Pit Pattern Classification in Colonoscopy using Wavelets - WaveLab

4 Automated pit pattern classification
4.3 Structure-based classification
While the classification methods presented in the previous sections were based on features
based on wavelet coefficients and therefore needed some classifier to be trained, the next
sections introduce a classification method, which does not involve any feature extraction
in terms of image features. Instead the “centroid classification” tries to assign pit pattern
classes to unknown images by decomposing the image and compare the resulting decomposition
structure to the centroids of the respective classes.
But first of all a quick introduction into quadtrees and a description of the used quadtree
distance metrics are given.
4.3.1 A quick quadtree introduction
A quadtree is a tree with the important property, that every node in a quadtree having child
nodes has exactly four child nodes. As all trees in mathematics a quadtree can be defined
like a graph by a vertex set V an edge set E. For a tree with n ∈ N + nodes this can be
written formally as
V = {v 1 , . . . , v n } with |V | = n (4.27)
E = {(v i , v j )|i ≠ j, v i , v j ∈ V } (4.28)
where the elements v i ∈ V are called vertices and the elements e j ∈ E are called edges.
Vertices which do not have any child nodes are called leaf nodes.
4.3.2 Distance by unique nodes
This distance metric tries to measure a distance between two quadtrees by first assigning
each node of the quadtrees an unique node value, which is unique among all possible
quadtrees. Then for each quadtree a list of quadtree node values is generated which are
then compared against each other to identify nodes which appear in one of the two trees
only.
4.3.2.1 Unique node values
To be able to compare different quadtrees, we must be able to uniquely identify a node
according to its position in the quadtree. To accomplish this we assign a unique number to
each node according to its position in the tree.
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