Thesis (PDF) - Signal & Image Processing Lab

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LIST OF FIGURES xiii 6.38 (a) <strong>Image</strong> restored by a median filter. (b) <strong>Image</strong> restored by an opening on the shape tree with 2x2 SE. . . . . . . . . . . . . . . . . . . . . . 104 6.39 Top hat, using cross SE, as a pre-processing for dust and scratch removal. (a) Original image (b) Top hat by reconstruction based on EWT (c) Top hat using median (d) Top hat using an averaging filter. 107 6.40 Zoom in. Top hat, using cross SE, as a pre-processing for dust and scratch removal. (a) Original image (b) Top hat by reconstruction based on EWT (c) Top hat using median (d) Top hat using an averaging filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6.41 Top hat, using SE 5x5, as a pre-processing for dust and scratch removal. (a) Original image (b) Top hat by reconstruction based on EWT (c) Top hat using median (d) Top hat using an averaging filter. . . . . . 109 6.42 Zoom in. Top hat, using SE 5x5, as a pre-processing for dust and scratch removal. (a) Original image (b) Top hat by reconstruction based on EWT (c) Top hat using median (d) Top hat using an averaging filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Abstract This research addresses a new image filtering methodology, based on mathematical morphology. In this thesis a new general framework for producing morphological, self-dual operators that are compatible to a given tree representation is proposed. For every tree representation, a set of morphological operators on a complete inf-semilattice in the corresponding tree-representation domain is derived. Morpho- logical erosion, opening, and opening by reconstruction operators are defined using this framework. The proposed image filtering scheme consists of three steps: 1. Transform the input image to the corresponding tree representation, 2. perform morphological operators in the tree representation domain, and 3. transform the resulting tree representation back to the image domain. A particular case of this general framework is presented and studied. It involves a new tree representation,which we also developed in this research, called the Extrema- Watershed Tree. The particular case example emphasizes the ability of the general framework to generate new and useful sets of morphological operators. A number of potential applications for the Extrema-Watershed Tree is proposed. The new morphological operators excel in tasks suited for the application of classical morphological operators, but that require, in addition, self-duality. The proposed applications are pre-processing for OCR (Optical Character Recognition) algorithms, de-noising of images, and preprocessing for dust and scratch detection. In addition we show that the tree has an implicit segmentation property that could be used in image segmentation algorithms. In a previous work, Keshet has defined a complete inf-semilattice of images of alternating sequences. In this research an efficient implementation of morphological operators in this semilattice is proposed. In addition, the “trench” problem that 1
Page 1 and 2: SELF-DUAL MORPHOLOGICAL OPERATORS B
Page 3 and 4: The Research Thesis was done under
Page 5 and 6: iv CONTENTS 3 Implementation of BTV
Page 7 and 8: List of Tables 2.1 The BTV transfor
Page 9 and 10: viii LIST OF FIGURES 2.9 An example
Page 11 and 12: x LIST OF FIGURES 4.17 A Simba imag
Page 13: xii LIST OF FIGURES 6.20 A Lena ima
Page 18 and 19: 4 List of Abbreviations and Symbols
Page 20 and 21: 6 CHAPTER 1. INTRODUCTION the image
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Page 52 and 53: 38 CHAPTER 3. IMPLEMENTATION OF BTV
Page 58 and 59: Chapter 4 The “trench” problem
Page 60 and 61: 46CHAPTER 4. THE “TRENCH” PROBL
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50CHAPTER 4. THE “TRENCH” PROBL
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Chapter 5 Tree Semilattices In this
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76 CHAPTER 6. EXTREMA-WATERSHED TRE
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Chapter 7 Conclusions and further r
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Appendix A 114
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Bibliography [1] J. Serra, Image An
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118 BIBLIOGRAPHY [21] Renato Keshet
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