Page 414 - Introduction to Information Optics

7.6. Pattern Classification
K

Fig. 7.37. An input arrangement for the JTC--NNC.

written in a correlation form as
N
E exp{[T[i? m(x + a)] - /T[w(x)]}. (7.44)

The correlation between the phase-transformed IWM and input pattern u(x)
can be easily realized by using a phase-modulated SLM. Notice that when
binary input exemplars are used, this phase-transformed NNC is actually the
Hamming net. In other words, the Hamming net is a special case of the
proposed phase-transformed NNC.
Let the size of the stored exemplars be N x x N y. The joint input to the JTC
is illustrated in Fig. 7.37, in which a set of M x x M y exemplars are displayed
on the left-hand side. The corresponding phase representation can be written as
M x - 1 My
/(x, y) = £. m xm y(x + m xb x, y + m yb y) expO'prc + iqn)w b(x, y)

pu(x - (7.45.)

where (b x,b y) and (d x,d y) are the dimensions shown in the figure and
pu(x, v) exp{iT[ti(x, >?)]}.
The corresponding nonzero-order JTPS can be shown as

NJTPS=4 Z I W mxmy(p,q)PU(p,q) cos[«50 WH(p,
m x = 0 m y = 0
MX - 1 Mv- 1
+ 4 W;(p-7t,<!-7r)Pl7(p,<3f) , (7.46)