Thesis (PDF) - Signal & Image Processing Lab

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86 CHAPTER 6. EXTREMA-WATERSHED TREE EXAMPLE (a) (b) Figure 6.11: A Binary image corrupted by the Salt&Pepper noise. (a) Original Image (b) Noisy Binary Image (a) (b) Figure 6.12: Filtering Noisy Binary Image using the Extrema watershed tree. (a) Inverse transform of the Extrema watershed tree eroded by cross structuring element (b) Inverse transform of Extrema watershed tree opened by cross structuring element.
6.2. MORPHOLOGICAL OPERATIONS ON THE EXTREMA-WATERSHED TREE 87 6.2.2 Opening by reconstruction We can define an opening by reconstruction operator in the extrema-watershed tree. The classical version of this morphology operator is defined in [3] as a single erosion operation followed by a sequence of conditional dilation operations. The sequence is stopped when stability is reached - meaning that a dilation followed by the minimum operation does not change the resulting image. Using an opening operator defined on a tree, an opening by reconstruction operator is equivalent to tree pruning, where the pruning criteria is whether the vertex in question exists in the opened image. The tree pruning for opening by reconstruction is done using the following steps: 1. Apply an opening operator on the source image. 2. In a tree, for every label remaining in the tree, mark all vertices of the path starting from this label until the tree root, as still existing in the tree. 3. Replace every label in the input image by the closest parent label that was marked as still existing in the tree. Let’s demonstrate the method using an example illustrated in Fig. 6.13. In this example a source image consists of three rectangles located on a background. In the corresponding tree, those shapes have indexes V1, V2 and V3. In the example, a regular opening operator and an opening by reconstruction are applied on the image. The structuring element is a square that is bigger than V2, but smaller than the other shapes. The regular opening, shown in the figure, will leave the root label V5 shown in the image instead of V2. However, the opening by reconstruction will remove V2, as shown, and then reconstruct label V4 instead. Additional examples can be seen on Figs. 6.14 and 6.15.
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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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Page 50 and 51: 36 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 76 and 77: Chapter 5 Tree Semilattices In this
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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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Thesis (PDF) - Signal & Image Processing Lab

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