Abstract

We suggest a new type of optimized composite filter, i.e., the asymmetric segmented phase-only filter (ASPOF), for improving the effectiveness of a VanderLugt correlator (VLC) when used for face identification. Basically, it consists in merging several reference images after application of a specific spectral optimization method. After segmentation of the spectral filter plane to several areas, each area is assigned to a single winner reference according to a new optimized criterion. The point of the paper is to show that this method offers a significant performance improvement on standard composite filters for face identification. We first briefly revisit composite filters [adapted, phase-only, inverse, compromise optimal, segmented, minimum average correlation energy, optimal trade-off maximum average correlation, and amplitude-modulated phase-only (AMPOF)], which are tools of choice for face recognition based on correlation techniques, and compare their performances with those of the ASPOF. We illustrate some of the drawbacks of current filters for several binary and grayscale image identifications. Next, we describe the optimization steps and introduce the ASPOF that can overcome these technical issues to improve the quality and the reliability of the correlation-based decision. We derive performance measures, i.e., PCE values and receiver operating characteristic curves, to confirm consistency of the results. We numerically find that this filter increases the recognition rate and decreases the false alarm rate. The results show that the discrimination of the ASPOF is comparable to that of the AMPOF, but the ASPOF is more robust than the trade-off maximum average correlation height against rotation and various types of noise sources. Our method has several features that make it amenable to experimental implementation using a VLC.

© 2012 Optical Society of America

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    [CrossRef]
  8. A. Alfalou, G. Keryer, and J. L. de Bougrenet de la Tocnaye, “Optical implementation of segmented composite filtering,” Appl. Opt. 38, 6129–6135 (1999).
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  9. H. J. Caufield and W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 8, 2354–2356 (1969).
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  10. C. F. Hester and D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980).
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  11. A. Mahalanobis, B. V. K. V. Kumar, and D. Casassent, “Minimum average correlation energy filters,” Appl. Opt. 26, 3633–3640 (1987).
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  15. V. H. Diaz-Ramirez, “Constrained composite filter for intraclass distortion invariant object recognition, ” Opt. Lasers Eng. 48, 1153–1160 (2010).
    [CrossRef]
  16. A. Alsamman and M. S. Alam, “Comparative study of face recognition techniques that use joint transform correlation and principal component analysis,” Appl. Opt. 44, 688–692 (2005).
    [CrossRef]
  17. S. Romdhani, J. Ho, T. Vetter, and D. J. Kriegman, “Face recognition using 3-D models: pose and illumination,” Proc. IEEE 94, 1977–1999 (2006).
    [CrossRef]
  18. J. L. Tribillon, Corrélation Optique (Teknéa1999).
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    [CrossRef]
  20. B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
    [CrossRef]
  21. M. S. Alam and M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. 32, 4344–4350 (1993).
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  22. M. S. Alam and S. F. Goh, “Three-dimensional fringe-adjusted joint transform correlation,” Appl. Opt. 43, 3680–3685 (2004).
    [CrossRef]
  23. G. Keryer, J. L. de Bougrenet de la Tocnaye, and A. Alfalou, “Performance comparison of ferroelectric liquid-crystal-technology-based coherent optical multichannel correlators,” Appl. Opt. 36, 3043–3055 (1997).
    [CrossRef]
  24. A. Alfalou, “Implementation of optical multichannel correlators: application to pattern recognition,” Ph.D. thesis (Université de Rennes 1—Ecole Nationale Supérieure des Télécommunications Bretagne, 1999).
  25. B. V. K. V. Kumar and L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
    [CrossRef]
  26. J. L. Horner, “Metrics for assessing pattern-recognition performance,” Appl. Opt. 31, 165–166 (1992).
    [CrossRef]
  27. J. P. Egan, Signal Detection Theory and ROC Analysis, Academic Press Series in Cognition and Perception(Academic, 1975).
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  29. A. Pe’er, D. Wang, A. W. Lohmann, and A. A. Friesem, “Apochromatic optical correlation,” Opt. Lett. 25, 776–778 (2000).
    [CrossRef]
  30. M. Rahman, A. A. S. Awwal, and K. S. Gudmundsson, “Composite filter for search time reduction for 3D model based object recognition,” Proc. SPIE 5201, 97–107 (2003).
    [CrossRef]
  31. T. Mohammad, M. Rahman, A. A. S. Awwal, and K. S. Gudmundsson, “Optical pattern recognition of three dimensional images using composite binary phase only filters,” Proc. SPIE 5556, 146–157 (2004).
    [CrossRef]
  32. D. Casasent and G. Ravichandran, “Advanced distortion-invariant MACE filters,” Appl. Opt. 31, 1109–1116(1992).
    [CrossRef]
  33. K. M. Iftekharuddin, F. Ahmad, and M. A. Karim, “Rotation invariant target recognition using amplitude coupled minimum average correlation energy filter,” Opt. Eng. 35, 1009–1014 (1996).
    [CrossRef]
  34. A. A. S. Awwal, “What can we learn from the shape of a correlation peak for position estimation?” Appl. Opt. 49, B40–B50 (2010).
    [CrossRef]
  35. A. A. S. Awwal, M. A. Karim, and S. R. Jahan, “Improved correlation discrimination using an amplitude-modulated phase-only filter,” Appl. Opt. 29, 233–236 (1990).
    [CrossRef]
  36. A. A. S. Awwal, W. A. McClay, W. S. Fergusson, J. V. Candy, J. T. Salmon, and P. J. Wegner, “Detection and tracking of the back reflection of KDP images in the presence or absence of a phase mask,” Appl. Opt. 45, 3038–3048 (2006).
    [CrossRef]
  37. K. M. Iftekharuddin, M. A. Karim, P. W. Eloe, and A. A. S. Awwal, “Discretized amplitude modulated phase only filter,” Opt. Laser Technol. 28, 93–100 (1996).
    [CrossRef]
  38. K. M. Iftekharuddin, M. A. Karim, and A. A. S. Awwal, “Optimization of amplitude modulated inverse filter,” Math. Comput. Model. 24, 103–112 (1996).
    [CrossRef]
  39. A. Mahalanobis, B. K. V. V. Kumar, S. Song, S. R. F. Sims, and J. F. Epperson, “Unconstrained correlation filters,” Appl. Opt. 33, 3751–3759 (1994).
    [CrossRef]
  40. H. Zhou and T.- H. Chao, “MACH filter synthesizing for detecting targets in cluttered environment for grayscale optical correlator,” Proc. SPIE 3715, 394 (1999).
    [CrossRef]

