filters that have different center weights. As a result, the MSM filter is equivalent to an adaptive CWM filter with a space varying center weight which is dependent on local signal statistics. The original switching median filter cannot detect the noise pixel whose value is close to its neighbors if the threshold is designed for emphasizing the detail preservation. Therefore, it is hard to recognize a noise-like pixel as a noise or a noise-free pixel in the sliding window. So, a Modified Switching Median filter (MSWMF) [99] is proposed by adding one more noise detector to improve the capability of impulse noise removal. The proposed [99] impulse noise detector is established based on the rank order arrangement of the pixels in the sliding window. This detector overcomes the above weakness such that the switching median filter is much effective in impulse noise removal. The new impulse detection concept called advanced impulse detection based on pixel-wise MAD is proposed [46]. Although it does not require optimizing parameters or previous 106

126 Chapter 6: Neural Network based Random Valued Impulsive Noise Suppression Scheme training, still, it removes impulse noise very efficiently, while preserving image details. Both of its steps i.e. the detection and the estimation, are based on the same median structure, so, only a simple median filter is required for practical realization. An iterative pixel-wise modification of MAD (PWMAD) provides reliable removal of arbitrarily distributed impulse noise. New PWMAD is straightforward and outperforms the majority of far more complex schemes published recently. A new detection mechanism has been proposed in [100] for universal noise filtering framework which is based on the nonlocal means (NL-means). The operation is carried out in two stages, i.e., detection followed by filtering. In the first stage, the robust outlyingness ratio (ROR) is proposed for measuring how impulse like each pixel is, and then all the pixels are divided into four clusters according to the ROR values. In second stage, different decision rules are used to detect the impulse noise based on the absolute deviation to the median in each cluster. This performance of this scheme is good for removing salt and pepper noise and random valued impulse noise as compared to other schemes. A novel algorithm has been proposed [101] based on finding the optimal direction used as a measure to detect whether the tested pixel is noisy or noise-free pixel. For detecting the central pixel whether it is noisy or noise-free pixel, a similarity parameter, S is calculated by measuring the normalized distance between the tested pixel, and the pixels in the optimal direction. Then by using a proper threshold, it can decide whether the test pixel is a noisy or an original pixel. Also, more edge pixels can be detected if the accurate or optimal direction of the edge is determined. The noisy pixel that has small deviations with the pixels in the optimal direction is deemed an original pixel. A new median filter, called tri-state median (TSM) filter [37], is proposed. By incorporating the SM filter and the CWM filter [90] into an impulse noise detection framework, a tri-state switching or decision mechanism is formed for effectively reducing impulse noise while preserving image details. 6.2 Computation of robust outlyingness ratio (ROR) and similarity measure (S) The impulse noise can be considered as an outlier in the image. The statistics called robust outlyingness ratio (ROR) as well the similarity measure(s) are used to find how much a pixel looks like an impulse noise. The ROR and S are computed by Algorithm 6.1 and Algorithm 6.2 respectively [22, 101,102]. 107

127 Development of Noise Removal Algorithms for Images Algorithm 6.1 : Computation of ROR Step 1: Step 2: Step 3: Consider a 5 x 5 window, W with centre pixel as the test pixel y Compute Med(y) as the median of the window Compute the median of absolute deviation, MAD as, ( ) * ( ) + Step 4: Compute MADN(y) empirically as, ( ) ( ) Step 5: Compute ( ) ( ( )) ( ) Algorithm 6.2 : Computation of S Step 1: Consider a 5 x 5 window and let the first pixel be denoted as. The total pixels in the window, except the central pixel ( ) ( ), are divided into four directions as shown in Figure 6.2. The pixels in each direction are listed in terms of their coordinates as follows: *( ) ( ) ( ) ( )+ *( ) ( ) ( ) ( )+ *( ) ( ) ( ) ( )+ *( ) ( ) ( ) ( )+ Figure 6.2: A 5 5 window divided into four directions. Step 2: Sort the pixels in each direction in ascending order so that the outlier pixels can be specified. The new vector that attained from the corresponding sorted direction is defined as; { ( ) } 108

