Pit Pattern Classification in Colonoscopy using Wavelets - WaveLab

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4 Automated pit pattern classification Figure 4.3: An example quadtree 4.3.3.2 The distance function Using DS 1 and DS 2 from above, we can now determine the similarity of the quadtrees T 1 and T 2 by comparing the according decomposition strings. This is done by comparing the strings character by character. As long as the strings are identical we know that the underlying quadtree structure is identical too. A difference at some position in the strings means that one of the strings has further child nodes where the other quadtree has no child nodes. When such a situation arises the decomposition string which contains more child nodes is scanned further until the string traversal reaches again the quadtree position of the other quadtree node which has no more child nodes. During this process for each character of the first string the difference value dv is updated according to the depth level of the different child nodes as follows: dv = dv + 1 d (4.52) where d is the depth of the child nodes not contained within the other quadtree. This process is repeated until DS 1 and DS 2 are scanned until their ends. dv then represents the number of different nodes with the according depth levels taken into account. Therefore a difference in upper levels of the quadtrees contributes more to the difference value than a difference deeper in the quadtree. Finally, to clamp the distance value between 0 and 1 the resulting difference value is divided by the sum of the lengths of DS 1 and DS 2 . The final distance can then be written as d(T 1 , T 2 ) = ∑ n i=1 1 d i |DS 1 | + |DS 2 | (4.53) 50
4.3 Structure-based classification tree distance B1 0,1 B2 0,0833 B3 0,0583 B4 0,8552 Table 4.2: Distances to tree A according to figure 4.2 using “distance by decomposition strings” where n is the number of different nodes among the two quadtrees T 1 and T 2 and d i is the depth level of the i-th different node. It is obvious that the distance for equal trees is 0 since in that case the sum is zero. It can also easily be seen that the distance for two completely different quadtrees never exceeds 1 since for two completely different quadtrees n becomes |DS 1 | + |DS 2 | which can also be written as d(T 1 , T 2 ) = ∑ n i=1 n 1 d i (4.54) Since 1 d i is always less than 1 it is easy to see that the upper part of the fraction is always less than n. Therefore the distance is always less than 1. In table 4.2 the resulting distances according to figure 4.2 using “distance by decomposition strings” are shown. Again, just like the previous method, the results in the table clearly show, that, as intended, differences in the upper levels of a quadtree contribute more to the distance than differences in the lower levels. Compared to the distances in table 4.1, the results in table 4.2 are quite similar as long as the number of differences between two trees is low. But the more differences between two trees are present, the more different are the distance values between the two presented methods. The method based on decomposition strings shows significantly higher distance values if there are many differences between the trees. 4.3.3.3 Best basis method using structural features (BBS) This method is very similar to the best-basis method presented section 4.2.1.1 in that it is also based on the best-basis algorithm. But in contrast to the best-basis method, this method uses feature extractors which are not based on the coefficients of the subbands resulting from a wavelet decomposition but on the decomposition structures resulting from the best-basis algorithm. For this we developed three distinct feature extractors. 51
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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 24 and 25: 2 Wavelets Logarithm of energy (Log
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
Page 74 and 75: 5 Results Pit Pattern Type I II III
Page 76 and 77: 5 Results Feature Feature vector le
Page 80 and 81: 5 Results 5.2.2 Best-basis method b
Page 82 and 83: 5 Results (a) All classes (b) Pit P
Page 84 and 85: 5 Results (a) All classes (b) Non-n
Page 86 and 87: 5 Results (a) All classes (b) Class
Page 88 and 89: 5 Results classes case all the entr
Page 90 and 91: 5 Results the behaviour described a
Page 92 and 93: 5 Results (a) All classes (b) Non-n
Page 94 and 95: 5 Results (a) All classes (b) Class
Page 96 and 97: 5 Results (a) 2 classes (b) 6 class
Page 100 and 101: 5 Results and 85%, respectively. Th
Page 102 and 103: 6 Conclusion correctly. But also in
Page 104 and 105: List of Figures 96
Page 106 and 107: List of Tables 98
Page 108 and 109:
Bibliography [13] Huang C.R., Sheu
Page 110:
Bibliography [40] Naoki Saito. Clas
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