Abstract

We compare several recently proposed filters for pattern recognition and show that they approximate more or less the optimal filter, which, however, is not so easy to implement.

© 1992 Optical Society of America

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  1. A. B. VanderLugt, “Signal detection by complex matched spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
    [CrossRef]
  2. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  3. J. L. Horner, J. R. Leger “Pattern recognition with binary phase-only filters,” Appl. Opt. 24, 609–611 (1985).
    [CrossRef] [PubMed]
  4. G.-G. Mu, X.-M. Wang, Z.-Q. Wang, “Amplitude-compensated matched filtering,” Appl. Opt. 27, 3461–3463 (1988).
    [CrossRef] [PubMed]
  5. B. V. K. Vijaya Kumar, Z. Bahri, “Phase-only filters with improved signal to noise ratio,” Appl. Opt. 28, 250–257 (1989).
    [CrossRef]
  6. A. A. S. Awwal, M. A. Karim, S. R. Jahan, “Improved correlation discrimination using an amplitude-modulated phase-only filter,” Appl. Opt. 29, 233–236 (1990).
    [CrossRef] [PubMed]
  7. F. M. Dickey, B. V. K. Vijaya Kumar, L. A. Romero, J. M. Connelly, “Complex ternary matched filters yielding high signal to noise ratio,” Opt. Eng. 29, 994–1001 (1990).
    [CrossRef]
  8. W. W. Farn, J. W. Goodman “Optimal binary phase-only matched filters,” Appl. Opt. 27, 4431–4437 (1988).
    [CrossRef] [PubMed]
  9. K. Chlanska-Macukow, T. Nitka, “Phase-only filter as matched filter with enhanced discrimination capability,” Opt. Commun. 64, 224–228 (1987).
    [CrossRef]
  10. A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum average correlation energy filters,” Appl. Opt. 26, 3633–3640 (1987).
    [CrossRef] [PubMed]
  11. A. Mahalanobis, D. Casasent “Performance evaluation of minimum average correlation energy filters,” Appl. Opt. 30, 561–572 (1991).
    [CrossRef] [PubMed]
  12. M. Fleisher, U. Mahlab, J. Shamir, “Entropy optimized filter for pattern recognition,” Appl. Opt. 29, 2091–2098 (1990).
    [CrossRef] [PubMed]
  13. U. Mahlab, M. Fleisher, J. Shamir, “Error probability in optical pattern recognition,” Opt. Commun. 77, 415–422 (1990).
    [CrossRef]
  14. L. P. Yaroslavsky, Digital Picture Processing: an Introduction (Springer-Verlag, Berlin, 1985), p. 276.
  15. L. P. Yaroslavsky, “Applied problems of digital optics,” in Advances in Electronics and Electron Physics, P. Hawkes, ed. (Academic, Orlando, Fla., 1986), Vol. 66, pp. 1–140.
    [CrossRef]
  16. L. P. Yaroslavsky, “Detection and localization of picture details,” Vopr. Radioelektron. ser. Obschetekhnicheskaya 8, 70–74 (1975), in Russian.
  17. L. P. Yaroslavsky, “Optical device for object detection,” Soviet Patent No.536,497, L. P. Yaroslavsky, Byull. Izobretenii (Bulletin of Inventions) 43, 135–137 (1976), in Russian.
  18. L. P. Yaroslavsky, Introduction to Digital Picture Processing (Soviet Radio Publication, Moscow, 1979), p. 312, in Russian.
  19. V. N. Dudinov, V. A. Krishtal′, L. P. Yaroslavsky, “About objects localization by the methods of coherent optics,” Geodez. Kartogr. 1, 42–47 (1977), in Russian.
  20. H. J. Caulfield, W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 8, 2354–2356 (1969).
    [CrossRef] [PubMed]
  21. S. Lowenthal, Y. Belvaux, “Reconnaissance des formes par filtrage des frequences spatiales,” Opt. Acta 14, 245–258 (1967).
    [CrossRef]
  22. R. A. Binns, A. Dickinson, B. M. Watrasiewicz, “Method of increasing discrimination of optical filtering,” Appl. Opt. 7, 1047–1051 (1968).
    [CrossRef] [PubMed]
  23. As it was communicated to this author by A. Lohmann, a concept of Ref. 25 has also been independently developed in experiment and theory by A. VanderLugt (Department of Electrical and Computer Engineering, North Carolina State University, P.O. Box 7911, Raleigh, N.C. 27695-7911) in his Ph.D. dissertation.
  24. B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
    [CrossRef] [PubMed]
  25. B. Javidi, “Comparison of nonlinear joint transform correlator and nonlinearly transformed matched filter based correlator,” Opt. Eng. 29, 1013–1020 (1990).
    [CrossRef]
  26. B. Javidi “Comparison of binary joint transform image correlators and phase-only matched filter correlators,” Opt. Eng. 28, 267–272 (1989).
  27. 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]
  28. M. A. Kaura, W. T. Rhodes, “Optical correlator performance using a phase-with-constrained-magnitude complex spatial filter,” Appl. Opt. 29, 2587–2593 (1990).
    [CrossRef] [PubMed]