2011

M. Elbouz, A. Alfalou, and C. Brosseau, “Fuzzy logic and optical correlation-based face recognition method for patient monitoring application in home video surveillance,” Opt. Eng. 50, 067003 (2011).
[CrossRef]

A. Alfalou and C. Brosseau, “Robust and discriminating method for face recognition based on correlation technique and independent component analysis model,” Opt. Lett. 36, 645–647 (2011).
[CrossRef]

2010

A. A. S. Awwal, “What can we learn from the shape of a correlation peak for position estimation?” Appl. Opt. 49, B40–B50 (2010).
[CrossRef]

I. Leonard, A. Arnold-Bos, and A. Alfalou, “Interest of correlation-based automatic target recognition in underwater optical images: theoretical justification and first results,” Proc. SPIE 7678, 76780O (2010).
[CrossRef]

V. H. Diaz-Ramirez, “Constrained composite filter for intraclass distortion invariant object recognition, ” Opt. Lasers Eng. 48, 1153–1160 (2010).
[CrossRef]

2006

2005

2004

M. S. Alam and S. F. Goh, “Three-dimensional fringe-adjusted joint transform correlation,” Appl. Opt. 43, 3680–3685 (2004).
[CrossRef]

T. Mohammad, M. Rahman, A. A. S. Awwal, and K. S. Gudmundsson, “Optical pattern recognition of three dimensional images using composite binary phase only filters,” Proc. SPIE 5556, 146–157 (2004).
[CrossRef]

