Thesis (PDF) - Signal & Image Processing Lab

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80 CHAPTER 6. EXTREMA-WATERSHED TREE EXAMPLE Figure 6.3: The Extrema Watershed Tree associated to the example in Fig. 6.2. Algorithm 3 Create maxima watershed tree A list of symbols : Eq A sorted queue of edges in G containing extremum region. Ngh A sorted queue of edges, a subset of Eq, neighbors of Vextr, V2. Lbl The current label number, initialized to zero. 1: Find all extremum region ,Vextr, in G. 2: Find all edges connected to the extremum regions and put them in Eq. 3: Sort Eq according to the comparison function in alg. 2. 4: while Eq not empty do 5: (Vextr, V2) ← F irst(Eq) 6: Lbl = Lbl + 1 7: Create new vertex V 8: Lbl(V ) ← Lbl 9: GL(V ) ← GL(V2) ⊲ The new vertex always gets GL other then extremum 10: Size(V ) ← Size(Vextr) + Size(V2) 11: F ather(Vextr) ← V ; F ather(V2) ← V 12: Ngh ← all pairs in Eq containing Vextr or V2 13: Substitute Vextr and V2 by V in Ngh. 14: Remove all pairs in Ngh where the first vertex is not extremum anymore. 15: Sort Ngh according to the comparison function in alg. 2. 16: Merge Eq and Ngh preserving the order. 17: end while 18: Root ← Lbl ⊲ the last added label is defined as the root
6.2. MORPHOLOGICAL OPERATIONS ON THE EXTREMA-WATERSHED TREE 81 The result of the erosion and the opening operations on the image Lena are shown in Figs. 6.4 and 6.5, respectively. As one can see, these operators create no significant artifacts (unlike the the trenches that are added by boundary topographic operators, as shown in Chapter 4). Very small components were removed, whereas the larger ones were preserved (by opening) or shrank (by erosion). Moreover, the average gray level of the picture did not change; in particular, the picture did not become darker, which is what usually happens after a standard erosion or opening. In addition, in Fig. 6.7 the filtering effect on a corrupted Lena image is shown. The image is corrupted with salt and pepper noise constituting of random black and white pixels. It is seen that after the filtering there is no sign of noise, and the resulted image is very similar to a filtered image without the noise. A comparison between the two results (filtered with and without the noise) is shown in Fig. 6.8. The image shown is the gray level difference between the filtered original and filtered noisy images, both obtained by opening and erosion. An additional example is shown in Figs. 6.11 and 6.10, with respect to the synthetic image “Simba”. The Fig. 6.12 results of filtering a binary image, first introduced in Fig. 1.1, are presented. All the noise, except for noise on the edges, has been removed.
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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 130 and 131: Bibliography [1] J. Serra, Image An
Page 132: 118 BIBLIOGRAPHY [21] Renato Keshet
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