Biomedical Engineering Reference
In-Depth Information
the feature space. Accordingly, let us denote the points belonging to class
q
as
X
j
q
=(
x
j
1
q
,
,
x
jk
q
). Then the potential functions
f
s
and
f
q
for the classes
s
and
q
can
take the following form:
...
X
1
f
s
¼
a
;
2
2
ð
x
1
x
i
1
s
Þ
þ ...þð
x
k
x
ik
s
Þ
þ
i
(6.4)
X
1
f
q
¼
a
;
2
2
ð
x
1
x
j
1
q
Þ
þ ...þð
x
k
x
jk
q
Þ
þ
j
where
x
1
,
...
,
x
k
are the coordinates of the arbitrary point of the space, and
a
is the
small positive value which prevents division into zero. If a quantity of classes is
more than two, then similar functions
f
r
,
f
w
...
are written for the remaining classes,
and during the recognition the maximum
max
(
f
s
,
f
q
,
f
r
,
f
w
,
) is found.
In order to decrease the quantity of support points in the memory, only those
points that cannot be recognized correctly using previously collected support points
are saved. This procedure leads to the concentration of support points along the
surfaces that divide the patterns, thus improving the quality of recognition. Never-
theless, in the spaces of large dimensionality with nonlinear dividing surfaces in the
presence of the multiconnected regions, the quantity of support points must be very
large. In the task of recognizing natural textures, the number of support points can
reach several thousand. The method was programmed and realized for textural
features described above. The comparative analysis of the results of the texture
recognition is given below.
The method of potential functions was tested in ten photographs described above
(five texture classes). The results of the texture recognition with the aid of APNN
and the method of potential functions are given in Fig.
6.4
. (1 - by the method of
potential functions, 2 - with the aid of associative-projective neural networks). The
percentage of correct recognition by the method of potential functions is somewhat
higher than that with the aid of APNN. The number of support points in the method
of potential functions achieved is 1,712.
...
Fig. 6.4
Texture recognition
with the aid of APNN
(curve 2) and the method of
potential functions (curve 1)
