Thesis (PDF) - Signal & Image Processing Lab

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94 CHAPTER 6. EXTREMA-WATERSHED TREE EXAMPLE tree and shape tree on the corrupted image shown in Fig. 6.20. A difference between the two approaches is shown in Fig. 6.21. It is interesting that there is a major difference in the erosion result, but almost no difference in the opening result. This is because in the erosion picture of the extrema watershed tree trenches are revealed. The trenches in extrema watershed tree exposes flat zones located deep into the tree. There is no similar effect in a shape tree because its tree structure is different. Note that noise connected to the image border is not filtered in the Tree of shapes and is filtered in the EWT tree. Noise is left by the shape tree filter because its “fillhole” operator does not consider this boundary noise as a hole that can be filled during tree creation process. 6.3.3 Filtering using Extrema watershed tree versus traditional morphological filtering In this section, filtering results using the EWT are compared with traditional erosion, dilation, opening, closing, open-close, close-open operators and median filter in a complete lattice of gray level functions. In Figs. 6.24 and 6.24, results of conventional morphological filters (erosion, dilation, opening, closing) are shown. As expected, their results are not symmetric with respect to a gray and dark pixels. Because of that, those filters cannot be compared with the extrema-watershed tree. An additional morphological filter that has a pseudo symmetrical effect is a com- bined open-close or close-open filters as described in Chapter 8 of [3]. Their results are shown in Fig. 6.26. In Fig. 6.27 a median filter result is shown and compared to the EWT result. Those two figures enable a comparison between the proposed filter and traditional approaches. It can be seen the the EWT filtered result is in general similar to an open-close and close-open results, but without a bias towards dark pixels as a close-open or towards a light pixels as an open-close filter. The median filter is unbiased, but a number of noisy pixels have survived the filtering by it, and the median filter lacks other important features. For example it is not an idempotent filter.
6.3. STUDY OF EWT PROPERTIES 95 (a) (b) Figure 6.20: A Lena image corrupted by the Salt&Pepper noise. (a) Original Image (b) Noisy Lena Image. (a) (b) Figure 6.21: Difference between filtering results of Tree of shapes minus filtering results of Extrema watershed tree of Noisy Lena Image. In both filtering approaches we have used structuring element 2×2. (a) Difference between erosion results of Tree of shapes minus erosion results of Extrema watershed tree (b) Difference between opening results of Tree of shapes minus opening results of Extrema watershed tree.
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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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38 CHAPTER 3. IMPLEMENTATION OF BTV
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Page 58 and 59: Chapter 4 The “trench” problem
Page 60 and 61: 46CHAPTER 4. THE “TRENCH” PROBL
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Page 130 and 131: Bibliography [1] J. Serra, Image An
Page 132: 118 BIBLIOGRAPHY [21] Renato Keshet
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