Abstract

A tutorial survey is presented of the many composite filter designs proposed for distortion-invariant optical pattern recognition. Remarks are made throughout regarding areas for further investigation.

© 1992 Optical Society of America

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1992 (3)

1991 (8)

1990 (12)

T. Walsh, M. Giles, “Statistical filtering of time-sequenced peak correlation responses for distortion-invariant recognition of multiple input objects,” Opt. Eng. 29, 1052–1064 (1990).
[CrossRef]

S. I. Sudharsanan, A. Mahalanobis, M. K. Sundareshan, “Selection of optimum output correlation values in synthetic discriminant function design,” J. Opt. Soc. Am. A 7, 611–616 (1990).
[CrossRef]

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

M. Fleisher, U. Mahlab, J. Shamir, “Entropy optimized filter for pattern recognition,” Appl. Opt. 29, 2091–2098 (1990).
[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, 1209–1214 (1990).
[CrossRef] [PubMed]

L. Hassebrook, B. V. K. Vijaya Kumar, L. Hostetler, “Linear phase coefficient composite filter banks for distortion-invariant optical pattern recognition,” Opt. Eng. 29, 1033–1043 (1990).
[CrossRef]

Ph. Refregier, “Filter design for optical pattern recognition: multicriteria optimization approach,” Opt. Lett. 15, 854–856 (1990).
[CrossRef] [PubMed]

S. I. Sudharsanan, A. Mahalanobis, M. K. Sundareshan, “A unified framework for the synthesis of synthetic discriminant functions with reduced noise variance and sharp correlation structure,” Opt. Eng. 29, 1021–1028 (1990).
[CrossRef]

P. A. Molley, K. T. Stalker, “Acousto-optic signal processing for real-time image recognition,” Opt. Eng. 29, 1073–1080 (1990).
[CrossRef]

U. Mahlab, J. Rosen, J. Shamir, “Iterative generation of holograms on spatial light modulator,” Opt. Lett. 15, 556–558 (1990).
[CrossRef] [PubMed]

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

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

1989 (13)

B. V. K. Vijaya Kumar, A. Lee, J. M. Connelly, “Estimating object rotation and scale using correlation filters,” Opt. Eng. 28, 474–481 (1989).

M. W. Farn, J. W. Goodman, “Optimal maximum correlation filters for arbitrarily constrained devices,” Appl. Opt. 28, 3326–3366 (1989).

R. D. Juday, “Correlation with a spatial light modulator having phase and amplitude cross coupling,” Appl. Opt. 28, 4865–4869 (1989).
[CrossRef] [PubMed]

U. Mahlab, J. Shamir, “Phase-only entropy optimized filter generated by simulated annealing,” Opt. Lett. 14, 1168–1170 (1989).
[CrossRef] [PubMed]

F. M. Dickey, B. D. Hansche, “Quad-phase correlation filters for pattern recognition,” Appl. Opt. 28, 1611–1613 (1989).
[CrossRef] [PubMed]

B. V. K. Vijaya Kumar, D. Casasent, A. Mahalanobis, “Correlation filters for target in a Markov model background clutter,” Appl. Opt. 28, 3112–3119 (1989).
[CrossRef]

L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation invariant phase-only and binary phase-only correlation,” Appl. Opt. 28, 1251–56 (1989).
[CrossRef] [PubMed]

Y. Sheng, H. H. Arsenault, “Object detection from a real scene using the correlation peak coordinates of multiple circular harmonic filters,” Appl. Opt. 28, 245–249 (1989).
[CrossRef] [PubMed]

H. F. Yau, C. C. Chang, “Phase-only circular harmonic matched filtering,” Appl. Opt. 28, 2070–2074 (1989).
[CrossRef] [PubMed]

K. H. Fielding, S. K. Rogers, M. Kabrisky, J. P. Mills, “Position, scale and rotation invariant halographic associative memory,” Opt. Eng. 28, 849–853 (1989).

D. L. Flannery, J. L. Horner, “Fourier optical processors,” Proc. IEEE 77, 1511–1527 (1989).
[CrossRef]

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

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]

1988 (6)

1987 (11)

J. Rosen, J. Shamir, “Distortion-invariant pattern recognition with phase filters,” Appl. Opt. 26, 2315–2319 (1987).
[CrossRef] [PubMed]

R. D. Juday, B. J. Daiuto, “Relaxation method of compensation in an optical correlator,” Opt. Eng. 26, 1094–1101 (1987).

D. W. Sweeney, E. Ochoa, G. F. Schils, “Experimental use of iteratively designed rotation invariant correlation filters,” Appl. Opt. 26, 3485–3465 (1987).
[CrossRef]

D. Casasent, A. Mahalanobis, “Rule-based symbolic processor for object recognition,” Appl. Opt. 26, 4795–4802 (1987).
[CrossRef] [PubMed]

