Pit Pattern Classification in Colonoscopy using Wavelets - WaveLab

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2 Wavelets Logarithm of energy (LogEnergy) cost(I) = N∑ log ∗ (s) with s = I(i) 2 i=1 Entropy N∑ cost(I) = − s log ∗ (s) with s = I(i) 2 i=1 L p -Norm cost(I) = N∑ |I(i)| p i=1 Threshold cost(I) = N∑ { 1 if I(i) > t a with a = 0 else i=1 where I is the input sequence (the subband), N is the length of the input, log ∗ is the logfunction with the convention log(0) = 0 and t is some threshold value. (a) Source image (b) LogEnergy (c) Entropy (d) L-Norm (e) Threshold Figure 2.3: Different decomposition trees resulting from different cost functions using the Haar wavelet. 16
2.6 Wavelet packets (a) Source image (b) LogEnergy (c) Entropy (d) L-Norm (e) Threshold Figure 2.4: Different decomposition trees resulting from different cost functions using the biorthogonal Daubechies 7/9 wavelet. In figure 2.3 the resulting decomposition trees for an example image using different cost functions are shown. The image in 2.3(a) was decomposed using the Haar wavelet with a maximum decomposition level of 5. In this example the threshold value t for the threshold cost function was set to 0. In figure 2.4 again the resulting decomposition trees for different cost functions are shown. But this time the biorthogonal Daubechies 7/9 wavelet was used. The parameters used for the decomposition and the source image are the same as used to produce the decomposition trees in figure 2.3. Note the difference between the decomposition trees in figure 2.3 and 2.4. While using the threshold cost function in these examples results in quite similar decomposition trees (figure 2.3(e) and 2.4(e)), the other cost functions exhibit fairly different decomposition trees. The best-basis algorithm has proven to be well suited for signal compression but is not necessarily as good for classification problems. A further example of a basis found with the best-basis algorithm is shown in figure 2.2(b). 2.6.1.2 Tree-structured wavelet transform The tree-structured wavelet transform introduced by Chang and Kuo [10] is another adaptive decomposition method for wavelets which is very similar to the best-basis algorithm. But instead of pruning the decomposition tree in a bottom-up manner, as it is done in the best-basis algorithm, the decisions which subbands to decompose further are already made during the top-down decomposition process. 17
Page 1: Pit Pattern Classification in Colon
Page 5: Preface Time is the school in which
Page 8 and 9: Contents 4.3.1 A quick quadtree int
Page 10 and 11: 1 Introduction endoscope represents
Page 12 and 13: 1 Introduction Pit pattern type I I
Page 14 and 15: 1 Introduction 6
Page 16 and 17: 2 Wavelets (a) Haar (b) Mexican hat
Page 18 and 19: 2 Wavelets For the discrete wavelet
Page 20 and 21: 2 Wavelets Now, that we have define
Page 22 and 23: 2 Wavelets 2.5 Pyramidal wavelet tr
Page 26 and 27: 2 Wavelets While the best-basis alg
Page 28 and 29: 2 Wavelets Euclidean distance D(p a
Page 30 and 31: 2 Wavelets 22
Page 32 and 33: 3 Texture classification image retr
Page 34 and 35: 3 Texture classification By approxi
Page 36 and 37: 3 Texture classification where E i
Page 38 and 39: 3 Texture classification After the
Page 40 and 41: 3 Texture classification and ⃗x i
Page 42 and 43: 3 Texture classification 34
Page 44 and 45: 4 Automated pit pattern classificat
Page 70 and 71: 5 Results (a) Pit Pattern I (b) Pit
Page 72 and 73: 5 Results (a) Canvas002 (b) Carpet0
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5 Results Pit Pattern Type I II III
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5 Results Feature Feature vector le
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5 Results 5.2.2 Best-basis method b
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5 Results (a) All classes (b) Pit P
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5 Results (a) All classes (b) Non-n
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5 Results (a) All classes (b) Class
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5 Results classes case all the entr
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5 Results the behaviour described a
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5 Results (a) All classes (b) Non-n
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5 Results (a) All classes (b) Class
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5 Results (a) 2 classes (b) 6 class
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5 Results and 85%, respectively. Th
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6 Conclusion correctly. But also in
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List of Figures 96
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List of Tables 98
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Bibliography [13] Huang C.R., Sheu
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Bibliography [40] Naoki Saito. Clas
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Pit Pattern Classification in Colonoscopy using Wavelets - WaveLab

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