Image Processing Reference

In-Depth Information

and − 90 ° of
w
− 1 pixels. In such a case, each pixel of the image can be seen as the intersection

FIGURE 3
Each image pixel can be seen as the intersection of four elements of the parti-

tions.

Since for each partition, it is possible to define a
C
-set, each pixel can be seen as belonging

to the partition obtained by the product of the original four
C
-set:

where
C
i
is the composite set corresponding to partition
Υ
i
. We shall define as
scale
the size

w
of each partition element. The product operator is neither idempotent nor increasing. The

fact that this operator is not idempotent allows it to be iteratively applied to the input signal

in order to construct the scales pace. The multiscale construction follows that of a fuzzy NN

looking upon an 2
n
× 2
n
image. By fixing the initial dimension of
CRC
(
C
andidate
R
egion to be

C
ategorized), each pyramidal network is constituted by
n
−
R
multiresolution levels. Each pro-

cessing element (
i
,
j
) at the
r
th level of the first pyramid (respectively, second pyramid) com-

putes the minimum value (respectively maximum value) over a 2
w
× 2
w
area at the (
r
− 1)th

level. The pyramidal structures are computed in a top-down manner, firstly analyzing re-

gions as large as possible and then proceeding by spliting regions turned out to be not of in-

terest. The mechanism of spliting operates as follows. If we suppose to be at the
r
th level of

both pyramid-networks and analyze a region
w
×
w
which is the intersection of four 2
w
× 2
w

regions, the minimum and maximum values computed inside are denoted by
m
s
,
t
and
M
s
,
t
,

s
=
i
, …,
i
+
w
,
t
=
j
, …,
j
+
w
. The combination of the minima and maxima values is made up at

the output layer, i.e.,

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