Pit Pattern Classification in Colonoscopy using Wavelets - WaveLab

4 Automated pit pattern classification
(a) Source image (b) According co-occurrence matrix (d =
5, direction is 0 degrees)
Figure 4.1: An example image with its according co-occurrence matrix
In figure 4.1 a gray scale image with its according co-occurrence matrix is shown. The
relation R used to construct the co-occurrence matrix shown in figure 4.1(b) uses a distance
value d of 5 pixel and a direction of 0 degrees, which is horizontal directed to the right.
Since gray levels are discrete values, but wavelet coefficients contained within a subband
are not, the wavelet coefficients have to be quantized before an according co-occurrence
matrix can be constructed. The quantization is done by first shifting the wavelet coefficients
such that all wavelet coefficients become positive. Then each coefficient is converted to its
according discrete value c d using the following formula
⌊ c(L − 1)
⌋
c d = 1 +
m
(4.14)
where c is the already shifted coefficient value to be converted, L is the desired number of
different levels and m is the highest value among all shifted coefficients.
Now that the wavelet coefficients are converted to discrete values ∈ [1, L], we can construct
a co-occurrence matrix with size L × L and update its contents based on the discrete
wavelet coefficients.
Possible features based on the co-occurrence matrix of a subband S i are for example contrast,
energy, entropy, the inverse difference moment, cluster shade and cluster prominence.
For a co-occurrence matrix C i of size w × w for a subband S i the respective formulas are as
follows:
Contrast
∑w−1
∑w−1
f i = (x − y) 2 C i (x, y) (4.15)
y=0 x=0
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