Page 413 - Introduction to Information Optics

398 7. Pattern Recognition with Optics

3, Terminate the iteration process when k=\ or f = log 2[(0 max — 0 min)/A#],
where t is the iteration number, and A$ is the minimum value that the
AT-maxnet can resolve.

Notice that in the AT-maxnet, only a maximum number of

iterations is needed to make a decision, which is independent of the number of
stored exemplars. For example, given $ max = 256, O min = 0, and A<5 = 1, less
than eight iterations are needed to search for the maximum node. Furthermore,
the AT-maxnet can tell when multiple maximum nodes occur by checking
whether k is greater than one or not, after Iog 2[(0 max — 0 min)/A0] iterations,
while the conventional niaxnet cannot.

7.6.2. OPTICAL IMPLEMENTATION

It has been shown in a preceding section that transforming real-valued
functions to phase-only functions offers higher light efficiency and better
pattern discriminability in a JTC. Let

(v m(x), m = 0,1,..., M - 1, x = 0,1,..., N}

be a set of exemplars. The phase representation of v m(x) is given by

/"* f
min ^rnax
where T[-] represents a gray-level-to-phase transformation operator, G min =
min m>s[i; m(x)}, and G max = max m<x{v m(x)}. The phase-transformed IWM of the
inner-product layer can be written as

w m (x) - exp{zT[u m(x)]}, m = 1, 2, . . . , M, x = 1, 2, . . . , N.

Thus, the inner product between w m(x) and the phase representation of the
input w(x) can be expressed as

Pc m = I exp{iTO m(x)] - /TTXx)]}.

To introduce the shift-invariance property, the preceding equation can be