1991 (1)

A. Mahalanobis, D. Casasent “Performance evaluation of minimum average correlation energy filters,” Appl. Opt. 30, 561–572 (1991).
[CrossRef] [PubMed]

1990 (6)

F. M. Dickey, B. V. K. Vijaya Kumar, L. A. Romero, J. M. Connelly, “Complex ternary matched filters yielding high signal to noise ratio,” Opt. Eng. 29, 994–1001 (1990).
[CrossRef]

U. Mahlab, M. Fleisher, J. Shamir, “Error probability in optical pattern recognition,” Opt. Commun. 77, 415–422 (1990).
[CrossRef]

B. Javidi, “Comparison of nonlinear joint transform correlator and nonlinearly transformed matched filter based correlator,” Opt. Eng. 29, 1013–1020 (1990).
[CrossRef]

A. A. S. Awwal, M. A. Karim, S. R. Jahan, “Improved correlation discrimination using an amplitude-modulated phase-only filter,” Appl. Opt. 29, 233–236 (1990).
[CrossRef] [PubMed]

M. Fleisher, U. Mahlab, J. Shamir, “Entropy optimized filter for pattern recognition,” Appl. Opt. 29, 2091–2098 (1990).
[CrossRef] [PubMed]

M. A. Kaura, W. T. Rhodes, “Optical correlator performance using a phase-with-constrained-magnitude complex spatial filter,” Appl. Opt. 29, 2587–2593 (1990).
[CrossRef] [PubMed]

1989 (3)

1988 (2)

1987 (2)

K. Chlanska-Macukow, T. Nitka, “Phase-only filter as matched filter with enhanced discrimination capability,” Opt. Commun. 64, 224–228 (1987).
[CrossRef]

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

1986 (1)

1985 (1)

1984 (1)

1977 (1)

V. N. Dudinov, V. A. Krishtal′, L. P. Yaroslavsky, “About objects localization by the methods of coherent optics,” Geodez. Kartogr. 1, 42–47 (1977), in Russian.

1975 (1)

L. P. Yaroslavsky, “Detection and localization of picture details,” Vopr. Radioelektron. ser. Obschetekhnicheskaya 8, 70–74 (1975), in Russian.

1969 (1)

1968 (1)

1967 (1)

S. Lowenthal, Y. Belvaux, “Reconnaissance des formes par filtrage des frequences spatiales,” Opt. Acta 14, 245–258 (1967).
[CrossRef]

1964 (1)

A. B. VanderLugt, “Signal detection by complex matched spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Awwal, A. A. S.

Bahri, Z.

Belvaux, Y.

