Abstract

We present a simple method of constructing synthetic discriminant function filters optimized to take into account the modulation of liquid-crystal devices. This relaxation algorithm, a generalization of the Jared and Ennis method, is an iterative method that includes arbitrary modulations for both scene and filter, extending the problem to the complex plane. Simulated and experimental results obtained in a VanderLugt correlator are presented for a two-class recognition problem. The optimal number of images needed to describe an object in a filter generated in this way is discussed, and the influence of the spatial light modulation resolution on the correlation is studied.

© 2004 Optical Society of America

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  1. C. F. Hester, D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980).
    [CrossRef] [PubMed]
  2. Y. N. Hsu, H. H. Arsenault, “Optical character recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
    [CrossRef] [PubMed]
  3. D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
    [CrossRef]
  4. S. Jutamulia, T. Asakura, “Rotation-invariant joint transform correlator,” Appl. Opt. 33, 5440–5442 (1994).
    [CrossRef] [PubMed]
  5. R. D. Juday, “Optimal realizable filters and the minimum Euclidean distance principle,” Appl. Opt. 32, 5100–5111 (1993).
    [CrossRef] [PubMed]
  6. 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]
  7. D. Casasent, W. A. Rozzi, “Computer-generated and phase-only synthetic discriminant function filters,” Appl. Opt. 25, 3767–3772 (1986).
    [CrossRef] [PubMed]
  8. R. R. Kallman, “Direct construction of phase-only filters,” Appl. Opt. 26, 5200–5201 (1987).
    [CrossRef] [PubMed]
  9. D. A. Jared, D. J. Ennis, “Inclusion of filter modulation in synthetic-discriminant-function construction,” Appl. Opt. 28, 232–239 (1989).
    [CrossRef] [PubMed]
  10. M. Montes-Usategui, J. Campos, I. Juvells, “Computation of arbitrarily constrained synthetic discriminant functions,” Appl. Opt. 34, 3904–3914 (1995).
    [CrossRef] [PubMed]
  11. R. D. Juday, “Generality of matched filtering and minimum Euclidean distance projection for optical pattern recognition,” J. Opt. Soc. Am. A 18, 1882–1896 (2001).
    [CrossRef]
  12. M. B. Reid, P. W. Ma, J. D. Downie, E. Ochoa, “Experimental verification of modified synthetic discriminant function filters for rotation invariance,” Appl. Opt. 29, 1209–1212 (1990).
    [CrossRef] [PubMed]
  13. P. C. Miller, R. S. Caprari, “Demonstration of improved automatic target-recognition performance by moment analysis of correlation peaks,” Appl. Opt. 38, 1325–1331 (1999).
    [CrossRef]
  14. D. W. Carlson, B. V. K. Vijaya Kumar, “Synthetic discriminant functions for implementations on arbitrarily constrained devices,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1772, 10–20 (1992).
  15. C. Zeile, E. Lüder, “Complex transmission of liquid crystal light modulators in optical signal processing applications,” in Liquid Crystal Materials, Devices, and Applications II, U. Efron, M. D. Wand, eds., Proc. SPIE1911, 195–206 (1993).
  16. E. Martín-Badosa, A. Carnicer, I. Juvells, S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation,” Meas. Sci. Technol. 8, 764–772 (1997).
    [CrossRef]
  17. M. Montes-Usategui, S. E. Monroe, R. D. Juday, “Automated self-alignment procedure for optical correlators,” Opt. Eng. 36, 1782–1791 (1997).
    [CrossRef]

2001 (1)

1999 (1)

1997 (2)

E. Martín-Badosa, A. Carnicer, I. Juvells, S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation,” Meas. Sci. Technol. 8, 764–772 (1997).
[CrossRef]

M. Montes-Usategui, S. E. Monroe, R. D. Juday, “Automated self-alignment procedure for optical correlators,” Opt. Eng. 36, 1782–1791 (1997).
[CrossRef]

1995 (1)

1994 (1)

1993 (1)

1990 (1)

1989 (1)

1988 (1)

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

1987 (1)

1986 (1)

1985 (1)

1982 (1)

1980 (1)

Arsenault, H. H.

Asakura, T.

Campos, J.

Caprari, R. S.

Carlson, D. W.

D. W. Carlson, B. V. K. Vijaya Kumar, “Synthetic discriminant functions for implementations on arbitrarily constrained devices,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1772, 10–20 (1992).

Carnicer, A.

E. Martín-Badosa, A. Carnicer, I. Juvells, S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation,” Meas. Sci. Technol. 8, 764–772 (1997).
[CrossRef]

Casasent, D.

Downie, J. D.

Ennis, D. J.

Gianino, P. D.

Hester, C. F.

