Pit Pattern Classification in Colonoscopy using Wavelets - WaveLab

4.2 Classification based on features
with
F i = {f 1 , f 2 , . . . , f smax } (4.7)
where F is the feature extractor chosen and f i is the feature for a subband S i .
But the feature vectors just created can not yet be fed into any classifier, since we still
have a major problem. Due to the fact that the best-basis algorithm most times will produce
different decomposition structures and therefore different lists of subbands for different images,
it can not be assured that later, during the classification process, the features of the
same subbands among the images are compared. It is even possible, that a feature for a
subband, which is present in the subband list for one image is not present in the subband list
for another image.
Therefore, when the feature vectors for all images have been created we have to perform the
following steps to post-process the feature vectors:
1. We create a dominance tree T D , which is a full wavelet packet tree with a decomposition
depth l max (the maximum decomposition depth among all decomposition trees
for all images).
2. This dominance tree is now updated using the decomposition tree T i for a training
image indexed by i.
This updating process is done by comparing the tree T i and T d node by node. For each
node T d,j present in T d we try to find the according node T i,j at the same position j in
the tree T i .
Such a node in the dominance tree holds the following two values:
• A counter c d,j , which is incremented by one if the tree T i has a node at the tree
position j too, which additionally is marked as being a feature node.
Thus, after the dominance tree has been updated with all trees for all training
images, this counter stores the number of times that specific node at tree position
j was present and selected as a feature node among all trees of the training
images.
This counter is used later as a measure of relevance for a specific subband and
to decide whether that specific subband should be included in the process of
feature vector creation. In other words, the higher the counter for a specific
node (subband) is, the higher is the chance that the according subband will be
chosen to construct a part of the feature vector from its coefficients.
• A flag f d,j , indicating whether at least one of the trees of the training images has
a node located at tree position j. This flag is set the first time a tree T i has a node
located at position j. This flag is used during the pruning process following in
the next step.
3. When T D has been updated for all T i , T D gets pruned. This is done by traversing
the tree from the leafs upwards to the root and deleting any child nodes not present
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