Pit Pattern Classification in Colonoscopy using Wavelets - WaveLab

4 Automated pit pattern classification
where S is the number of different nodes in the two trees and u 1 z is the z-th node value which
is only contained in the first quadtree subtracted from 5 ml+1 . The same procedure is done
for all nodes in the second tree. We sum up all unique node values of the second tree which
are not contained within the first quadtree.
sv 2 =
S∑
u 2 z (4.48)
z=1
The final similarity value is then
sv = sv 1 + sv 2 (4.49)
Finally this similarity value is normalized to always be between 0 and 1. This is done by
dividing sv by the maximum difference which can occur in terms of the unique node values.
This results in the final formula for sv:
sv = sv 1 + sv 2
t 1 + t 2
(4.50)
It is obvious that sv is 0 for equal trees since then the expression sv 1 + sv 2 equals zero.
And it is also obvious that sv can never exceed 1, since if all nodes are different sv 1 + sv 2
becomes t 1 + t 2 which results in a similarity value of 1.
This function already satisfies the requirement of the distance function from equation (4.40)
for equal trees to be 0, thus the final distance can be formulated as
d(T 1 , T 2 ) = sv (4.51)
This distance in now in the range between 0 (for equal trees) and 1 for completely different
trees. Apart from that the distance has the property that differences in the first levels of the
quadtree contribute more to the distance than differences in the deeper levels. This is due
to the fact that the unique numbers contained within L T1 and L T2 get smaller down the tree.
The biggest value is therefore assigned to the root node of the trees.
Figures 4.2(b)-(e) show some example quadtrees for which the distances to the tree in
figure 4.2(a) have been measured. The resulting distances listed in table 4.1 clearly show,
that, as intended, differences in the upper levels of a quadtree contribute more to the distance
than differences in the lower levels.
4.3.3 Distance by decomposition strings
This approach measures the distance between two quadtrees by creating a decomposition
string for each tree and comparing these strings for equal string sequences.
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