Simulation of Optical CNN Template Library Based on t 2 -JTC Ahmed Ayoub ∗ , Szabolcs Tõkés ∗ and László Orzó ∗ ∗ Analogical and Neural Computing Systems Laboratory, Computer and Automation Institute - Hungarian Academy of Sciences, Kende u. 13-17, 1111 Budapest, Hungary, E-mail: ayoub@sztaki.hu, Tel.: +361 279 6135, Fax: (361)-209-5264. Abstract –To enhance the performance and robustness of our modified Joint Transform Correlator (t 2 -JTC), we numerically simulate the optical system which starts to create an optical CNN feedforward template library. Sample results are included for optical templates as well as algorithms. 1 INTRODUCTION A normalized first order continuous-time CNN and its vector notation are represented by Eqs. 1 and 2, respectively [1]: ∑ ∑ + + + − = kl kl kl ij kl kl kl ij ij ij z u B y A x x ; ; & (1) z u B y A x x ij ij + ⊗ + ⊗ + − = & (2) Where, x ij , A, B, u, y, and z are the present state, feedback template, feedforward template, input, output and threshold respectively. While i, j denotes present cell location and k, l are surrounding cell coordinate within the sphere of influence and ‘⊗’ denotes correlation operation. In consistence, the feedforward CNN is represented by Eq. 3 and its block diagram as in Figure 1. z u b x x kl l j k i kl ij ij + + − = ∑ + + , & (3) Figure 1 Zero-feedback (feedforward) continuous time CNN block diagram This continuous-time class of CNN cannot be realized optically by utilizing the present t 2 -JTC correlator [2], but only in discrete-time. Hence, Eq. 3 becomes: z m u b m x k l l j k i kl ij + = + ∑∑ + + ) ( ) 1 ( , (4) It is important to notice that there is no term representing the present state, x(m), in the right hand side of Eq. 4. The output, Eq. 5: )) 1 ( ( ) 1 ( + = + m x f m y ij ij (5) where f(.) could be a nonlinear function representing gray scale or a hard-limiter nonlinear function between [0,1] or [-1,1] representing binary output. This work uses a nonlinear optical output function, f 0 (.), within [0,1] to represent gray scale and a hard limiter with 0 and 1 to represent binary output, Figure 2. Figure 2 Output function of (a) CNN (b) Optical CNN; doted lines represent hard limiter The block diagram of discrete-time CNN would be as in Figure 3. Figure 3 Zero-feedback (feedforward) discrete time CNN block diagram. It is seen from Eqs. 2 and 5 that the CNN state equation is the sum of two cross correlations and a bias. The bias term is a constant and thus can be combined with the threshold function [2]. Accordingly, Eqs. 2 and 5 can be rewritten as: u B y A m x ⊗ + ⊗ = + ) 1 ( (6) )) 1 ( ( ) 1 ( 1 + = + m x f m y ij ij (7) where f 1 (.), the modified output function is: ) ( ) ( 1 z x f x f + = (8) In this case the block diagram of the discrete time CNN with a modified output function appears as shown in Figure 4. 1 1 -1 (a) -1 f(.) 1 1 (b) f0(.) b(m) f(.) u(m) uij(m) + z yij(m+1) x(m+1) B f(.) u uij + z - yij f(.) ij x &