2003

M. Rahman, A. A. S. Awwal, and K. S. Gudmundsson, “Composite filter for search time reduction for 3D model based object recognition,” Proc. SPIE 5201, 97–107 (2003).
[CrossRef]

2000

1999

H. Zhou and T.- H. Chao, “MACH filter synthesizing for detecting targets in cluttered environment for grayscale optical correlator,” Proc. SPIE 3715, 394 (1999).
[CrossRef]

A. Alfalou, G. Keryer, and J. L. de Bougrenet de la Tocnaye, “Optical implementation of segmented composite filtering,” Appl. Opt. 38, 6129–6135 (1999).
[CrossRef]

1997

1996

K. M. Iftekharuddin, F. Ahmad, and M. A. Karim, “Rotation invariant target recognition using amplitude coupled minimum average correlation energy filter,” Opt. Eng. 35, 1009–1014 (1996).
[CrossRef]

K. M. Iftekharuddin, M. A. Karim, P. W. Eloe, and A. A. S. Awwal, “Discretized amplitude modulated phase only filter,” Opt. Laser Technol. 28, 93–100 (1996).
[CrossRef]

K. M. Iftekharuddin, M. A. Karim, and A. A. S. Awwal, “Optimization of amplitude modulated inverse filter,” Math. Comput. Model. 24, 103–112 (1996).
[CrossRef]

1994

1993

1992

1990

1989

1988

1987

1984

1980

1969

1966

1964

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

Ahmad, F.

K. M. Iftekharuddin, F. Ahmad, and M. A. Karim, “Rotation invariant target recognition using amplitude coupled minimum average correlation energy filter,” Opt. Eng. 35, 1009–1014 (1996).
[CrossRef]

Alam, M. S.

Alfalou, A.

A. Alfalou and C. Brosseau, “Robust and discriminating method for face recognition based on correlation technique and independent component analysis model,” Opt. Lett. 36, 645–647 (2011).
[CrossRef]

M. Elbouz, A. Alfalou, and C. Brosseau, “Fuzzy logic and optical correlation-based face recognition method for patient monitoring application in home video surveillance,” Opt. Eng. 50, 067003 (2011).
[CrossRef]

I. Leonard, A. Arnold-Bos, and A. Alfalou, “Interest of correlation-based automatic target recognition in underwater optical images: theoretical justification and first results,” Proc. SPIE 7678, 76780O (2010).
[CrossRef]

A. Alfalou, G. Keryer, and J. L. de Bougrenet de la Tocnaye, “Optical implementation of segmented composite filtering,” Appl. Opt. 38, 6129–6135 (1999).
[CrossRef]

G. Keryer, J. L. de Bougrenet de la Tocnaye, and A. Alfalou, “Performance comparison of ferroelectric liquid-crystal-technology-based coherent optical multichannel correlators,” Appl. Opt. 36, 3043–3055 (1997).
[CrossRef]

A. Alfalou and C. Brosseau, “Understanding correlation techniques for face recognition: from basics to applications,” in Face Recognition, M. Oravec, ed. (In-Tech, 2010).

I. Leonard, A. Alfalou, and C. Brosseau, “Face recognition based on composite correlation filters: analysis of their performances,” in Face Recognition: Methods, Applications and Technology, A. Quaglia and C. M. Epifano, eds. (Nova, 2012).

A. Alfalou, “Implementation of optical multichannel correlators: application to pattern recognition,” Ph.D. thesis (Université de Rennes 1—Ecole Nationale Supérieure des Télécommunications Bretagne, 1999).

Alsamman, A.

Arnold-Bos, A.

I. Leonard, A. Arnold-Bos, and A. Alfalou, “Interest of correlation-based automatic target recognition in underwater optical images: theoretical justification and first results,” Proc. SPIE 7678, 76780O (2010).
[CrossRef]

Awwal, A. A. S.

