Abstract

An algorithm for computing correlation filters based on synthetic discriminant functions that can be displayed on current spatial light modulators is presented. The procedure is nondivergent, computationally feasible, and capable of producing multiple solutions, thus overcoming some of the pitfalls of previous methods.

© 1995 Optical Society of America

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  1. B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
    [CrossRef]
  2. A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum average correlation energy filters,” Appl. Opt. 26, 3633–3640 (1987).
    [CrossRef] [PubMed]
  3. B. V. K. Vijaya Kumar, “Minimum variance synthetic discriminant functions,” J. Opt. Soc. Am. A 3, 1579–1584 (1986).
    [CrossRef]
  4. Ph. Réfrégier, “Optimal trade-off filters for noise robustness, sharpness of the correlation peak and Horner efficiency,” Opt. Lett. 16, 829–831 (1991).
    [CrossRef] [PubMed]
  5. Ph. Réfrégier, “Méthodes de reconnaissance des formes pour la corrélation optique,” Rev. Tech. Thomson-CSF 22, 649–734 (1990).
  6. R. D. Juday, “Optimal realizable filters and the minimum Euclidean distance principle,” Appl. Opt. 32, 5100–5111 (1993).
    [CrossRef] [PubMed]
  7. V. Laude, Ph. Réfrégier, “Multicriteria characterization of coding domains with optimal Fourier spatial light modulators filters,” Appl. Opt. 33, 4465–4471 (1994).
    [CrossRef] [PubMed]
  8. J. L. Horner, P. D. Gianino, “Applying the phase-only filter concept to the synthetic discriminant function correlation filter,” Appl. Opt. 24, 851–855 (1985).
    [CrossRef] [PubMed]
  9. D. Casasent, W. A. Rozzi, “Computer-generated and phase-only synthetic discriminant function filters,” Appl. Opt. 25, 3767–3772 (1986).
    [CrossRef] [PubMed]
  10. R. R. Kallman, “Optimal low noise phase-only and binary phase-only optical correlation filters for threshold detectors,” Appl. Opt. 25, 4216–4217 (1986).
    [CrossRef] [PubMed]
  11. D. A. Jared, D. J. Ennis, “Inclusion of filter modulation in synthetic-discriminant-function construction,” Appl. Opt. 28, 232–239 (1989).
    [CrossRef] [PubMed]
  12. Z. Bahri, B. V. K. Vijaya Kumar, “Algorithms for designing phase-only synthetic discriminant functions,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1151, 138–147 (1989).
  13. D. W. Carlson, B. V. K. Vijaya Kumar, “Synthetic discriminant functions for implementation on arbitrarily constrained devices,” in Optical Information Processing Systems and Architectures IV, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1772, 10–20 (1992).
  14. U. Mahlab, J. Shamir, “Phase-only entropy-optimized filter generated by simulated annealing,” Opt. Lett. 14, 1168–1170 (1989).
    [CrossRef] [PubMed]
  15. J. Rosen, J. Shamir, “Application of the projection-onto-constraint-sets algorithm for optical pattern recognition,” Opt. Lett. 16, 752–754 (1991).
    [CrossRef] [PubMed]
  16. D. C. Youla, H. Webb, “Image restoration by the method of convex projections: Part 1-theory,” IEEE Trans. Med. Imaging 1, 81–94 (1982).
    [CrossRef] [PubMed]
  17. Z. Bahri, B. V. K. Vijaya Kumar, “Generalized synthetic discriminant functions,” J. Opt. Soc. Am. A 5, 562–571 (1988).
    [CrossRef]
  18. B. V. K. Vijaya Kumar, Z. Bahri, A. Mahalanobis, “Constrained phase optimization in minimum variance synthetic discriminant functions,” Appl. Opt. 27, 409–413 (1988).
    [CrossRef]
  19. Ph. Réfrégier, J. P. Huignard, “Phase selection of synthetic discriminant functions filters,” Appl. Opt. 29, 4772–4778 (1990).
    [CrossRef] [PubMed]
  20. B. V. K. Vijaya Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
    [CrossRef]

1994 (1)

1993 (1)

1992 (1)

1991 (2)

1990 (3)

1989 (2)

1988 (2)

1987 (1)

1986 (3)

1985 (1)

1982 (1)

D. C. Youla, H. Webb, “Image restoration by the method of convex projections: Part 1-theory,” IEEE Trans. Med. Imaging 1, 81–94 (1982).
[CrossRef] [PubMed]

Bahri, Z.