S. Lowenthal, Y. Belvaux, “Reconnaissance des formes par filtrage des frequences spatiales,” Opt. Acta 14, 245–258 (1967).
[CrossRef]

Binns, R. A.

Casasent, D.

A. Mahalanobis, D. Casasent “Performance evaluation of minimum average correlation energy filters,” Appl. Opt. 30, 561–572 (1991).
[CrossRef] [PubMed]

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

Caulfield, H. J.

Chlanska-Macukow, K.

K. Chlanska-Macukow, T. Nitka, “Phase-only filter as matched filter with enhanced discrimination capability,” Opt. Commun. 64, 224–228 (1987).
[CrossRef]

Connelly, J. M.

F. M. Dickey, B. V. K. Vijaya Kumar, L. A. Romero, J. M. Connelly, “Complex ternary matched filters yielding high signal to noise ratio,” Opt. Eng. 29, 994–1001 (1990).
[CrossRef]

Dickey, F. M.

F. M. Dickey, B. V. K. Vijaya Kumar, L. A. Romero, J. M. Connelly, “Complex ternary matched filters yielding high signal to noise ratio,” Opt. Eng. 29, 994–1001 (1990).
[CrossRef]

Dickinson, A.

Dudinov, V. N.

V. N. Dudinov, V. A. Krishtal′, L. P. Yaroslavsky, “About objects localization by the methods of coherent optics,” Geodez. Kartogr. 1, 42–47 (1977), in Russian.

Farn, W. W.

Fleisher, M.

M. Fleisher, U. Mahlab, J. Shamir, “Entropy optimized filter for pattern recognition,” Appl. Opt. 29, 2091–2098 (1990).
[CrossRef] [PubMed]

U. Mahlab, M. Fleisher, J. Shamir, “Error probability in optical pattern recognition,” Opt. Commun. 77, 415–422 (1990).
[CrossRef]

Gianino, P. D.

Goodman, J. W.

Horner, J. L.

Jahan, S. R.

Javidi, B.

B. Javidi, “Comparison of nonlinear joint transform correlator and nonlinearly transformed matched filter based correlator,” Opt. Eng. 29, 1013–1020 (1990).
[CrossRef]

B. Javidi “Comparison of binary joint transform image correlators and phase-only matched filter correlators,” Opt. Eng. 28, 267–272 (1989).

B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
[CrossRef] [PubMed]

Kallman, R. R.

Karim, M. A.

Kaura, M. A.

Krishtal', V. A.

V. N. Dudinov, V. A. Krishtal′, L. P. Yaroslavsky, “About objects localization by the methods of coherent optics,” Geodez. Kartogr. 1, 42–47 (1977), in Russian.

Leger, J. R.

Lowenthal, S.

S. Lowenthal, Y. Belvaux, “Reconnaissance des formes par filtrage des frequences spatiales,” Opt. Acta 14, 245–258 (1967).
[CrossRef]

Mahalanobis, A.

A. Mahalanobis, D. Casasent “Performance evaluation of minimum average correlation energy filters,” Appl. Opt. 30, 561–572 (1991).
[CrossRef] [PubMed]

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

Mahlab, U.

M. Fleisher, U. Mahlab, J. Shamir, “Entropy optimized filter for pattern recognition,” Appl. Opt. 29, 2091–2098 (1990).
[CrossRef] [PubMed]

U. Mahlab, M. Fleisher, J. Shamir, “Error probability in optical pattern recognition,” Opt. Commun. 77, 415–422 (1990).
[CrossRef]

Maloney, W. T.

Mu, G.-G.

Nitka, T.

K. Chlanska-Macukow, T. Nitka, “Phase-only filter as matched filter with enhanced discrimination capability,” Opt. Commun. 64, 224–228 (1987).
[CrossRef]

Rhodes, W. T.

Romero, L. A.

