Biomedical Engineering Reference
In-Depth Information
U
¼
ufgð
i
¼
1
;
K
;
N
Þ
(4.5)
where
u
i
= 0 or 1. This vector contains
K
1s, where
K
N
. In our experiments,
K
=
16, and the number of neurons
N
was changed from 32,000 to 512,000. The
positions of 1s in the vector
U
s
are selected randomly for each feature
F
s
.This
procedure generates the list of the positions of 1s for each feature and saves all such
lists in the memory. We term the “mask” of the feature
F
s
the vector
U
s
.
In the next stage of encoding, it is necessary to transform the auxiliary vector
U
to the new vector
U
*
, which corresponds to the feature location in the image. This
transformation is made with permutations of the vector
U
components (Fig. 4.7).
The number of permutations depends on the feature location on the image. The
permutations in horizontal (
X
) (Fig.
4.7a
) and vertical (
Y
) (Fig.
4.7b
) directions
have different permutation schemes and are applied to the vector
U
sequentially.
Firstly, we have to apply
X
permutations, which give the vector
U
00
, and then apply
Y
permutations to the vector
U
00
to obtain the resulting vector
U
*
.
The problem is to obtain such binary codes of the features that are strongly
correlated if the distance between the feature locations is small and those that are
weakly correlated if the distance is large. For example, if the feature
F
s
is extracted
at the top point of the handwritten digit and the same feature is extracted at the
bottom point of the digit, they must be coded by different binary vectors
U
*
s1
and
U
*
s
2
, that have a weak correlation. If the same features are extracted at the
neighboring points, they must be coded with almost the same vectors
U
*
s
3
and
U
*
s
4
. This property makes the recognition system insensitive to the small displace-
ments of the digits in the image.
<<
a
E(X) =
0
E(X) =
1
E(X) =
2
E(X) =
3
U1
U1
U1
U1
U2
U2
U2
U2
U3
U3
U3
U3
U4
U4
U4
U4
U5
U5
U5
U5
U6
U6
U6
U6
U7
U7
U7
U7
U8
U8
U8
U8
U9
U9
U9
U9
Fig. 4.7a Permutation pattern for
X
coordinate