A. A. S. Awwal, “What can we learn from the shape of a correlation peak for position estimation?” Appl. Opt. 49, B40–B50 (2010).
[CrossRef]

A. A. S. Awwal, W. A. McClay, W. S. Fergusson, J. V. Candy, J. T. Salmon, and P. J. Wegner, “Detection and tracking of the back reflection of KDP images in the presence or absence of a phase mask,” Appl. Opt. 45, 3038–3048 (2006).
[CrossRef]

T. Mohammad, M. Rahman, A. A. S. Awwal, and K. S. Gudmundsson, “Optical pattern recognition of three dimensional images using composite binary phase only filters,” Proc. SPIE 5556, 146–157 (2004).
[CrossRef]

M. Rahman, A. A. S. Awwal, and K. S. Gudmundsson, “Composite filter for search time reduction for 3D model based object recognition,” Proc. SPIE 5201, 97–107 (2003).
[CrossRef]

K. M. Iftekharuddin, M. A. Karim, and A. A. S. Awwal, “Optimization of amplitude modulated inverse filter,” Math. Comput. Model. 24, 103–112 (1996).
[CrossRef]

K. M. Iftekharuddin, M. A. Karim, P. W. Eloe, and A. A. S. Awwal, “Discretized amplitude modulated phase only filter,” Opt. Laser Technol. 28, 93–100 (1996).
[CrossRef]

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

Brosseau, C.

M. Elbouz, A. Alfalou, and C. Brosseau, “Fuzzy logic and optical correlation-based face recognition method for patient monitoring application in home video surveillance,” Opt. Eng. 50, 067003 (2011).
[CrossRef]

A. Alfalou and C. Brosseau, “Robust and discriminating method for face recognition based on correlation technique and independent component analysis model,” Opt. Lett. 36, 645–647 (2011).
[CrossRef]

A. Alfalou and C. Brosseau, “Understanding correlation techniques for face recognition: from basics to applications,” in Face Recognition, M. Oravec, ed. (In-Tech, 2010).

I. Leonard, A. Alfalou, and C. Brosseau, “Face recognition based on composite correlation filters: analysis of their performances,” in Face Recognition: Methods, Applications and Technology, A. Quaglia and C. M. Epifano, eds. (Nova, 2012).

Candy, J. V.

Casasent, D.

Casassent, D.

Caufield, H. J.

Chao, T.- H.

H. Zhou and T.- H. Chao, “MACH filter synthesizing for detecting targets in cluttered environment for grayscale optical correlator,” Proc. SPIE 3715, 394 (1999).
[CrossRef]

de Bougrenet de la Tocnaye, J. L.

Diaz-Ramirez, V. H.

V. H. Diaz-Ramirez, “Constrained composite filter for intraclass distortion invariant object recognition, ” Opt. Lasers Eng. 48, 1153–1160 (2010).
[CrossRef]

Egan, J. P.

J. P. Egan, Signal Detection Theory and ROC Analysis, Academic Press Series in Cognition and Perception(Academic, 1975).

Elbouz, M.

M. Elbouz, A. Alfalou, and C. Brosseau, “Fuzzy logic and optical correlation-based face recognition method for patient monitoring application in home video surveillance,” Opt. Eng. 50, 067003 (2011).
[CrossRef]

Eloe, P. W.

K. M. Iftekharuddin, M. A. Karim, P. W. Eloe, and A. A. S. Awwal, “Discretized amplitude modulated phase only filter,” Opt. Laser Technol. 28, 93–100 (1996).
[CrossRef]

Epperson, J. F.

Fergusson, W. S.

Friesem, A. A.

Gianino, P. D.

Goh, S. F.

Goodman, J. W.

Gudmundsson, K. S.

T. Mohammad, M. Rahman, A. A. S. Awwal, and K. S. Gudmundsson, “Optical pattern recognition of three dimensional images using composite binary phase only filters,” Proc. SPIE 5556, 146–157 (2004).
[CrossRef]

M. Rahman, A. A. S. Awwal, and K. S. Gudmundsson, “Composite filter for search time reduction for 3D model based object recognition,” Proc. SPIE 5201, 97–107 (2003).
[CrossRef]

Hassebrook, L.

Hester, C. F.

