Pit Pattern Classification in Colonoscopy using Wavelets - WaveLab

4 Automated pit pattern classification
4.3.4 Centroid classification (CC)
Similar to the best-basis method presented in section 4.2.1.1 this method is based on the
calculation of the best wavelet packet basis too. But in contrast to the best-basis method
this method is not based on features extracted from the subbands resulting from the wavelet
packet decomposition but on the quadtrees resulting from the wavelet packet decomposition.
The idea behind this method is the question whether images decomposed using the
wavelet packets algorithm in conjunction with the best-basis algorithm result in decomposition
trees which can be further used for classification. A perfect classification would
then be possible if trees of one image class are more similar than trees resulting from images
of different classes. In other words, the similarity between trees of the same class must
be much higher than the similarity of trees of different classes to be able to perform some
useful classification.
The similarity of two quadtrees can be expressed by the distance between them as explained
in section 4.3.1.
It is worthwhile to mention that having a method to express the distances between two
quadtrees we could easily use that distance measure for a k-NN classification. This is exactly
what the feature extractor KNNTD (see section 4.3.3.3 above) does. Since we know the
classes for all training images, for an unknown test image we create the respective bestbasis
decomposition tree and calculate the quadtree distances to all trees of the training
images. The class, which dominates over the k nearest training images is then assigned to
the unknown training image.
Now, having a method to express the distance between two quadtrees and a set of images
I T used for training, first of all the distances between all possible pairs of quadtrees of
images out of this set are calculated as follows
d i,j = d(T i , T j ) i, j ∈ {1, . . . , n} (4.58)
where T i and T j are the decomposition trees of the i-th and the j-th image respectively, n is
the number of images in I T and d is the quadtree distance metric used. I Tc is the subset of
I T which contains all images of class c.
I T = I T1 ∪ I T2 ∪ · · · ∪ I TC (4.59)
where C is the total number of classes of images.
The trees T i and T j , as stated above, are the result of the best-basis algorithm and are the
optimal basis for the respective images in respect to a certain cost function such as the ones
listed in section 4.2.1.1.
The distances d i,j obtained above are now used to construct a distance matrix D of size
n × n with
d Ti ,T i
= 0 ∀i = 1, . . . , n (4.60)
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