Abstract

A genetic algorithm is used to generate binary reference functions for optical pattern recognition and classification. Procedures based on the properties of convex functions can be implemented directly on hybrid electro-optical systems. Computer simulations demonstrate the efficiency of this novel approach.

© 1991 Optical Society of America

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References

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  1. B. V. K. Vijaya Kumar, Z. Bahri, L. Hassebrook, Proc. Soc. Photo-Opt. Instrum. Eng. 960, 18 (1988).
  2. R. Kallman, Appl. Opt. 25, 1032 (1986).
    [CrossRef] [PubMed]
  3. M. Fleisher, U. Mahlab, J. Shamir, Appl. Opt. 29, 2091 (1990).
    [CrossRef] [PubMed]
  4. U. Mahlab, J. Shamir, Opt. Lett. 14, 146 (1989).
    [CrossRef]
  5. P. J. M. van Luarhoven, E. H. L. Aarts, Simulated Annealing: Theory and Applications (Reidel, Dordrecht, The Netherlands, 1987).
  6. J. Rosen, U. Mahlab, J. Shamir, Opt. Eng. 29, 1101 (1990).
    [CrossRef]
  7. D. Lawrence, Genetic Algorithm and Simulated Annealing (Kaufmann, Los Altos, Calif., 1987).
  8. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1987).
  9. J. Ziv, M. Zakai, IEEE Trans. Inf. Theory IT-19, 275 (1973).
    [CrossRef]
  10. A. W. Robert, D. E. Veberg, Convex Function (Academic, New York, 1973).
  11. D. A. Gregory, J. A. Loudin, Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 198 (1989).

1990 (2)

1989 (2)

D. A. Gregory, J. A. Loudin, Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 198 (1989).

U. Mahlab, J. Shamir, Opt. Lett. 14, 146 (1989).
[CrossRef]

1988 (1)

B. V. K. Vijaya Kumar, Z. Bahri, L. Hassebrook, Proc. Soc. Photo-Opt. Instrum. Eng. 960, 18 (1988).

1986 (1)

1973 (1)

J. Ziv, M. Zakai, IEEE Trans. Inf. Theory IT-19, 275 (1973).
[CrossRef]

Aarts, E. H. L.

P. J. M. van Luarhoven, E. H. L. Aarts, Simulated Annealing: Theory and Applications (Reidel, Dordrecht, The Netherlands, 1987).

Bahri, Z.

B. V. K. Vijaya Kumar, Z. Bahri, L. Hassebrook, Proc. Soc. Photo-Opt. Instrum. Eng. 960, 18 (1988).

Fleisher, M.

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1987).

Gregory, D. A.

D. A. Gregory, J. A. Loudin, Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 198 (1989).

Hassebrook, L.

B. V. K. Vijaya Kumar, Z. Bahri, L. Hassebrook, Proc. Soc. Photo-Opt. Instrum. Eng. 960, 18 (1988).

Kallman, R.

Lawrence, D.

D. Lawrence, Genetic Algorithm and Simulated Annealing (Kaufmann, Los Altos, Calif., 1987).

Loudin, J. A.

D. A. Gregory, J. A. Loudin, Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 198 (1989).

Mahlab, U.

Robert, A. W.

A. W. Robert, D. E. Veberg, Convex Function (Academic, New York, 1973).

Rosen, J.

J. Rosen, U. Mahlab, J. Shamir, Opt. Eng. 29, 1101 (1990).
[CrossRef]

Shamir, J.

van Luarhoven, P. J. M.

P. J. M. van Luarhoven, E. H. L. Aarts, Simulated Annealing: Theory and Applications (Reidel, Dordrecht, The Netherlands, 1987).

Veberg, D. E.

A. W. Robert, D. E. Veberg, Convex Function (Academic, New York, 1973).

Vijaya Kumar, B. V. K.

B. V. K. Vijaya Kumar, Z. Bahri, L. Hassebrook, Proc. Soc. Photo-Opt. Instrum. Eng. 960, 18 (1988).

Zakai, M.

J. Ziv, M. Zakai, IEEE Trans. Inf. Theory IT-19, 275 (1973).
[CrossRef]

Ziv, J.

J. Ziv, M. Zakai, IEEE Trans. Inf. Theory IT-19, 275 (1973).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Inf. Theory (1)

J. Ziv, M. Zakai, IEEE Trans. Inf. Theory IT-19, 275 (1973).
[CrossRef]

Opt. Eng. (1)

J. Rosen, U. Mahlab, J. Shamir, Opt. Eng. 29, 1101 (1990).
[CrossRef]

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

B. V. K. Vijaya Kumar, Z. Bahri, L. Hassebrook, Proc. Soc. Photo-Opt. Instrum. Eng. 960, 18 (1988).

D. A. Gregory, J. A. Loudin, Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 198 (1989).

Other (4)

P. J. M. van Luarhoven, E. H. L. Aarts, Simulated Annealing: Theory and Applications (Reidel, Dordrecht, The Netherlands, 1987).

D. Lawrence, Genetic Algorithm and Simulated Annealing (Kaufmann, Los Altos, Calif., 1987).

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1987).

A. W. Robert, D. E. Veberg, Convex Function (Academic, New York, 1973).

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Figures (4)

Fig. 1
Fig. 1

Input training set: (a) the pattern to be detected (the letter H), (b) the pattern to be rejected (the letter E).

Fig. 2
Fig. 2

Two different members of the population of reference functions. Black represents +1, white represents −1.

Fig. 3
Fig. 3

Output correlation intensity with (a) the reference function produced by GA (discrimination ratio of 1:7.1) and (b) the original function as reference (discrimination ratio of 1:2.7).

Fig. 4
Fig. 4

Joint-transform correlator architecture for electro-optical implementation of learning algorithm. One of the reference functions and the training set are presented on the upper SLM, and the control computer (not shown) analyzes the output signal detected by the lower charge-coupled-device (CCD) camera.

Equations (9)

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c ( x 0 , y 0 ) = - - f ( x , y ) h * ( x + x 0 , y + y 0 ) d x d y ,
Φ ( x , y ) = L [ c ( x , y ) ] - - L [ c ( x , y ) ] d x d y ,
S = - - - Ψ [ Φ ( x , y ) ] d x d y ,
Φ D ( m , n ) = { 1 at ( m = k , n = l ) ( domain of Φ ) 0 otherwise ,
Φ R ( m , n ) = 1 ( 2 N - 1 ) 2 ,             ( m , n ) .
Ψ ( x ) = x 2 ,
S min D = - 1 ,             S max R = - 1 ( 2 N - 1 ) 2 ,
M = f n D S D - f n R S R
M min = M [ h GEF ( i , j ) ] .

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