Pit Pattern Classification in Colonoscopy using Wavelets - WaveLab

4 Automated pit pattern classification
Throughout this thesis an extended version of the euclidean distance metric from equation
(3.5) is used:
s∑
max
d(F a , W a , F b , W b ) = (F a (i)W a (i) − F b (i)W a (i)) 2 (4.62)
i=1
where W a and W b are weighting vectors for the according feature vectors. The weights in
these vectors are derived from the cost information obtained by a wavelet decomposition.
The motivation behind using a weighted version of the euclidean distance is that feature
vector entries associated with large weights (features from subbands with high energy for
example) should contribute more to the distance the more these entries differ among different
feature vectors.
However, regarding our test results presented in chapter 5 it does not make much of a
difference whether we use the common version of the euclidean distance from equation
(3.5) or the weighted version from equation (4.62).
4.4.2 Support vector machines (SVM)
The other classifier chosen for this thesis is the SVM classifier (see section3.3.3). For our
implementation we use the libSVM [8].
For the training process of this classifier the training data for all images in I is calculated
and provided to the classifier.
The classification is similar to the k-NN classifier - for a given image I α , which should be
classified, the according feature vector F α is calculated and presented to the SVM classifier.
The SVM classifier then returns a class prediction which is used to assign the given test
image to a specific pit pattern class.
To improve classification accuracy the feature vectors extracted from the subbands are
scaled down to the range between −1 and +1 before they are used to train the SVM classifier
as suggested in [20]. As a consequence the feature vectors used to test the classifier must be
scaled down by the same factor before they can be used for classification.
Additionally to scaling down the feature space we use a naive grid search for the SVM
parameters γ and ν [20]. γ is a parameter used in the gaussian radial basis function kernel
type. The parameter ν is used to control the number of support vectors and errors [9].
Since optimal values for γ and ν are not known beforehand we employ a naive grid search
to find the best choices for these parameters for a single test run. The goal is to identify such
γ and ν that the classifier is able to classify unknown data as accurate as possible. The grid
search is done by iterating two values a and b which are then used as follows to calculate γ
and ν:
γ = 2 a with a l ≤ a ≤ a u and a, a l , a u ∈ Z (4.63)
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