Abstract

A binary phase only filter is encoded with a simulated annealing algorithm to classify two similar characters in a variety of fonts. Characters that cannot be distinguished with conventional filter encoding methods are clearly distinguished with the optimized binary phase only filter using a simulated annealing algorithm. This method gives zero error classification rate for tested characters. Correlation performance of the optimized binary phase only filter is compared with the binary phase only filters encoded with conventional methods. The computational requirements for optimizing the filter are not excessive.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. L. Horner, J. R. Leger, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. 24, 609–611 (1985).
    [Crossref] [PubMed]
  2. D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlations with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
    [Crossref]
  3. D. M. Cottrell, R. A. Lilly, J. A. Davis, T. Day, “Optical Correlator Performance of Binary Phase-Only Filters Using Fourier and Hartley Transforms,” Appl. Opt. 26, 3755–3761 (1987).
    [Crossref] [PubMed]
  4. M. W. Farn, J. W. Goodman, “Optimal Binary Phase-Only Matched Filters,” Appl. Opt. 27, 4431–4437 (1988).
    [Crossref] [PubMed]
  5. A. B. Vanderlugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  6. H. J. Caulfield, R. Haimes, D. Casasent, Opt. Eng. 19, 152–156 (1980).
  7. S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–679 (1983).
    [Crossref]
  8. S. Geman, D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-6, 721–741 (1984).
    [Crossref]
  9. M. S. Kim, M. R. Feldman, C. C. Guest, “Optimum Encoding of Binary Phase Only Filters with a Simulated Annealing Algorithm,” Opt. Lett. 14, 545–547 (1989).
    [Crossref] [PubMed]
  10. H. Szu, “Nonconvex Optimization by Fast Simulated Annealing,” Proc. IEEE 75, 1538–1540 (1987).
    [Crossref]
  11. M. S. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of Digital Holograms by Direct Binary Search,” Appl. Opt. 26, 2788–2798 (1987).
    [Crossref] [PubMed]
  12. H. Szu, “Three Layers of Vector Outer Product Neural Networks for Optical Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 312–330 (1986).
  13. M. S. Kim, C. C. Guest, submitted to Appl. Opt.
  14. Q. Tian, Y. Fainman, Z. H. Gu, S. H. Lee, “Comparison of Statistical Pattern-Recognition Algorithms for Hybrid Processing. I. Linear-Mapping Algorithms,” J. Opt. Soc. Am. A 5, 1655–1669 (1988).
    [Crossref]

1989 (1)

1988 (2)

1987 (3)

1986 (1)

H. Szu, “Three Layers of Vector Outer Product Neural Networks for Optical Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 312–330 (1986).

1985 (1)

1984 (2)

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlations with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[Crossref]

S. Geman, D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-6, 721–741 (1984).
[Crossref]

1983 (1)

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–679 (1983).
[Crossref]

1980 (1)

H. J. Caulfield, R. Haimes, D. Casasent, Opt. Eng. 19, 152–156 (1980).

1964 (1)

A. B. Vanderlugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Allebach, J. P.

Casasent, D.

H. J. Caulfield, R. Haimes, D. Casasent, Opt. Eng. 19, 152–156 (1980).

Caulfield, H. J.

H. J. Caulfield, R. Haimes, D. Casasent, Opt. Eng. 19, 152–156 (1980).

Cottrell, D. M.

Davis, J. A.

Day, T.

Fainman, Y.

Farn, M. W.

Feldman, M. R.

Gelatt, C. D.

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–679 (1983).
[Crossref]

Geman, D.

S. Geman, D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-6, 721–741 (1984).
[Crossref]

Geman, S.

S. Geman, D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-6, 721–741 (1984).
[Crossref]

Goodman, J. W.

Gu, Z. H.

Guest, C. C.

Haimes, R.

H. J. Caulfield, R. Haimes, D. Casasent, Opt. Eng. 19, 152–156 (1980).

Horner, J. L.

Kim, M. S.

Kirpatrick, S.

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–679 (1983).
[Crossref]

Lee, S. H.

Leger, J. R.

Lilly, R. A.

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlations with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[Crossref]

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlations with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[Crossref]

Seldowitz, M. S.

Sweeney, D. W.

Szu, H.

H. Szu, “Nonconvex Optimization by Fast Simulated Annealing,” Proc. IEEE 75, 1538–1540 (1987).
[Crossref]

H. Szu, “Three Layers of Vector Outer Product Neural Networks for Optical Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 312–330 (1986).

Tian, Q.

Vanderlugt, A. B.

