Pit Pattern Classification in Colonoscopy using Wavelets - WaveLab

4.4 Classification
decomposition trees. Therefore D is
⎛
D =
⎜
⎝
0 d D11 ,D 12
. . . d D11 ,D 1n
. . . d D11 ,D C1
. . . d D11 ,D Cn
d D12 ,D 11
0 . . . d D12 ,D 1n
. . . d D12 ,D C1
. . .
.
. . . . . . . .
d D12 ,D Cn
.
d D1n ,D 11
d D1n ,D 12
. . . 0 . . . d D1n ,D C1
. . .
.
. . . . .. . .
d D1n ,D Cn
.
d DC1 ,D 11
d DC1 ,D 12
. . . d DC1 ,D 1n
. . . 0 . . .
.
. . . . . . ..
d DC1 ,D Cn
.
d DCn ,D 11
d DCn ,D 12
. . . d DCn ,D 1n
. . . d DCn ,D C1
. . . 0
⎞
⎟
⎠
where d Dij ,D kl
now is the euclidean distance between the j-th image (distance vector) of
class i and the l-th image (distance vector) of class k.
Then similar to section 4.3.4, the centroids for all classes can be calculated. But in this
approach the centroids are not decomposition trees anymore, but distance vectors. Thus, a
centroid in this context is the distance vector of the image of class c, which has the smallest
average euclidean distance to all other distance vectors of class c.
Once the centroids have been calculated, the classification is done by first decomposing
an arbitrary test image I T into the according decomposition tree T T using the best-basis algorithm.
Then the distance vector D T between the decomposition tree T T and the LDB tree
T LDB is calculated. Having calculated the distance vector, the class of the closest centroid
can be assigned to the image T T , where the closest centroid is the one having the smallest
euclidean distance to D T .
4.4 Classification
In this section we present the two concrete classifiers used in this thesis - namely the k-
nearest neighbour classifier and the support vector machines.
4.4.1 K-nearest neighbours (k-NN)
The k-NN classifier (see section 3.3.1) was chosen due to its simplicity when it comes to
implementation. And yet this classifier already delivers promising results.
To apply the k-NN classifier to the data first of all the feature vector F α for the image I α to
classify is calculated. Then the k-NN algorithm searches for the k training images for which
the respective feature vectors have the smallest distances to F α according to some distance
function such as the euclidean distance. The class label which is represented most among
these k images is then assigned to the image I α .
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