Thesis (PDF) - Signal & Image Processing Lab

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Contents 1 Introduction 5 1.1 Self-Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Background and motivation . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Original contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Summary and thesis organization . . . . . . . . . . . . . . . . . . . . 9 2 Theoretical Background 12 2.1 Graph theory notions . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Known tree representations . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.1 Max-Tree and Min-Tree . . . . . . . . . . . . . . . . . . . . . 14 2.2.2 Binary Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.3 Tree of Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 Theoretical Background on semilattices . . . . . . . . . . . . . . . . . 18 2.3.1 Complete Semilattices and Lattices . . . . . . . . . . . . . . . 18 2.3.2 Morphology on Semilattices . . . . . . . . . . . . . . . . . . . 20 2.3.3 Supremum and Dilations . . . . . . . . . . . . . . . . . . . . . 21 2.4 Shape Tree Semilattice Background . . . . . . . . . . . . . . . . . . . 23 2.4.1 Tree of Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4.2 Inf-Semilattice of Binary Sequences . . . . . . . . . . . . . . . 25 2.4.3 Images of Shape Sequences . . . . . . . . . . . . . . . . . . . . 26 2.4.4 Inf-Semilattice of Images of Shape Sequences . . . . . . . . . . 27 2.4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.5 Alternating Sequences Semilattice Background . . . . . . . . . . . . . 31 2.5.1 Boundary Topographic Distance (BTD) . . . . . . . . . . . . 31 2.5.2 An extension of boundary topographic distance definition . . . 32 2.5.3 Boundary Topographic Variation (BTV) Transform . . . . . . 32 2.5.4 Semilattice in BTV Domain . . . . . . . . . . . . . . . . . . . 35 iii
iv CONTENTS 3 Implementation of BTVT 37 3.1 Topographic Distance Tree definition . . . . . . . . . . . . . . . . . . 37 3.2 Topographic Distance Tree implementation . . . . . . . . . . . . . . . 38 3.3 Implementation of the BTV Transform . . . . . . . . . . . . . . . . . 40 4 The “trench” problem and the proposed solutions 44 4.1 Filtering using an adaptive structuring element . . . . . . . . . . . . 48 4.2 Filtering using multiple minimal paths . . . . . . . . . . . . . . . . . 53 4.3 Filtering using a combined method . . . . . . . . . . . . . . . . . . . 55 4.4 Results Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.4.1 Comparison of different methods for avoiding trenches . . . . 55 4.4.2 Filtering of AS images versus traditional morphological filtering 55 5 Tree Semilattices 62 5.1 The Complete Inf-Semilattice of Tree Representations . . . . . . . . . 63 5.2 Image Processing on Tree Semilattices . . . . . . . . . . . . . . . . . 69 5.2.1 Proposed Approach . . . . . . . . . . . . . . . . . . . . . . . . 69 5.2.2 Examples and Particular Cases . . . . . . . . . . . . . . . . . 71 5.3 Semilattice of Images . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.3.1 Structure Induction . . . . . . . . . . . . . . . . . . . . . . . . 72 5.4 Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 73 6 Extrema-Watershed Tree example 75 6.1 Extrema watershed tree description . . . . . . . . . . . . . . . . . . . 76 6.2 Morphological operations on the extrema-watershed tree . . . . . . 78 6.2.1 Erosion and opening . . . . . . . . . . . . . . . . . . . . . . . 78 6.2.2 Opening by reconstruction . . . . . . . . . . . . . . . . . . . 87 6.3 Study of EWT properties . . . . . . . . . . . . . . . . . . . . . . . . 89 6.3.1 Implicit segmentation . . . . . . . . . . . . . . . . . . . . . . 89 6.3.2 Comparison to the Shape Tree . . . . . . . . . . . . . . . . . 92 6.3.3 Filtering using Extrema watershed tree versus traditional morphological filtering . . . . . . . . . . . . . . . . . . . . . . . . 94 6.4 Application examples . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.4.1 Pre-processing for car license plate number recognition . . . 99
Page 1 and 2: SELF-DUAL MORPHOLOGICAL OPERATORS B
Page 3: The Research Thesis was done under
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 and 14: xii LIST OF FIGURES 6.20 A Lena ima
Page 15 and 16: Abstract This research addresses a
Page 18 and 19: 4 List of Abbreviations and Symbols
Page 20 and 21: 6 CHAPTER 1. INTRODUCTION the image
Page 22 and 23: 8 CHAPTER 1. INTRODUCTION disadvant
Page 24 and 25: 10 CHAPTER 1. INTRODUCTION 3. A gen
Page 26 and 27: Chapter 2 Theoretical Background 2.
Page 28 and 29: 14 CHAPTER 2. THEORETICAL BACKGROUN
Page 52 and 53: 38 CHAPTER 3. IMPLEMENTATION OF BTV
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40 CHAPTER 3. IMPLEMENTATION OF BTV
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42 CHAPTER 3. IMPLEMENTATION OF BTV
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Chapter 4 The “trench” problem
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46CHAPTER 4. THE “TRENCH” PROBL
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Chapter 5 Tree Semilattices In this
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64 CHAPTER 5. TREE SEMILATTICES sec
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66 CHAPTER 5. TREE SEMILATTICES Fig
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68 CHAPTER 5. TREE SEMILATTICES tre
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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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