A. B. Vanderlugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Vecchi, M. P.

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–679 (1983).
[Crossref]

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlations with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[Crossref]

Appl. Opt. (4)

IEEE Trans. Inf. Theory (1)

A. B. Vanderlugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

IEEE Trans. Pattern Anal. Machine Intell. (1)

S. Geman, D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-6, 721–741 (1984).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlations with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[Crossref]

H. J. Caulfield, R. Haimes, D. Casasent, Opt. Eng. 19, 152–156 (1980).

Opt. Lett. (1)

Proc. IEEE (1)

H. Szu, “Nonconvex Optimization by Fast Simulated Annealing,” Proc. IEEE 75, 1538–1540 (1987).
[Crossref]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

H. Szu, “Three Layers of Vector Outer Product Neural Networks for Optical Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 312–330 (1986).

Science (1)

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–679 (1983).
[Crossref]

Other (1)

M. S. Kim, C. C. Guest, submitted to Appl. Opt.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Training set in P-class.

Fig. 2
Fig. 2

Training set in R-class.

Fig. 3
Fig. 3

Test set in P-class.

Fig. 4
Fig. 4

Test set in R-class.

Fig. 5
Fig. 5

Flow diagram to optimize the BPOF with the SA algorithm.

Fig. 6
Fig. 6

System energy vs temperature parameter for optimizing the BPOF with the training characters in Figs. 1 and 2.

Fig. 7
Fig. 7

Phase vs temperature parameter for optimizing the BPOF with the training characters in Figs. 1 and 2.

Fig. 8
Fig. 8

Classification performance of the OBPOF. Intensity units of I1 and I2 are arbitrary in Figs. 8 to 10.

Fig. 9
Fig. 9

Classification performance of the BPOF encoded by Eq. (1).

Fig. 10
Fig. 10

Classification performance of the BPOF encoded by Eq. (1) after the filter function is calculated by the unified pseudo-inverse algorithm.

Tables (1)

Tables Icon

Table I Calculated Values of I1 and I2a with the Training Characters In Figs. 1 and 2 and the Test Characters In Figs. 3 and 4

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

F ^ ( u , v ) = 1 for Im [ F ( u , v ) ] 0 F ^ ( u , v ) = - 1 otherwise
F ^ ( u , v ) = 1 for Re [ F ( u , v ) ] > 0 F ^ ( u , v ) = - 1 otherwise
F ^ ( u , v ) = [ 1 - exp ( j ϕ ) ] B ( u , v ) + exp ( j ϕ ) ,
F ^ ( u , v ) = 1 for B ( u , v ) = 1 exp ( j ϕ ) for B ( u , v ) = 0.
G ( u , v ) = [ 1 - exp ( j ϕ ) ] B ( u , v ) A ( u , v ) + exp ( j ϕ ) A ( u , v ) .
G ( u , v ) = [ 1 - exp ( j ϕ ) ] k = - K / 2 K / 2 l = - L / 2 L / 2 B k l A k l × rect ( u - k Δ u Δ u , v - l Δ v Δ v ) + exp ( j ϕ ) k = - K / 2 K / 2 l = - L / 2 L / 2 A k l rect ( u - k Δ u Δ u , v - l Δ v Δ v ) ,
g ( x , y ) = [ 1 - exp ( j ϕ ) ] C g ˜ ( x , y ) + exp ( j ϕ ) C a ˜ ( x , y ) ,
g ˜ ( x , y ) = k l B k l A k l exp [ - 2 π j ( k x Δ u + l y Δ v ) ] ,
a ˜ ( x , y ) = k l A k l exp [ - 2 π j ( k x Δ u + l y Δ v ) ] .
g ( m Δ x , n Δ y ) = [ 1 - exp ( j ϕ ) ] C g ˜ m n + exp ( j ϕ ) C a ˜ m n
g ˜ m n = k l B k l A k l exp [ - 2 π j ( k m / K + l n / L ) ] a ˜ m n = k l A k l exp [ - 2 π j ( k m / K + l n / L ) ] .
g m n = [ 1 - exp ( j ϕ ) ] g ˜ m n + exp ( j ϕ ) a ˜ m n ,
P ( Δ E ) = 1 1 + exp ( Δ E / T ) ,
E = i = 1 N { ( T A - A C [ P i , P ] ) 2 + ( T A - A C [ R i , R ] ) 2 } + i = 1 N { ( T C - C C [ P i , R ] ) 2 + ( T C - C C [ R i , P ] ) 2 } + i = 1 N { ( T P - A C [ P i , P ] / C C [ P i , R ] ) 2 + ( T R - A C [ R i , R ] / C C [ R i , P ] ) 2 } ,
g ˜ m n new = g ˜ m n old - A k l exp [ - 2 π j ( m k / K + n l / L ) ] .
g ˜ m n new = g ˜ m n old + A k l exp [ - 2 π j ( m k / K + n l / L ) ] .

Metrics