Ho, J.

S. Romdhani, J. Ho, T. Vetter, and D. J. Kriegman, “Face recognition using 3-D models: pose and illumination,” Proc. IEEE 94, 1977–1999 (2006).
[CrossRef]

Horner, J. L.

Iftekharuddin, K. M.

K. M. Iftekharuddin, M. A. Karim, P. W. Eloe, and A. A. S. Awwal, “Discretized amplitude modulated phase only filter,” Opt. Laser Technol. 28, 93–100 (1996).
[CrossRef]

K. M. Iftekharuddin, F. Ahmad, and M. A. Karim, “Rotation invariant target recognition using amplitude coupled minimum average correlation energy filter,” Opt. Eng. 35, 1009–1014 (1996).
[CrossRef]

K. M. Iftekharuddin, M. A. Karim, and A. A. S. Awwal, “Optimization of amplitude modulated inverse filter,” Math. Comput. Model. 24, 103–112 (1996).
[CrossRef]

Jahan, S. R.

Javidi, B.

Jutamulia, S.

F. T. S. Yu and S. Jutamulia, Optical Pattern Recognition (Cambridge University1998).

Karim, M. A.

K. M. Iftekharuddin, M. A. Karim, P. W. Eloe, and A. A. S. Awwal, “Discretized amplitude modulated phase only filter,” Opt. Laser Technol. 28, 93–100 (1996).
[CrossRef]

K. M. Iftekharuddin, M. A. Karim, and A. A. S. Awwal, “Optimization of amplitude modulated inverse filter,” Math. Comput. Model. 24, 103–112 (1996).
[CrossRef]

K. M. Iftekharuddin, F. Ahmad, and M. A. Karim, “Rotation invariant target recognition using amplitude coupled minimum average correlation energy filter,” Opt. Eng. 35, 1009–1014 (1996).
[CrossRef]

M. S. Alam and M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. 32, 4344–4350 (1993).
[CrossRef]

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

Keryer, G.

Kriegman, D. J.

S. Romdhani, J. Ho, T. Vetter, and D. J. Kriegman, “Face recognition using 3-D models: pose and illumination,” Proc. IEEE 94, 1977–1999 (2006).
[CrossRef]

Kumar, B. K. V. V.

Kumar, B. V. K. V.

Kuo, C.-J.

Leonard, I.

I. Leonard, A. Arnold-Bos, and A. Alfalou, “Interest of correlation-based automatic target recognition in underwater optical images: theoretical justification and first results,” Proc. SPIE 7678, 76780O (2010).
[CrossRef]

I. Leonard, A. Alfalou, and C. Brosseau, “Face recognition based on composite correlation filters: analysis of their performances,” in Face Recognition: Methods, Applications and Technology, A. Quaglia and C. M. Epifano, eds. (Nova, 2012).

Lohmann, A. W.

Mahalanobis, A.

Maloney, W. T.

McClay, W. A.

Mohammad, T.

T. Mohammad, M. Rahman, A. A. S. Awwal, and K. S. Gudmundsson, “Optical pattern recognition of three dimensional images using composite binary phase only filters,” Proc. SPIE 5556, 146–157 (2004).
[CrossRef]

Pe’er, A.

Rahman, M.

T. Mohammad, M. Rahman, A. A. S. Awwal, and K. S. Gudmundsson, “Optical pattern recognition of three dimensional images using composite binary phase only filters,” Proc. SPIE 5556, 146–157 (2004).
[CrossRef]

M. Rahman, A. A. S. Awwal, and K. S. Gudmundsson, “Composite filter for search time reduction for 3D model based object recognition,” Proc. SPIE 5201, 97–107 (2003).
[CrossRef]

Ravichandran, G.

Romdhani, S.

S. Romdhani, J. Ho, T. Vetter, and D. J. Kriegman, “Face recognition using 3-D models: pose and illumination,” Proc. IEEE 94, 1977–1999 (2006).
[CrossRef]

Salmon, J. T.

Sims, S. R. F.

Song, S.

Tribillon, J. L.