128 Chapter 6: Neural Network based Random Valued Impulsive Noise Suppression Scheme Step 3: The optimal direction is attained by finding the vector that has minimum standard deviation σ: Here, { is the standard deviation of the pixels in the vector }. The gives the optimum direction is the direction that has the most similar pixels. Step 4: The similarity measure S for the central pixel ( ) ( ) is defined as, where, is the pixel in the optimal direction. In this way we compute the ROR and S measure for each pixel in the entire noisy image. The corresponding image is attached with a tag 0 or 1 based on whether it is noisy or non-noisy. Hence, a set of training patterns consisting of [(ROR, S): tag] are collected to train a neural network with structure as shown in Figure 6.3. The trained BPNN is used as the noise detector at the time filtering operation. bias bias ROR Noise Free / Noisy pixel S Figure 6.3: BPNN Structure for noise detection 109

129 Development of Noise Removal Algorithms for Images 6.3 Proposed scheme In the proposed scheme, the test pixel is identified as noisy or not through the trained BPNN. If it is found out to be noisy, the median filter is applied to the test pixel else the pixel is left unaltered. The structure of overall noise suppression scheme is shown in Figure 6.4. Z -1 Noisy Image OR Gate activate Windower Z -1 ROR S Median Filter Impulse Detector (BPNN) Figure 6.4: Structure of NNDF filter 110

130 Chapter 6: Neural Network based Random Valued Impulsive Noise Suppression Scheme 6.4 Simulation and results To compare the efficacy of proposed NNDF scheme, standard images like Lena, Bridge, Boat, Pepper etc. are corrupted with different noise probabilities. The NNDF scheme along with the best performing counterparts like ACWMF, ADMAD, ASWMF, ATBMF, MSM, MSWMF, PWMAD, SDOOD, TSM are simulated to obtain the restored results. Initially, the BPNN is trained with Lena image with RVIN with 20% noise density. A total number of 2000 pixels (1000 noisy and 1000 noise free) are selected randomly to generate the training patterns. The patterns consist of ROR and S statistics for each pixel and its noise status. The training convergence characteristic is shown in Figure 6.5. The trained detector is used for detecting RVIN on other images like Bridge, Boat, Pepper and Goldhill. Figure 6.5: Convergence characteristic of the neural network 111

131 Development of Noise Removal Algorithms for Images The performance evaluation is based on efficiency of noise detection and a measure of reconstruction error as described in chapter 1. The Bridge, Boat, Goldhill and Pepper images are corrupted by 10%, 15%, 20%, 25%, 30%, 35% and 40% of noise densities. The seven noisy images thus generated are filtered with the proposed scheme along with other reported schemes. The restored Boat images with its Image Quality Map of nine reported scheme along with our proposed schemes at 10%, 20%, and 30% noise are shown in Figure 6.6. The restored image of Boat, Bridge, Pepper and Goldhill images at 20%, 30% and 40% noise density applied by proposed approach are shown in Figure 6.7 and Figure 6.8 which shows good visual quality restored images. The simulated results of PSNR(dB) and IQI are presented in the Table , Table for Bridge and Pepper image respectively. It is observed from the simulated results of PSNR (db) and IQI as presented in the table that our proposed scheme is better as compared to other nine reported schemes. The comparative analysis of PSNR(dB) and IQI vs. noise density(%) are plotted for various filters in Bridge and Pepper images in Figure 6.9 and Figure 6.10 respectively. From the plots it is inferred that our proposed schemes (NNDF) is better than other nine reported schemes. 112

132 Chapter 6: Neural Network based Random Valued Impulsive Noise Suppression Scheme Methods Original image 10% RVIN 20% RVIN 30% RVIN Restored Images Image Quality Map of Restored Images From 10% From 20% From 30% From10% From20% From30% ACWMF ADMAD ASWMF ATBMF MSM MSWMF PWMAD SDOOD TSM NNDF Figure 6.6 : Comparative analysis of restored images and image quality map at various noise densities of Boat image. 113

133 Development of Noise Removal Algorithms for Images Original boat image Original bridge image (a) RVIN at 20% noise density (b) RVIN at 30% noise density (c) RVIN at 40% noise density Noisy boat image Restored boat image Noisy bridge image Restored bridge image Figure 6.7: Restored image of Boat and Bridge images at 20%, 30% and 40% noise density applied by proposed (NNDF) approach. 114

134 Chapter 6: Neural Network based Random Valued Impulsive Noise Suppression Scheme Original Pepper image Original Goldhill image (a) RVIN at 20% noise density (b) RVIN at 30% noise density (c) RVIN at 40% noise density Noisy pepper image Restored pepper image Noisy gold hill image Restored gold hill image Figure 6.8: Restored image of Pepper and Gold hill images at 20%, 30% and 40% noise density applied by proposed(nndf) approach. 115

