Thesis (PDF) - Signal & Image Processing Lab

More documents

Recommendations

Info

List of Figures 1.1 (a) A noisy binary image, (b) Erosion by a 3 × 3 squared structuring element, (c) The result of opening-closing with the same s.e., and (d) The result of closing-opening with the same s.e. . . . . . . . . . . . . 7 2.1 Max Tree representation of images. . . . . . . . . . . . . . . . . . . . 15 2.2 Example of Binary Partition Tree creation with a region merging al- gorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 (a) The trees of connected components of upper and lower level sets of a simple image. (b) The resulting tree of shapes corresponding to the same image. Notice that D is a hole in F. . . . . . . . . . . . . . . . . 19 2.4 Shape decomposition and associated Tree of shapes. (a) Original grayscale image f and (b)-(f) its shapes. The white shapes correspond to connected components of the collection of upper levels sets {θt(f)}, whereas the black shapes correspond to connected components of the collection of lower level sets {θt(f) c }. . . . . . . . . . . . . . . . . . . 24 2.5 Tree of shapes associated with Fig. 2.4. (a) Original tree; the numbers in parenthesis are the gray-levels of the shapes. (b) Modified tree; the number in parenthesis are the differences s(τ) between the levels of each shape τ and its parent p(τ). Notice that shape F was duplicated. 25 2.6 (a)-(b) Two grayscale images, and (c) their infimum according to ⊑. The supremum does not exist in this case. . . . . . . . . . . . . . . . 28 2.7 Erosion in the complete inf-semilattice of shape sequences. (a) Origi- nal gray-scale image, (b) proposed self-dual erosion, and (c) standard erosion. The structuring element in both cases is the cross 7 × 7. . . . 29 2.8 (a) Original grayscale image, (b) shape-tree erosion, (c) opening, and (d) top-hat. A square structuring element of size 2 × 2 was used in all cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 vii
viii LIST OF FIGURES 2.9 An example of different topographic distance reference. (a) An original image. (b) An image of a topographic distance from the boundary. (c) An image of a topographic distance from a center flat zone. . . . . . . 33 2.10 Plot of 1-D Function f(x). . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1 An example of a given image and its TD-tree. Each flat zone of the image corresponds to a node of the TD-tree (indicated by the letter V, followed by the node number), its gray-level (shown in the variable GL), and its boundary topographic distance (shown in the variable TD). 38 3.2 Synthetic image with the corresponding image of topographic distances. 42 3.3 Noisy image of Simba with the corresponding image of topographic distances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.4 Image of Lena 256x256 with the corresponding image of topographic distances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.5 Noisy Image of Lena 256x256 with the corresponding image of topographic distances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1 Result of BTV-based erosion ˆεB. (a) Original Synthetic Image, and (b) Erosion of Synthetic Image for a 2 × 2 structuring element. . . . . 45 4.2 Result of BTV-based opening ˆγB. (a) Original Synthetic Image, and (b) Opening of Synthetic Image for a 2 × 2 structuring element. . . . 45 4.3 Results of BTV-based erosion ˆεB. (a) Original Natural Image, and (b) erosion of Natural Image for a 2 × 2 structuring element. . . . . . . . 46 4.4 Results of BTV-based opening ˆγB. (a) Original Natural Image, and (b) opening of Natural Image for a 2 × 2 structuring element. . . . . 46 4.5 Results of BTV-based erosion ˆεB. (a) Function f(x), and (b) Erosion of f(x). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.6 A tree representing the BTV transform of function f(x). . . . . . . . 48 4.7 An example of filtering a dual-pixel noise : A black component - 3, is located on brighter background - 1 and 2. After erosion with erosion depth limit of 1, the upper pixel of the 3-rd component is untouched. 49 4.8 Results of BTV-based erosion ˆεB, using adaptive SE. (a) Original Nat- ural Image, and (b) erosion of Natural Image for a 2 × 2 structuring element. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
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: List of Tables 2.1 The BTV transfor
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
Page 58 and 59:
Chapter 4 The “trench” problem
Page 60 and 61:
46CHAPTER 4. THE “TRENCH” PROBL
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Chapter 5 Tree Semilattices In this
Page 78 and 79:
64 CHAPTER 5. TREE SEMILATTICES sec
Page 80 and 81:
66 CHAPTER 5. TREE SEMILATTICES Fig
Page 82 and 83:
68 CHAPTER 5. TREE SEMILATTICES tre
Page 84 and 85:
70 CHAPTER 5. TREE SEMILATTICES If
Page 86 and 87:
72 CHAPTER 5. TREE SEMILATTICES sam
Page 88 and 89:
74 CHAPTER 5. TREE SEMILATTICES rep
Page 90 and 91:
76 CHAPTER 6. EXTREMA-WATERSHED TRE
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
100 CHAPTER 6. EXTREMA-WATERSHED TR
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
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
show all

Thesis (PDF) - Signal & Image Processing Lab

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?