F. M. Dickey, B. V. K. Vijaya Kumar, L. A. Romero, J. M. Connelly, “Complex ternary matched filters yielding high signal to noise ratio,” Opt. Eng. 29, 994–1001 (1990).
[CrossRef]

Shamir, J.

M. Fleisher, U. Mahlab, J. Shamir, “Entropy optimized filter for pattern recognition,” Appl. Opt. 29, 2091–2098 (1990).
[CrossRef] [PubMed]

U. Mahlab, M. Fleisher, J. Shamir, “Error probability in optical pattern recognition,” Opt. Commun. 77, 415–422 (1990).
[CrossRef]

VanderLugt, A.

As it was communicated to this author by A. Lohmann, a concept of Ref. 25 has also been independently developed in experiment and theory by A. VanderLugt (Department of Electrical and Computer Engineering, North Carolina State University, P.O. Box 7911, Raleigh, N.C. 27695-7911) in his Ph.D. dissertation.

VanderLugt, A. B.

A. B. VanderLugt, “Signal detection by complex matched spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Vijaya Kumar, B. V. K.

Wang, X.-M.

Wang, Z.-Q.

Watrasiewicz, B. M.

Yaroslavsky, L. P.

V. N. Dudinov, V. A. Krishtal′, L. P. Yaroslavsky, “About objects localization by the methods of coherent optics,” Geodez. Kartogr. 1, 42–47 (1977), in Russian.

L. P. Yaroslavsky, “Detection and localization of picture details,” Vopr. Radioelektron. ser. Obschetekhnicheskaya 8, 70–74 (1975), in Russian.

L. P. Yaroslavsky, “Optical device for object detection,” Soviet Patent No.536,497, L. P. Yaroslavsky, Byull. Izobretenii (Bulletin of Inventions) 43, 135–137 (1976), in Russian.

L. P. Yaroslavsky, Introduction to Digital Picture Processing (Soviet Radio Publication, Moscow, 1979), p. 312, in Russian.

L. P. Yaroslavsky, Digital Picture Processing: an Introduction (Springer-Verlag, Berlin, 1985), p. 276.

L. P. Yaroslavsky, “Applied problems of digital optics,” in Advances in Electronics and Electron Physics, P. Hawkes, ed. (Academic, Orlando, Fla., 1986), Vol. 66, pp. 1–140.
[CrossRef]

Appl. Opt. (1)

A. Mahalanobis, D. Casasent “Performance evaluation of minimum average correlation energy filters,” Appl. Opt. 30, 561–572 (1991).
[CrossRef] [PubMed]

Appl. Opt. (13)

M. Fleisher, U. Mahlab, J. Shamir, “Entropy optimized filter for pattern recognition,” Appl. Opt. 29, 2091–2098 (1990).
[CrossRef] [PubMed]

H. J. Caulfield, W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 8, 2354–2356 (1969).
[CrossRef] [PubMed]

J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

J. L. Horner, J. R. Leger “Pattern recognition with binary phase-only filters,” Appl. Opt. 24, 609–611 (1985).
[CrossRef] [PubMed]

G.-G. Mu, X.-M. Wang, Z.-Q. Wang, “Amplitude-compensated matched filtering,” Appl. Opt. 27, 3461–3463 (1988).
[CrossRef] [PubMed]

B. V. K. Vijaya Kumar, Z. Bahri, “Phase-only filters with improved signal to noise ratio,” Appl. Opt. 28, 250–257 (1989).
[CrossRef]

A. A. S. Awwal, M. A. Karim, S. R. Jahan, “Improved correlation discrimination using an amplitude-modulated phase-only filter,” Appl. Opt. 29, 233–236 (1990).
[CrossRef] [PubMed]

W. W. Farn, J. W. Goodman “Optimal binary phase-only matched filters,” Appl. Opt. 27, 4431–4437 (1988).
[CrossRef] [PubMed]

