Thesis (PDF) - Signal & Image Processing Lab

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Chapter 4 The “trench” problem and the proposed solutions The BTV-domain morphological operators (erosion, opening etc.) proposed by Keshet in [16] are self-dual. This means that those operators treat bright and dark “objects” similarly. However, when applying those operators, a “trench” problem may arise. This chapter studies this problem, and proposes solutions for it. The BTV-domain morphological filtering approach involves three steps. First, the BTV transform is performed on the input image, using the TD-tree representation of the image. Then the transformed image is simplified using morphological filtering, based on the partial ordering of images of alternating sequences, defined in Section 2.5.4. Finally output image is constructed from the processed image by an inverse BTV transform, using Equation (2.21). Figs. 4.1 and 4.3 show the output of the erosion ˆεB on two test images. Figs. 4.2 and 4.4 show the corresponding opening ˆγB of the same two test images. Notice that the results of self-dual erosion and opening (Figs. 4.1-4.2) on the synthetic image are as expected. The corresponding erosion has the effect of shrinking all the elements of the image, regardless to their contrast. The opening rounds the corners that SE can not get into in all the elements of the image, bright and dark. However, the results on the natural image are very strange; the output shows many “trenches” that do not appear to have any justification to exist. These are typical results. When the number of gray levels is small, and the image is not very complex, the BTV-based erosion returns useful results. However, when 44
(a) (b) Figure 4.1: Result of BTV-based erosion ˆεB. (a) Original Synthetic Image, and (b) Erosion of Synthetic Image for a 2 × 2 structuring element. (a) (b) Figure 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
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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
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
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94 CHAPTER 6. EXTREMA-WATERSHED TRE
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100 CHAPTER 6. EXTREMA-WATERSHED TR
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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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