Pit Pattern Classification in Colonoscopy using Wavelets - WaveLab

4.3 Structure-based classification
(unique node value in this context), which is not present among the other feature vectors (denoted
by v, w, x and y in the colored boxes). Since the feature vectors are not compareable in
this form, a zero is inserted at each position, where a feature vector is missing a unique node
value which is present in another feature vector. The resulting feature vectors are shown
in figure 4.4(b). Now, the unique node values are located at the same positions among all
feature vectors and the feature vectors can be compared by some distance metric.
When using this feature extractor along with the k-NN classifier, the distance metric used
to calculate the distances between the feature vectors is the euclidean distance metric already
presented in equation (3.5).
For example the distance between the feature vectors for images 1 and 2 presented in figure
4.4(b) along with euclidean distance metric would then result in the following distance
D(f 1 , f 2 ) = v 2 + w 2 (4.56)
where f 1 and f 2 are the first two feature vectors from figure 4.4(b).
Tree structure (FETS) This feature extractor is very similar to the feature extractor
presented in the previous paragraph since it is based on the unique node values too. But
instead of limiting the number of subbands to use for feature vector generation, this feature
extractor always uses the complete decomposition tree for the process of feature vector
creation. A feature vector for a decomposition tree T i can be written as
F i = {U 1 , U 2 , . . . , U n } (4.57)
where U j denotes the unique node value of the j-th leaf node of T i and n is the total number
of leaf nodes in T i .
Since this feature extractor uses all subbands of a decomposition tree to construct the
feature vector from the dominance tree extension is not needed. But due to the nature of the
best-basis algorithm it is also possible, like it was the case for the FEUNV feature extractor,
that some feature vector contains a unique node value, which is not present among the other
feature vectors. Thus, again the process illustrated in figure 4.4 is applied to the feature
vectors before they are passed into any classifier.
Again, if this feature extractor is used along with the k-NN classifier, the distance metric
is the euclidean distance metric from equation (3.5).
Tree distances (KNNTD) The last structural feature extractor we developed, uses the
quadtree structures resulting from the best-basis algorithm directly to compute the k nearest
neighbours in the k-NN algorithm. Thus we search for the k nearest neighbours with respect
to the decomposition trees which can be regarded here as feature vectors, along with a
quadtree distance metric. As quadtree distance metric we use the “distance based on unique
node values” here (see section 4.3.2)
53