K. F. Cheung, L. E. Atlas, J. A. Ritcey, C. A. Green, R. J. Marks, “Conventional and composite matched filters with error correction: a comparison,” Appl. Opt. 26, 4235–4239 (1987).
[CrossRef] [PubMed]

S. Leibowitz, D. Casasent, “Error-correction coding in an associative processor,” Appl. Opt. 26, 999–1006 (1987).
[CrossRef]

Y. Sheng, H. H. Arsenault, “Method for determining expansion centers and predicting sidelobe levels for circular-harmonic filter,” J. Opt. Soc. Am. A 4, 1793–1797 (1987).
[CrossRef]

H. H. Arsenault, Y. Sheng, J. Bulabois, “Modified composite filter for pattern recognition in the presence of noise with non-zero mean,” Opt. Commun. 63, 15–20 (1987).
[CrossRef]

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

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

Z. H. Gu, S. H. Lee, “Classification of multiclassed stochastic images buried in additive noise,” J. Opt. Soc. Am. A 4, 712–719 (1987).
[CrossRef]

1986 (10)

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

R. R. Kallman, “The construction of low noise optical correlation filters,” Appl. Opt. 25, 1032–1033 (1986).
[CrossRef] [PubMed]

B. V. K. Vijaya Kumar, “Minimum variance synthetic discriminant functions,” J. Opt. Soc. Am. A 3, 1579–1584 (1986).
[CrossRef]

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]

H. H. Arsenault, C. Ferreira, M. P. Levesque, T. Szpolik, “Simple filter with limited rotation invariance,” Appl. Opt. 25, 3230–3234 (1986).
[CrossRef] [PubMed]

A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Spatial-temporal correlation filter for inplane distortion invariance,” Appl. Opt. 25, 4466–4472 (1986).
[CrossRef] [PubMed]

K. Mersereau, G. M. Morris, “Scale, rotation and shift invariant image recognition,” Appl. Opt. 25, 2338–2342 (1986).
[CrossRef] [PubMed]

G. F. Schils, D. W. Sweeney, “Iterative technique for the synthesis of optical-correlation filters,” J. Opt. Soc. Am. A 3, 1433–1442 (1986).
[CrossRef]

B. V. K. Vijaya Kumar, E. Pochapsky, “Signal-to-noise ratio considerations in modified matched spatial filters,” J. Opt. Soc. Am. A 3, 777–786 (1986).
[CrossRef]

D. Casasent, W. T. Chang, “Correlation synthetic discriminant functions,” Appl. Opt. 25, 2343–2350 (1986).
[CrossRef] [PubMed]

1985 (2)

1984 (9)

Z. H. Gu, S. H. Lee, “Optical implementation of the Hotelling trace criterion for image classification,” Opt. Eng. 23, 727–731 (1984).

J. Riggins, S. Butler, “Simulation of synthetic discriminant function optical implementation,” Opt. Eng. 23, 721–726 (1984).

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

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

D. Psaltis, “Two-dimensional optical processing using one-dimensional input devices,” Proc. IEEE 72, 962–974 (1984).
[CrossRef]

R. Wu, H. Stark, “Rotation-invariant pattern recognition using a vector reference,” Appl. Opt. 23, 838–840 (1984).
[CrossRef] [PubMed]

Y. N. Hsu, H. H. Arsenault, “Pattern discrimination by multiple circular harmonic components,” Appl. Opt. 23, 841–844 (1984).
[CrossRef] [PubMed]

D. Casasent, “Unified synthetic discriminant function computation formulation” Appl. Opt. 23, 1620–1627 (1984).
[CrossRef] [PubMed]

D. Casasent, “Computer generated holograms for pattern recognition: a review,” Opt. Eng. 23, 1620–1627 (1984).

1983 (3)

B. V. K. Vijaya Kumar, “Efficient approach for designing linear combination filters,” Appl. Opt. 22, 1445–1448 (1983).
[CrossRef]

M. Wax, T. Kailath, “Efficient inversion of Toeplitz-block Toeplitz matrix,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 1218–1221 (1983).
[CrossRef]

S. Kirkpatrick, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

1982 (9)

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

H. Murakami, B. V. K. Vijaya Kumar, “Efficient calculation of primary images from a set of images,” IEEE Trans. Pattern Anal. Mach. Intell. 4, 511–515 (1982).
[CrossRef] [PubMed]

R. W. Gerchberg, W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik (Stuttgart) 34, 2758 (1982).

J. L. Horner, “Light utilization in optical correlators,” Appl. Opt. 21, 4511–4514 (1982).
[CrossRef] [PubMed]

H. J. Caulfield, “Role of the Horner efficiency in the optimization of spatial filters for optical pattern recognition,” Appl. Opt. 21, 4391–4392 (1982).
[CrossRef] [PubMed]