135 Development of Noise Removal Algorithms for Images Table 6.1: Comparative analysis of PSNR(dB) for various filters in Bridge image % of RVIN Methods ACWMF ADMAD ASWMF ATBMF MSM MSWMF PWMAD SDOOD TSM NNDF Table 6.2 : Comparative analysis of IQI for various filters in Bridge image % of RVIN Methods ACWMF ADMAD ASWMF ATBMF MSM MSWMF PWMAD SDOOD TSM NNDF

136 Chapter 6: Neural Network based Random Valued Impulsive Noise Suppression Scheme Table 6.3 : Comparative analysis of PSNR(dB) for various filters in Pepper image Methods % of RVIN ACWMF ADMAD ASWMF ATBMF MSM MSWMF PWMAD SDOOD TSM NNDF Table 6.4 : Comparative analysis of IQI for various filters in Pepper image % of RVIN Methods ACWMF ADMAD ASWMF ATBMF MSM MSWMF PWMAD SDOOD TSM NNDF

137 Development of Noise Removal Algorithms for Images (a) (b) Figure 6.9: Comparative analysis of (a) PSNR(dB) and (b) IQI for various filters in Bridge image 118

138 Chapter 6: Neural Network based Random Valued Impulsive Noise Suppression Scheme (a) (b) Figure 6.10: Comparative analysis of (a) PSNR(dB) and (b) IQI for various filters in Pepper image 119

139 Development of Noise Removal Algorithms for Images 6.5 Summary In this chapter, we propose a neural network detection based filter, namely, NNDF to recover images corrupted with random valued impulse noise. The filter works in two phases, namely, identification of corrupted locations followed by the filtering operation. The identification of noisy pixels from a selected window is made based on neural network derived from two different statistical parameters namely, robust outlyingness ratio (ROR) and similarity measure (S). Finally, the identified noisy pixels are filtered with a median filter. The performance of the algorithm has been tested at different random valued impulse noise densities on different standard grey scale images. The proposed scheme is evaluated both qualitatively as well as quantitatively. The comparative performance analysis in general shows that the NNDF outperforms the existing schemes like ACWMF, ADMAD, ASWMF, ATBMF, MSM, MSWMF, PWMAD, SDOOD, TSM both in terms of RVIN noise reduction and retention of images details. 120

140 Chapter 7: Comparative Study of Proposed Techniques Chapter 7 Comparative Study of Proposed Techniques To combat salt and pepper noise from images, several schemes have been suggested in the literature as well as in this thesis in the previous chapters. The proposed schemes are: (a) New Adaptive Median Filter (NAMF) : Chapter 2 (b) Dynamic Adaptive Median Filter (DAMF) : Chapter 3 (c) Fuzzy Based Adaptive Mean Filter (FBAMF): Chapter 4 (d) Efficient Adaptive Mean Filter (EAMF): Chapter 5 In the corresponding chapters, the performance of the proposed methods have been studied in isolation and compared with relevant standard techniques. In this chapter, we have compared our own proposed schemes to derive an overall inference about the performance of the schemes with respect to MSE, MAE, PSNR, ISNR, SSIM, and IQI. The restored images are also visually compared among the schemes. 7.1 Results and Discussions On the basis of noise densities, the salt and pepper noise has been classified into three different categories i.e. low, medium, and high density noise and their ranges are listed in Table7.1. Table 7.1: Classification of noise on the basis of noise density level Noise classification Noise density level Low 0-30% Medium 30% 60% High above 60% The suggested schemes are simulated on standard Lena and Boat images with noise levels varied between 10% to 90%. Computed results are compared on the basis of low, medium, and high noise conditions for MAE, MSE, PSNR, ISNR, SSIM and IQI as presented in Table for Lena image and Tables for Boat image respectively. Low noise density We know that low value of MAE and MSE leads to good performance of the filter. So far concerned MAE values of Lena image, the DAMF has low value at 10% noise density as compared to others. At 20%, the EAMF gives good result but the FBAMF shows good 121