J. L. Tribillon, Corrélation Optique (Teknéa1999).

VanderLugt, A.

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

Vetter, T.

S. Romdhani, J. Ho, T. Vetter, and D. J. Kriegman, “Face recognition using 3-D models: pose and illumination,” Proc. IEEE 94, 1977–1999 (2006).
[CrossRef]

Wang, D.

Weaver, C. S.

Wegner, P. J.

Yu, F. T. S.

F. T. S. Yu and S. Jutamulia, Optical Pattern Recognition (Cambridge University1998).

Zhou, H.

H. Zhou and T.- H. Chao, “MACH filter synthesizing for detecting targets in cluttered environment for grayscale optical correlator,” Proc. SPIE 3715, 394 (1999).
[CrossRef]

Appl. Opt.

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

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

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

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

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

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

D. Casasent and G. Ravichandran, “Advanced distortion-invariant MACE filters,” Appl. Opt. 31, 1109–1116(1992).
[CrossRef]

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

M. S. Alam and M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. 32, 4344–4350 (1993).
[CrossRef]

A. Mahalanobis, B. K. V. V. Kumar, S. Song, S. R. F. Sims, and J. F. Epperson, “Unconstrained correlation filters,” Appl. Opt. 33, 3751–3759 (1994).
[CrossRef]

G. Keryer, J. L. de Bougrenet de la Tocnaye, and A. Alfalou, “Performance comparison of ferroelectric liquid-crystal-technology-based coherent optical multichannel correlators,” Appl. Opt. 36, 3043–3055 (1997).
[CrossRef]

A. Alfalou, G. Keryer, and J. L. de Bougrenet de la Tocnaye, “Optical implementation of segmented composite filtering,” Appl. Opt. 38, 6129–6135 (1999).
[CrossRef]

M. S. Alam and S. F. Goh, “Three-dimensional fringe-adjusted joint transform correlation,” Appl. Opt. 43, 3680–3685 (2004).
[CrossRef]

A. Alsamman and M. S. Alam, “Comparative study of face recognition techniques that use joint transform correlation and principal component analysis,” Appl. Opt. 44, 688–692 (2005).
[CrossRef]

A. A. S. Awwal, W. A. McClay, W. S. Fergusson, J. V. Candy, J. T. Salmon, and P. J. Wegner, “Detection and tracking of the back reflection of KDP images in the presence or absence of a phase mask,” Appl. Opt. 45, 3038–3048 (2006).
[CrossRef]

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

J. L. Horner, “Metrics for assessing pattern-recognition performance,” Appl. Opt. 31, 165–166 (1992).
[CrossRef]

B. Javidi and C.-J. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
[CrossRef]

C. S. Weaver and J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
[CrossRef]

A. A. S. Awwal, “What can we learn from the shape of a correlation peak for position estimation?” Appl. Opt. 49, B40–B50 (2010).
[CrossRef]

IEEE Trans. Inf. Theory

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

Math. Comput. Model.

K. M. Iftekharuddin, M. A. Karim, and A. A. S. Awwal, “Optimization of amplitude modulated inverse filter,” Math. Comput. Model. 24, 103–112 (1996).
[CrossRef]

Opt. Eng.

K. M. Iftekharuddin, F. Ahmad, and M. A. Karim, “Rotation invariant target recognition using amplitude coupled minimum average correlation energy filter,” Opt. Eng. 35, 1009–1014 (1996).
[CrossRef]

M. Elbouz, A. Alfalou, and C. Brosseau, “Fuzzy logic and optical correlation-based face recognition method for patient monitoring application in home video surveillance,” Opt. Eng. 50, 067003 (2011).
[CrossRef]

Opt. Laser Technol.

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Figures (17)

Fig. 1.
Fig. 1.

Schematic of the principle of the VLC scheme.

Fig. 2.
Fig. 2.

Illustrating the saturation effect: (a) three 8 bit grayscale images. (b) Image obtained by a classical linear combination of the three images shown in (a). (c) Image obtained using an optimized merging (spectral segmentation).

Fig. 3.
Fig. 3.