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

R. A. Binns, A. Dickinson, B. M. Watrasiewicz, “Method of increasing discrimination of optical filtering,” Appl. Opt. 7, 1047–1051 (1968).
[CrossRef] [PubMed]

B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
[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]

M. A. Kaura, W. T. Rhodes, “Optical correlator performance using a phase-with-constrained-magnitude complex spatial filter,” Appl. Opt. 29, 2587–2593 (1990).
[CrossRef] [PubMed]

Geodez. Kartogr. (1)

V. N. Dudinov, V. A. Krishtal′, L. P. Yaroslavsky, “About objects localization by the methods of coherent optics,” Geodez. Kartogr. 1, 42–47 (1977), in Russian.

IEEE Trans. Inf. Theory (1)

A. B. VanderLugt, “Signal detection by complex matched spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Opt. Acta (1)

S. Lowenthal, Y. Belvaux, “Reconnaissance des formes par filtrage des frequences spatiales,” Opt. Acta 14, 245–258 (1967).
[CrossRef]

Opt. Eng. (1)

F. M. Dickey, B. V. K. Vijaya Kumar, L. A. Romero, J. M. Connelly, “Complex ternary matched filters yielding high signal to noise ratio,” Opt. Eng. 29, 994–1001 (1990).
[CrossRef]

Opt. Commun. (2)

K. Chlanska-Macukow, T. Nitka, “Phase-only filter as matched filter with enhanced discrimination capability,” Opt. Commun. 64, 224–228 (1987).
[CrossRef]

U. Mahlab, M. Fleisher, J. Shamir, “Error probability in optical pattern recognition,” Opt. Commun. 77, 415–422 (1990).
[CrossRef]

Opt. Eng. (2)

B. Javidi, “Comparison of nonlinear joint transform correlator and nonlinearly transformed matched filter based correlator,” Opt. Eng. 29, 1013–1020 (1990).
[CrossRef]

B. Javidi “Comparison of binary joint transform image correlators and phase-only matched filter correlators,” Opt. Eng. 28, 267–272 (1989).

Vopr. Radioelektron. ser. Obschetekhnicheskaya (1)

L. P. Yaroslavsky, “Detection and localization of picture details,” Vopr. Radioelektron. ser. Obschetekhnicheskaya 8, 70–74 (1975), in Russian.

Other (5)

L. P. Yaroslavsky, “Optical device for object detection,” Soviet Patent No.536,497, L. P. Yaroslavsky, Byull. Izobretenii (Bulletin of Inventions) 43, 135–137 (1976), in Russian.

L. P. Yaroslavsky, Introduction to Digital Picture Processing (Soviet Radio Publication, Moscow, 1979), p. 312, in Russian.

L. P. Yaroslavsky, Digital Picture Processing: an Introduction (Springer-Verlag, Berlin, 1985), p. 276.

L. P. Yaroslavsky, “Applied problems of digital optics,” in Advances in Electronics and Electron Physics, P. Hawkes, ed. (Academic, Orlando, Fla., 1986), Vol. 66, pp. 1–140.
[CrossRef]

As it was communicated to this author by A. Lohmann, a concept of Ref. 25 has also been independently developed in experiment and theory by A. VanderLugt (Department of Electrical and Computer Engineering, North Carolina State University, P.O. Box 7911, Raleigh, N.C. 27695-7911) in his Ph.D. dissertation.

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Figures (2)

Fig. 1
Fig. 1

Comparison of the matched filter, POF filter, and optimal filter.

Fig. 2
Fig. 2

Illustration of signal whitening by the optimal filter.

Equations (3)

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

H ( f ) = S o * ( f ) AV sn S r j ( f ) 2 ,
H ( f ) = 1 [ AV sn S r j ( f ) 2 ] 1 / 2 S o * ( f ) [ AV sn S r j ( f ) 2 ] 1 / 2 .
SNR = F S o ( f ) 2 AV sn S r j ( f ) 2 d f ,

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