Pit Pattern Classification in Colonoscopy using Wavelets - WaveLab

4 Automated pit pattern classification
in any of the T i . This is the moment the flag f d,j stored along with the nodes of the
dominance tree is used.
After the pruning process the dominance tree contains only nodes which are present
at least once among all T i .
4. Now a list D of all nodes in T D is created, which is then sorted by the counter c d,j
stored along with the nodes of the dominance tree. The first entries of this sorted list
are regarded as more relevant for feature extraction than those at the end of the list.
This, as mentioned above, is due to the fact that a higher counter value means, that
the according node was marked as a feature node more often than nodes at the end of
the sorted node list having lower counter values.
5. Finally all feature vectors are recreated based on this list of dominance tree nodes.
But instead of using the cost information stored along with the nodes in T i to choose
from which subbands to create the feature vectors, the subbands and the order of the
subbands to extract the feature vectors from are now derived from the information
stored in the dominance tree nodes.
If we remember that s max subbands are to be used to create the feature vector, we use
the first s max entries of the ordered list of the dominance tree nodes D to construct
the new feature vector from. This means, that the new feature vector F i for an image
indexed by i is created using a slightly modified version of equation (4.7)
F i = {f β1 , f β2 , . . . , f βsmax } (4.8)
where β k denotes the tree position for the k-th dominance tree node in D.
With this extension it can be assured that all feature vectors are created from the same
subbands with the same subband ordering. But there is still the problem that the dominance
tree may contain leaf nodes (subbands) which are simply not present in the decomposition
tree of an image indexed by i. This may happen if the decomposition tree of that image got
pruned at the parent node of such a node during the best-basis pruning. Although it is not
totally correct, for the sake of simplicity we insert a feature value of 0 for such a subband.
Now the feature vectors F i are ready to be fed into a classifier of choice.
There are a variety of functions to choose for the feature extractor such as energy, logarithm
of energy, variance, entropy and l-norm - just to name a few.
If S is a subband of size w × w, the formulas for this feature functions, which extract only
one feature value f i from a subband S i , are as follows:
Energy
f i =
w∑
2 −1
j=0
S i (j) 2 (4.9)
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