Thesis (PDF) - Signal & Image Processing Lab

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74 CHAPTER 5. TREE SEMILATTICES representation. The current definition of tree transform and operator definition does not assure the existence of the image semilattice (see section 5.3).
Chapter 6 Extrema-Watershed Tree example Chapter 5 presents a general framework for producing morphological operators that are compatible to a given tree representations. For every tree representation, a com- plete inf-semilattice in the tree-representation domain is derived, and a set of morphological operators on that inf-semilattice is obtained. As for any general framework, the strength and usefulness of the proposed morphological tree-based framework is measured by its ability to: 1) unify existing methods as much as possible, in a simple way, and 2) generate new and useful methods. The purpose if this chapter is to present an example of a new method that is obtained from the general framework, and to investigate its usefulness. This exemplifies the strength of the general framework, as a tool for generating new, useful sets of morphological operators. Based on the general framework of Chapter 5, all that is needed in order to obtain a new set of morphological operators is a given tree representation. The more this tree representation is useful, the more useful these morphological operators are likely to be, since many of the properties of the tree are inherited by the morphological operators (like self-duality). The tree representation selected for the method presented in this chapter is a particular case of a “Binary Partitioning Tree”, which is a state-of-the-art, general framework for tree generation, developed by Salembier in [10]. The proposed representation is built using an iterative merging process as presented by Salembier, Garrido and Garcia in [23]. 75
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SELF-DUAL MORPHOLOGICAL OPERATORS B
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The Research Thesis was done under
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iv CONTENTS 3 Implementation of BTV
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List of Tables 2.1 The BTV transfor
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viii LIST OF FIGURES 2.9 An example
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x LIST OF FIGURES 4.17 A Simba imag
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xii LIST OF FIGURES 6.20 A Lena ima
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Abstract This research addresses a
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4 List of Abbreviations and Symbols
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6 CHAPTER 1. INTRODUCTION the image
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8 CHAPTER 1. INTRODUCTION disadvant
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10 CHAPTER 1. INTRODUCTION 3. A gen
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Chapter 2 Theoretical Background 2.
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14 CHAPTER 2. THEORETICAL BACKGROUN
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Page 38 and 39: 24 CHAPTER 2. THEORETICAL BACKGROUN
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
Page 76 and 77: Chapter 5 Tree Semilattices In this
Page 78 and 79: 64 CHAPTER 5. TREE SEMILATTICES sec
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Page 90 and 91: 76 CHAPTER 6. EXTREMA-WATERSHED TRE
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Page 126 and 127: Chapter 7 Conclusions and further r
Page 128 and 129: Appendix A 114
Page 130 and 131: Bibliography [1] J. Serra, Image An
Page 132: 118 BIBLIOGRAPHY [21] Renato Keshet
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