Horner, J. L.

Hsu, Y. N.

Jared, D. A.

Juday, R. D.

Jutamulia, S.

Juvells, I.

E. Martín-Badosa, A. Carnicer, I. Juvells, S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation,” Meas. Sci. Technol. 8, 764–772 (1997).
[CrossRef]

M. Montes-Usategui, J. Campos, I. Juvells, “Computation of arbitrarily constrained synthetic discriminant functions,” Appl. Opt. 34, 3904–3914 (1995).
[CrossRef] [PubMed]

Kallman, R. R.

Konforti, N.

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

Lüder, E.

C. Zeile, E. Lüder, “Complex transmission of liquid crystal light modulators in optical signal processing applications,” in Liquid Crystal Materials, Devices, and Applications II, U. Efron, M. D. Wand, eds., Proc. SPIE1911, 195–206 (1993).

Ma, P. W.

Marom, E.

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

Martín-Badosa, E.

E. Martín-Badosa, A. Carnicer, I. Juvells, S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation,” Meas. Sci. Technol. 8, 764–772 (1997).
[CrossRef]

Mendlovic, D.

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

Miller, P. C.

Monroe, S. E.

M. Montes-Usategui, S. E. Monroe, R. D. Juday, “Automated self-alignment procedure for optical correlators,” Opt. Eng. 36, 1782–1791 (1997).
[CrossRef]

Montes-Usategui, M.

M. Montes-Usategui, S. E. Monroe, R. D. Juday, “Automated self-alignment procedure for optical correlators,” Opt. Eng. 36, 1782–1791 (1997).
[CrossRef]

M. Montes-Usategui, J. Campos, I. Juvells, “Computation of arbitrarily constrained synthetic discriminant functions,” Appl. Opt. 34, 3904–3914 (1995).
[CrossRef] [PubMed]

Ochoa, E.

Reid, M. B.

Rozzi, W. A.

Vallmitjana, S.

E. Martín-Badosa, A. Carnicer, I. Juvells, S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation,” Meas. Sci. Technol. 8, 764–772 (1997).
[CrossRef]

Vijaya Kumar, B. V. K.

D. W. Carlson, B. V. K. Vijaya Kumar, “Synthetic discriminant functions for implementations on arbitrarily constrained devices,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1772, 10–20 (1992).

Zeile, C.

C. Zeile, E. Lüder, “Complex transmission of liquid crystal light modulators in optical signal processing applications,” in Liquid Crystal Materials, Devices, and Applications II, U. Efron, M. D. Wand, eds., Proc. SPIE1911, 195–206 (1993).

Appl. Opt. (11)

C. F. Hester, D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980).
[CrossRef] [PubMed]

Y. N. Hsu, H. H. Arsenault, “Optical character recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
[CrossRef] [PubMed]

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, “Direct construction of phase-only filters,” Appl. Opt. 26, 5200–5201 (1987).
[CrossRef] [PubMed]

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

M. B. Reid, P. W. Ma, J. D. Downie, E. Ochoa, “Experimental verification of modified synthetic discriminant function filters for rotation invariance,” Appl. Opt. 29, 1209–1212 (1990).
[CrossRef] [PubMed]

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

S. Jutamulia, T. Asakura, “Rotation-invariant joint transform correlator,” Appl. Opt. 33, 5440–5442 (1994).
[CrossRef] [PubMed]

P. C. Miller, R. S. Caprari, “Demonstration of improved automatic target-recognition performance by moment analysis of correlation peaks,” Appl. Opt. 38, 1325–1331 (1999).
[CrossRef]

M. Montes-Usategui, J. Campos, I. Juvells, “Computation of arbitrarily constrained synthetic discriminant functions,” Appl. Opt. 34, 3904–3914 (1995).
[CrossRef] [PubMed]

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

Meas. Sci. Technol. (1)

E. Martín-Badosa, A. Carnicer, I. Juvells, S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation,” Meas. Sci. Technol. 8, 764–772 (1997).
[CrossRef]

Opt. Commun. (1)

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

Opt. Eng. (1)

M. Montes-Usategui, S. E. Monroe, R. D. Juday, “Automated self-alignment procedure for optical correlators,” Opt. Eng. 36, 1782–1791 (1997).
[CrossRef]

Other (2)

D. W. Carlson, B. V. K. Vijaya Kumar, “Synthetic discriminant functions for implementations on arbitrarily constrained devices,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1772, 10–20 (1992).

C. Zeile, E. Lüder, “Complex transmission of liquid crystal light modulators in optical signal processing applications,” in Liquid Crystal Materials, Devices, and Applications II, U. Efron, M. D. Wand, eds., Proc. SPIE1911, 195–206 (1993).

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