Image Processing Reference

In-Depth Information

The computation of the distance
d
p
(
F
,
G
) is straightforward. For a discrete dataset of size

n
, the complexity for computing the distance is
O
(
n
). On the other hand, the computation of

4 Experimental results and discussions

The CDF-based kernels and distances can be effective on continuous distributions as well.

the kernel functions. The first chart shows the original Gaussian mixture. The other two dis-

tributions are obtained by moving the middle mode. Clearly the second distribution is much

closer to the original distribution than the third one.

FIGURE 3
A Gaussian mixture and variations.

Indexed in the same order as in
Figure 3
, the Bhatacharyya kernel matrix for the three dis-

tributions is:

The Bhatacharyya kernel did not clearly distinguish the second and the third distributions

when comparing to the original. There is no significant difference between the kernel values

k
12
and
k
13
, which measure the similarities between the original distribution and the other two

perturbed distributions.

The kernel matrix of our proposed kernel is:

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