Image Processing Reference

In-Depth Information

If
c
i
,
j
1
and
c
i
,
j
2
satisfy a specific constraint, the region under consideration is seen as
RC

(
R
egion to be
C
ategorize) and the values are retained as elementary features of such a region.

Otherwise, the region is divided in four sub-regions each of dimension equal to
w
/2. The pre-

processing subnetwork is applied again to the newly defined regions. The fuzzy intersections

computed by the preprocessing subnetwork are fed to a clustering subnetwork which is fed

scribed in the following.

3.2 Clustering Subnetwork

each corresponding neuron at the previous layer. In particular, at each iteration, a learning

step is applied to the clustering subnetwork according to the minimization of a
Fuzzines Index

FIGURE 4
The preprocessing networks.

The output of a node
j
is then obtained as:

where and , where
w
j
,
i
q
indicates the connection weight

between the
j
ith node of the output layer and the
i
ith node of the previous layer in the
q
ith cell-

plane,
q
= 1, 2. Each sum is intended over all nodes
i
in the neighborhood of the
j
th node at

the upper hidden layer.
f
(the
membership function
) can be sigmoidal, hyperbolic, Gaussian, Ga-

borian, etc. with the accordance that if
o
j
takes the value 0.5, a small quantity (usually 0.001)

is added; this reflects into dropping out instability conditions.
g
is a similarity function, e.g.

correlation, Minkowsky distance, etc. To retain the value of each output node
o
j
in [0, 1], we

apply the following mapping to each input image pixel
g
:

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