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In the resulting dendrogram the images neu4 and neu4_r180 are clustered in differ-
ent groups (see Fig. 25).
If we virtually cut the dendrogram by a cophenetic similarity value of 0,0057, we
obtain the following groups G1={neu1;neu3}, G2={neu4_r180}, G3={neu2},
G4={neu4}, G5={gan128}, G6={parrot}, G7={cell}, and G8={monroe}. Except for
the images neu4 and parrot, these groups seem to better reflect the relationship be-
tween the image description and the parameter-set. The proper weighting of the fea-
tures can improve the grouping of the images. For this purpose we need to work out a
strategy in a further study.
5.2 Image Description as a Marginal Distribution for Columns and Lines, and
Diagonals
As another way to summarize the regional minima into an image description, we
chose to calculate the marginal distribution over x- and y-direction of an image as
well as over the diagonal. The marginal distribution is calculated by counting the
foreground pixels by column for the y-direction and row by row for the x-direction of
an image as well as for the diagonal. As a result, we have histograms over the col-
umns, the rows and the diagonal showing the frequency of foreground pixels in the
gradient image. The normalized marginal histogram for x- and y-direction for image
neu3 is presented in Fig. 27.
In the next step we compare the histograms for the columns, rows and diagonals
between two images by different distance functions.
Before we can calculate the marginal distribution for the foreground pixels, we
need to binarize the gradient image in order to decide which pixels are foreground or
background pixels. We used the thresholding algorithm of Otsu for the automatic
binarization. It is clear that this will put another constraint to our approach. However,
if it gives us a good image description and an automatic procedure, this is acceptable.
neu3
neu3
0,4
0,4
0,3
0,3
0,2
0,2
0,1
0,1
0,0
0,0
1
26
51
76
101
126
1
26
51
76
101
126
(a) Marginal distribution for columns
(b) Marginal distribution for rows
Fig. 27. Diagram of the Marginal Distribution of image neu3
The Kullback-Leibler divergence is usually the measure of choice when comparing
two histograms. The Kullback-Leibler divergence is defined as:
n
Hi
()
Sim
=
(()
H
i
H
( ln ()
i
2
(9)
HH
2
1
Hi
12
i
=
1
1
 
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