141 Development of Noise Removal Algorithms for Images performance at 30% noise density. At 10%, the DAMF has low MSE value, hence it is better. At 20%, the EAMF has low value. The FBAMF has low MSE value at 30% noise density but closer to EAMF. So far concerned PSNR values of Lena image, the EAMF performance is good as compared to other proposed scheme at low noise density. When we deal with the ISNR values, although at 10% noise density, the DAMF is better than other schemes, but both at 20% and 30% noise densities the EAMF is better than other three schemes. So far concerned SSIM values for Lena image, both FBAMF and EAMF are equally better than other two schemes. When we compare the IQI values, at 10% and 20% noise densities, the DAMF is better but at 30% noise density, the performance is low. As a whole, at low noise density, the performance of DAMF and FBAMF are better. Medium noise density So far concerned MAE and MSE values, the EAMF filter having low value of MAE and MSE as compared to other three filter. So, the performance of EAMF is good. The comparative analysis shows that the PSNR, ISNR, SSIM and IQI values of EAMF filter has larger value as compared to other three which leads to good performance filter. High noise density So far concerned PSNR, ISNR and SSIM values for Lena image, the EAMF filter having larger value as compared to other three filters. Up to 70% the IQI is better but it degrades beyond 70% noise density. The IQI value & the image quality map of the restored image has also been generated to evaluate the performance of the proposed filters applied on noisy images of 30%, 60% and 90% noise density as shown in Figure 7.1 for Lena image and Figure 7.2 for Boat images respectively. Brighter image quality map (IQI 1) indicates that the restored image is closer to the original image, and darker image quality map indicates that the restored image is more distant from the original image. It may be observed that the image quality map of the EAMF (proposed method) is brighter as compared to other for low as well as high density salt-andpepper noise. 122

142 Chapter 7: Comparative Study of Proposed Techniques Proposed Schemes Table 7.2: Comparative analysis of MAE for various filters in Lena image Low noise density (%) Medium noise density (%) High noise density (%) NAMF EAMF DAMF FBAMF Proposed schemes Table 7.3: Comparative analysis of MSE for various filters in Lena image Low noise density (%) Medium noise density (%) High noise density (%) NAMF EAMF DAMF FBAMF Table 7.4: Comparative analysis of PSNR(dB) for various filters in Lena image Proposed Low noise density (%) Medium noise density (%) High noise density (%) schemes NAMF EAMF DAMF FBAMF Proposed schemes Table 7.5: Comparative analysis of ISNR(dB) for various filters in Lena image Low noise density (%) Medium noise density (%) High noise density (%) NAMF EAMF DAMF FBAMF

143 Development of Noise Removal Algorithms for Images Table 7.6: Comparative analysis of SSIM for various filters in Lena image Proposed Low noise density (%) Medium noise density (%) High noise density (%) schemes NAMF EAMF DAMF FBAMF Table 7.7: Comparative analysis of IQI for various filters in Lena image Proposed Low noise density (%) Medium noise density (%) High noise density (%) schemes NAMF EAMF DAMF FBAMF Proposed schemes Table 7.8: Comparative analysis of MAE for various filters in Boat image Low noise density (%) Medium noise density (%) High noise density (%) NAMF EAMF DAMF FBAMF Proposed schemes Table 7.9: Comparative analysis of MSE for various filters in Boat image Low noise density (%) Medium noise density (%) High noise density (%) NAMF EAMF DAMF FBAMF

144 Chapter 7: Comparative Study of Proposed Techniques Proposed schemes Table 7.10: Comparative analysis of PSNR(dB) for various filters in Boat image Low noise density (%) Medium noise density (%) High noise density (%) NAMF EAMF DAMF FBAMF Proposed schemes Table 7.11: Comparative analysis of ISNR(dB) for various filters in Boat image Low noise density (%) Medium noise density (%) High noise density (%) NAMF EAMF DAMF FBAMF Table 7.12: Comparative analysis of SSIM for various filters in Boat image Proposed Low noise density (%) Medium noise density (%) High noise density (%) schemes NAMF EAMF DAMF FBAMF Proposed schemes Table 7.13: Comparative analysis of IQI for various filters in Boat image Low noise density (%) Medium noise density (%) High noise density (%) NAMF EAMF DAMF FBAMF

145 Development of Noise Removal Algorithms for Images Original image 30% noise noise 60% 90% noise Filters Restored Images From 30% From 60% From 90% Image Quality Map of Restored Images From 30% From 60% From 90% NAMF EAMF DAMF FBAMF Figure 7.1: Performance comparison of filters at different noise densities of Lena image. 126

146 Chapter 7: Comparative Study of Proposed Techniques Original image 30% noise 60% noise 90% noise Filters Restored Images From 30% From 60% From 90% Image Quality Map of Restored Images From 30% From 60% From 90% NAMF EAMF DAMF FBAMF Figure 7.2: Performance comparison of filters at different noise densities of Boat image. 127