Thesis (PDF) - Signal & Image Processing Lab

More documents

Recommendations

Info

46CHAPTER 4. THE “TRENCH” PROBLEM AND THE PROPOSED SOLUTIONS (a) (b) Figure 4.3: Results of BTV-based erosion ˆεB. (a) Original Natural Image, and (b) erosion of Natural Image for a 2 × 2 structuring element. (a) (b) Figure 4.4: Results of BTV-based opening ˆγB. (a) Original Natural Image, and (b) opening of Natural Image for a 2 × 2 structuring element.
the number of gray levels is high, or if the image is very complex, the BTV transform usually fails. The reason for that is the existence of skeleton (watershed) points in the BTV data, which have neighbors with potentially very dissimilar alternating sequences; when eroded, a “trench” may open at these points, because the infimum of the dissimilar alternating sequences yields a sequence that does not characterize any of the neighbors. Although some of the “trenches” disappear, when we perform opening instead of erosion, the results are still not good, see Fig. 4.4. Let us consider a one dimentional example, given in Table 2.1, in order to under- stand the origin of the trenches. In this example, x = 5 is a skeleton (or watershed) point of the BTV transform of function f(x), with two different transform possibil- ities {−2, 13, −1} and {8, −3, 5}. For x = 4 the alternating sequence is {−2, 13}. Therefore, the infimum between two neighbors {−2, 13} and {8, −3, 5} is {0}. This produce the trench at x = 4. Fig. 4.5 shows the output of the erosion ˆεB on the one dimentional function f(x). Figure 4.5: Results of BTV-based erosion ˆεB. (a) Function f(x), and (b) Erosion of f(x). Solutions for the “trench” problem are proposed in the following sub-sections. 47
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 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 62 and 63: 48CHAPTER 4. THE “TRENCH” PROBL
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 110 and 111:
96 CHAPTER 6. EXTREMA-WATERSHED TRE
Page 112 and 113:
98 CHAPTER 6. EXTREMA-WATERSHED TRE
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?