Pit Pattern Classification in Colonoscopy using Wavelets - WaveLab

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4 Automated pit pattern classification 4.2.1.2 Best-basis centroids (BBCB) Just like the best-basis method described in section 4.2.1.1 this method is based on the best-basis algorithm too. But there is a key difference between the method from section 4.2.1.1 and the method from this section. While the best-basis method resulted in different decomposition structures due to the underlying best-basis algorithm this method always exhibits the same decomposition structure. Just like in section 4.2.1.1 first of all the training images are decomposed using the bestbasis algorithm. But instead of using the resulting decomposition structures and subbands for feature extraction, a centroid (see section 4.3.4) based on the decomposition structures of all classes is calculated. This results in one centroid for all images. Then all images are decomposed again, but this time into the structure of the centroid. Although all images are transformed into the same subband structure, it is not guaranteed that the subbands are extracted in the same order for different images. This is due to the fact that, as explained in section 4.2.1.1, we use the first s max subbands from the ordered list of subbands in equation (4.3) which is ordered by cost information. But since the cost information for some specific subband sometimes will not be the same for all images, the ordered lists of subbands among all images may differ. Therefore this method uses the dominance tree extension too, to guarantee that all created feature vectors contain the same subbands in the same order. 4.2.1.3 Pyramidal wavelet transform (WT) This method is very similar to the method described in section 4.2.1.2. The are only small differences such as the usage of the pyramidal wavelet transform instead of the wavelet packets transform in conjunction with a centroid base. This again yields the same decomposition tree for all images in I T and for all testing images I α to be classified. Hence the number of subbands is equal among all images and the calculation of s max can be written as s max = 3l + 1 (4.23) since a wavelet transform of an image to l levels always results in 3l + 1 subbands. Another important difference is the lack of cost information in the pyramidal wavelet transform, since no pruning takes place. Therefore it is necessary to slightly extend the wavelet transform to store some cost information along with the decomposition tree nodes. This can be done by simply evaluating the cost of a node just as in the best-basis method. The remaining parts of the feature vector calculations and the classification process are just the same as in the previous method. Although the pyramidal decomposition always produces the same list of subbands for each image, the same problem as described in section 4.2.1.2 arises and it is not assured that for a s max the same subbands are used for the feature 42
4.2 Classification based on features vector creation process for all images. Therefore the dominance tree extension is used in this method too. Since the dominance tree extension is based on cost information stored along with the subbands but the pyramidal decomposition does not rely on any cost information, throughout this thesis the pyramidal decomposition additionaly stores the cost for each subband. To calculate the cost information the L 2 -norm is used. 4.2.1.4 Local discriminant bases (LDB) In contrast to the previous methods this method is already based on a feature extraction scheme which is highly focused on discrimination between classes. Since in the past the LDB algorithm has already been successfully applied to classification problems [37, 40, 41] it is an excellent candidate to be used for this thesis. While in all previous methods the training images are analyzed regardless of the classes the images belong to, this method, as already described in section 2.6.1, constructs a wavelet packet basis which is optimal for differentiating between images of different classes. Once this basis has been calculated all training images are decomposed into this basis, which yields the same number of subbands S max for all images in I T . And since this method is based already on discriminant power, the discriminant power for each subband is stored along with the respective node of the decomposition tree. This information is then used like in section 2.6.1.1 to construct the feature vector extracted from the most discriminant subbands. Again, if S i denotes the list of all subbands of an image i and S i denotes an arbitrary subband of the same image, S i can be written as S i = {S 1 , S 2 , . . . , S sIi } (4.24) After sorting this list by the discriminant power, a new list O i is created which is ordered now. with O i = {S α1 , S α2 , . . . , S αsIi } (4.25) p α1 ≥ p α2 ≥ . . . ≥ p αsIi (4.26) where p αj is the discriminant power for the α j -th subband. Now the feature vector is created like in the best-basis method, using the same set of possible feature functions F and using the first k most discriminant subbands. The remaining part of the classification process is the same as in the previous two methods. Since the nature of the LDB already defines the list of subbands to extract the features from and the ordering of the subbands, the dominance tree is not needed here. 43
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 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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