Technique used to classify the reference images in two subclasses.

Fig. 4.
Fig. 4.

Optimized assignment procedure for isolated pixels.

Fig. 5.
Fig. 5.

Merging technique based on the Fourier plane symmetry property.

Fig. 6.
Fig. 6.

PCEs obtained with ten-reference POF, SPOF, AMPOF, and ASPOF. (a) t=1, (b) t=5, (c) t=10, and (d) t=20.

Fig. 7.
Fig. 7.

PCEs obtained with a ten-reference ASPOF and t=10 pixels. (a) p1=p2=1, (b) p1=2 and p2=1.5.

Fig. 8.
Fig. 8.

PCEs obtained with the composite POF. The colors shown in the key denote the different filters as a function of the number of references used.

Fig. 9.
Fig. 9.

Discrimination results: (a) the target image is the letter V. (b) PCEs obtained with a filter fabricated with reference images of letter A. The colors shown in the key denote the different filters as a function of the number of references used.

Fig. 10.
Fig. 10.

PCEs obtained with the inverse composite filter. The colors shown in the key denote the different filters against the number of references used.

Fig. 11.
Fig. 11.

(a) Illustrating the letter A with additive background noise. (b) Same as in (a) with a rotation angle of 50°. (c) Illustrating the letter A with structured noise. (d) Same as in (c) with a rotation angle of 50°. (e) Illustrating the letter A for a weak contrast. (f) PCEs obtained with the OT composite filter taking α=0.6. The colors shown in the key denote the different filters versus the number of references used.

Fig. 12.
Fig. 12.

PCEs obtained with a ten-reference MACE when the target images are noiseless. Several examples of the rotated letter A are shown at the bottom of this figure. The inset shows two correlation planes. (Right) Autocorrelation obtained without rotation. (Left) Intercorrelation obtained with the letter A oriented at 75°.

Fig. 13.
Fig. 13.

Output normalized Fourier planes obtained by correlating of the same target image (letter A with a rotation angle of 75°) with (a) ASPOF, (b) composite filter, and (c) AMPOF.

Fig. 14.
Fig. 14.

Comparison between the different correlations of letter A (we consider rotation angles ranging between 90° and 90°) with the ten-reference composite filters: POF (blue line), segmented (red line), AMPOF (black line), and ASPOF (green line). (a) PCEs obtained using the optimization stage concerning the isolated pixels, (b) PCEs obtained without the optimization stage concerning the isolated pixels. (c) and (d) represent the PCEs obtained with noised target images.

Fig. 15.
Fig. 15.

ROC curves obtained with ten-reference composite filters: POF (red), SPOF (green), AMPOF (purple), and ASPOF (navy blue). The sky-blue line shows the random guess.

Fig. 16.
Fig. 16.

Example of face images from the PHPID that were captured under variable angle conditions, i.e., from top to bottom, +15°, 0°, +15°; from left to right, 90°, 0°, +90°. (a) Target faces; (b) references.

Fig. 17.
Fig. 17.

(a) ROC curves obtained by correlating faces of a given subject, e.g., Fig. 9(a), with six other individuals with five-reference ASPOF (navy blue) and POF (red) composite filters. The sky-blue line shows the random guess. (b) ROC curve obtained with an OT-MACH.

Tables (1)

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Table 1. Different Composite Filters Used in This Studya

Equations (5)

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PCE=(Energy in the correlation peak)/(overall in the correlation plane).
PCE=x=x0tx=x0+ty=y0ty=y0+t|C(x,y)|2/x=1x=Ny=1y=M|C(x,y)|2,
Eu,vli,jEi,jl><Eu,vki,jEi,jk,
HSPOF1={Spectu,vlifEu,vli,jEi,jlaEu,vki,jEi,jkwithl[0,N1]Not affectedotherwise.
PCEA=x=x0tx=x0+ty=y0ty=y0+t|2C(x,y)|2x=1x=Ny=1y=M|C(x,y)|2+3(x=x0tx=x0+ty=y0ty=y0+t|C(x,y)|2).

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