Abstract

Highly selective and efficient optical pattern recognition is implemented by using phase-only entropy-optimized filters generated by simulated annealing. An electro-optic architecture is proposed for filter generation.

© 1989 Optical Society of America

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References

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  1. D. Casasent, W. A. Rossi, Appl. Opt. 25, 184 (1986).
    [CrossRef] [PubMed]
  2. D. Casasent, W.-T. Chang, Appl. Opt. 25, 2343 (1986).
    [CrossRef] [PubMed]
  3. J. Shamir, H. J. Caulfield, J. Rosen, Appl. Opt. 26, 2311 (1987).
    [CrossRef] [PubMed]
  4. X. Mahalanobis, B. V. K. V. Kumar, D. Casasent, Appl. Opt. 26, 3633 (1987).
    [CrossRef] [PubMed]
  5. R. D. Juday, B. J. Daiuto, Opt. Eng. 26, 1094 (1987).
  6. M. Fleisher, U. Mahlab, J. Shamir, “Entropy-optimized filter for pattern recognition,” Appl. Opt. (to be published).
  7. P. J. M. van Luarhoven, E. H. L. Aarts, Simulated Annealing: Theory and Applications (Reidel, Dordrecht, The Netherlands, 1987).
  8. M. S. Kim, M. R. Feldman, C. C. Guest, Opt. Lett. 14, 545 (1989).
    [CrossRef] [PubMed]
  9. R. Kikuchi, B. H. Soffer, J. Opt. Soc. Am. 67, 1656 (1977).
    [CrossRef]

1989

1987

1986

1977

Aarts, E. H. L.

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

Casasent, D.

Caulfield, H. J.

Chang, W.-T.

Daiuto, B. J.

R. D. Juday, B. J. Daiuto, Opt. Eng. 26, 1094 (1987).

Feldman, M. R.

Fleisher, M.

M. Fleisher, U. Mahlab, J. Shamir, “Entropy-optimized filter for pattern recognition,” Appl. Opt. (to be published).

Guest, C. C.

Juday, R. D.

R. D. Juday, B. J. Daiuto, Opt. Eng. 26, 1094 (1987).

Kikuchi, R.

Kim, M. S.

Kumar, B. V. K. V.

Mahalanobis, X.

Mahlab, U.

M. Fleisher, U. Mahlab, J. Shamir, “Entropy-optimized filter for pattern recognition,” Appl. Opt. (to be published).

Rosen, J.

Rossi, W. A.

Shamir, J.

J. Shamir, H. J. Caulfield, J. Rosen, Appl. Opt. 26, 2311 (1987).
[CrossRef] [PubMed]

M. Fleisher, U. Mahlab, J. Shamir, “Entropy-optimized filter for pattern recognition,” Appl. Opt. (to be published).

Soffer, B. H.

van Luarhoven, P. J. M.

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

Appl. Opt.

J. Opt. Soc. Am.

Opt. Eng.

R. D. Juday, B. J. Daiuto, Opt. Eng. 26, 1094 (1987).

Opt. Lett.

Other

M. Fleisher, U. Mahlab, J. Shamir, “Entropy-optimized filter for pattern recognition,” Appl. Opt. (to be published).

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

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Figures (5)

Fig. 1
Fig. 1

Input pattern for optical correlator.

Fig. 2
Fig. 2

Correlation plane distribution with a phase-only EOF prepared to detect pattern (a) of Fig. 1 and reject pattern (b). (a) Calculated distribution with the two objects placed diagonally, (b) laboratory experiment with the intensity plot along the indicated scan line that crosses the two peaks shown in the calculated plot.

Fig. 3
Fig. 3

As in Fig. 2 but with a phase-only filter matched to pattern (a) of Fig. 1.

Fig. 4
Fig. 4

Point-spread function of (a) the filter of Fig. 2, (b) filter of Fig. 3.

Fig. 5
Fig. 5

Electro-optic learning architecture.

Equations (12)

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C ( x , y ) = f ( x , y ) h * ( x + x , y + y ) d x d y
ϕ ( x , y ) = | C ( x , y ) | 2 | C ( x , y ) | 2 d x d y .
S = ϕ ( x , y ) log ϕ ( x , y ) d x d y .
ϕ D ( m , n ) = { 1 m = k , n = 1 0 otherwise ,
ϕ R ( m , n ) = 1 ( 2 N 1 ) 2 , ( m , n ) .
S max R = log 1 ( 2 N 1 ) 2 , S min D = 0 .
M = { f n D } S D { f n R } S R ,
M min = M [ h EOF ( i , j ) ] .
Δ M = M ( H l + 1 ) M ( H l ) .
P r accept = exp ( Δ M / T ) ,
H ( x f , y f ) = exp [ j θ ( x f , y f ) ] , | H ( x f , y f ) | = 1 .
H 0 ( i , j ) = exp [ j θ 0 ( i , j ) ] , θ 0 ( i , j ) = π [ Rand ( 1 , 1 ) ] ,

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