Z. Bahri, B. V. K. Vijaya Kumar, “Generalized synthetic discriminant functions,” J. Opt. Soc. Am. A 5, 562–571 (1988).
[CrossRef]

B. V. K. Vijaya Kumar, Z. Bahri, A. Mahalanobis, “Constrained phase optimization in minimum variance synthetic discriminant functions,” Appl. Opt. 27, 409–413 (1988).
[CrossRef]

Z. Bahri, B. V. K. Vijaya Kumar, “Algorithms for designing phase-only synthetic discriminant functions,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1151, 138–147 (1989).

Carlson, D. W.

D. W. Carlson, B. V. K. Vijaya Kumar, “Synthetic discriminant functions for implementation on arbitrarily constrained devices,” in Optical Information Processing Systems and Architectures IV, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1772, 10–20 (1992).

Casasent, D.

Ennis, D. J.

Gianino, P. D.

Hassebrook, L.

Horner, J. L.

Huignard, J. P.

Jared, D. A.

Juday, R. D.

Kallman, R. R.

Laude, V.

Mahalanobis, A.

Mahlab, U.

Réfrégier, Ph.

Rosen, J.

Rozzi, W. A.

Shamir, J.

Vijaya Kumar, B. V. K.

Webb, H.

D. C. Youla, H. Webb, “Image restoration by the method of convex projections: Part 1-theory,” IEEE Trans. Med. Imaging 1, 81–94 (1982).
[CrossRef] [PubMed]

Youla, D. C.

D. C. Youla, H. Webb, “Image restoration by the method of convex projections: Part 1-theory,” IEEE Trans. Med. Imaging 1, 81–94 (1982).
[CrossRef] [PubMed]

Appl. Opt. (11)

J. L. Horner, P. D. Gianino, “Applying the phase-only filter concept to the synthetic discriminant function correlation filter,” Appl. Opt. 24, 851–855 (1985).
[CrossRef] [PubMed]

D. Casasent, W. A. Rozzi, “Computer-generated and phase-only synthetic discriminant function filters,” Appl. Opt. 25, 3767–3772 (1986).
[CrossRef] [PubMed]

R. R. Kallman, “Optimal low noise phase-only and binary phase-only optical correlation filters for threshold detectors,” Appl. Opt. 25, 4216–4217 (1986).
[CrossRef] [PubMed]

A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum average correlation energy filters,” Appl. Opt. 26, 3633–3640 (1987).
[CrossRef] [PubMed]

B. V. K. Vijaya Kumar, Z. Bahri, A. Mahalanobis, “Constrained phase optimization in minimum variance synthetic discriminant functions,” Appl. Opt. 27, 409–413 (1988).
[CrossRef]

D. A. Jared, D. J. Ennis, “Inclusion of filter modulation in synthetic-discriminant-function construction,” Appl. Opt. 28, 232–239 (1989).
[CrossRef] [PubMed]

B. V. K. Vijaya Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
[CrossRef]

B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
[CrossRef]

R. D. Juday, “Optimal realizable filters and the minimum Euclidean distance principle,” Appl. Opt. 32, 5100–5111 (1993).
[CrossRef] [PubMed]

V. Laude, Ph. Réfrégier, “Multicriteria characterization of coding domains with optimal Fourier spatial light modulators filters,” Appl. Opt. 33, 4465–4471 (1994).
[CrossRef] [PubMed]

Ph. Réfrégier, J. P. Huignard, “Phase selection of synthetic discriminant functions filters,” Appl. Opt. 29, 4772–4778 (1990).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging (1)

D. C. Youla, H. Webb, “Image restoration by the method of convex projections: Part 1-theory,” IEEE Trans. Med. Imaging 1, 81–94 (1982).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

Opt. Lett. (3)

Rev. Tech. Thomson-CSF (1)

Ph. Réfrégier, “Méthodes de reconnaissance des formes pour la corrélation optique,” Rev. Tech. Thomson-CSF 22, 649–734 (1990).

Other (2)

Z. Bahri, B. V. K. Vijaya Kumar, “Algorithms for designing phase-only synthetic discriminant functions,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1151, 138–147 (1989).

D. W. Carlson, B. V. K. Vijaya Kumar, “Synthetic discriminant functions for implementation on arbitrarily constrained devices,” in Optical Information Processing Systems and Architectures IV, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1772, 10–20 (1992).

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