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

J. R. Leger, S. H. Lee, “Hybrid optical processor for pattern recognition and classification using a generalized set of pattern functions,” Appl. Opt. 21, 274–287 (1982).
[CrossRef] [PubMed]

J. R. Leger, S. H. Lee, “Image classification by an optical implementation of Fukunaga–Koontz transform,” J. Opt. Soc. Am. 72, 556–564 (1982).
[CrossRef]

Z. H. Gu, J. R. Leger, S. H. Lee, “Optical implementation of the least-squares linear mapping technique for image classification,” J. Opt. Soc. Am. 72, 787–793 (1982).
[CrossRef]

1980 (2)

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

J. K. Mui, K. S. Fu, “Automated classification of nucleated blood cells using a binary tree classifier,” IEEE Trans. Pattern Anal. Mach. Intell. 2, 429–443 (1980).

1979 (2)

1978 (1)

H. Mostafavi, F. Smith, “Image correlation with geometric distortion—Part I: acquisition performance,” IEEE Trans. Aerosp. Electron. Sys. AES-14, 487–493 (1978).
[CrossRef]

1969 (1)

1966 (1)

1964 (1)

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

1963 (1)

D. O. North, “An analysis of the factors which determine signal/noise discriminations in pulsed carrier systems,” Proc. IEEE 51, 1016–1027 (1963).
[CrossRef]

Almeida, S. P.

Anderson, W. L.

W. L. Anderson, “Particle identification and counting,” in Applications of Optical Fourier Transform, H. Stark, ed. (Academic, New York, 1982), p. 95.

Arsenault, H. H.

L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation invariant phase-only and binary phase-only correlation,” Appl. Opt. 28, 1251–56 (1989).
[CrossRef] [PubMed]

Y. Sheng, H. H. Arsenault, “Object detection from a real scene using the correlation peak coordinates of multiple circular harmonic filters,” Appl. Opt. 28, 245–249 (1989).
[CrossRef] [PubMed]

H. H. Arsenault, Y. Sheng, J. Bulabois, “Modified composite filter for pattern recognition in the presence of noise with non-zero mean,” Opt. Commun. 63, 15–20 (1987).
[CrossRef]

Y. Sheng, H. H. Arsenault, “Method for determining expansion centers and predicting sidelobe levels for circular-harmonic filter,” J. Opt. Soc. Am. A 4, 1793–1797 (1987).
[CrossRef]

H. H. Arsenault, C. Ferreira, M. P. Levesque, T. Szpolik, “Simple filter with limited rotation invariance,” Appl. Opt. 25, 3230–3234 (1986).
[CrossRef] [PubMed]

Y. N. Hsu, H. H. Arsenault, “Pattern discrimination by multiple circular harmonic components,” Appl. Opt. 23, 841–844 (1984).
[CrossRef] [PubMed]

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

J. Campos, H. H. Arsenault, “Optimum sidelobe-reducing invariant matched filters for pattern recognition,” in Optical Computing ’88, P. Chavel, J. W. Goodman, G. Robin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.963, 298–303 (1988).
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H. H. Arsenault, “Rotation invariant composite filters,” in Nonlinear Optics and Applications, P. A. Yeh, ed., Proc. Soc. Photo-Opt. Instrum. Eng.613, 239–244 (1986).

Atlas, L. E.

Bahri, Z.

Z. Bahri, B. V. K. ViJaya Kumar, “Generalized synthetic discriminant functions,” J. Opt. Soc. Am. A 5, 562–571 (1988).
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B. V. K. Vijaya Kumar, Z. Bahri, A. Mahalanobis, “Constraint phase optimization in minimum variance synthetic discriminant functions,” Appl. Opt. 27, 409–413 (1988).
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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).

Z. Bahri, “Some generalizations of synthetic discriminant functions,” M.S. thesis (Carnegie Mellon University, Pittsburgh, Pa., 1986).

Ben-Yosef, N.

Blahut, R. E.

R. E. Blahut, Principles and Practice of Information Theory (Addison-Wesley, Reading, Mass., 1987).

Bollapraggada, S.

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Brasher, J.

J. Brasher, C. F. Hester, D. W. Lawson, S. R. F. Sims, “Multi-state higher-order filters,” in Hybrid Image and Signal Processing II, D. P. Casasent, A. G. Tescher, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1297, 103–109 (1990).

Braunecker, B.

Breipohl, A. M.

K. S. Shanmugan, A. M. Breipohl, Random Signals: Detection, Estimation and Data Analysis (Wiley, New York, 1988).

Bulabois, J.

H. H. Arsenault, Y. Sheng, J. Bulabois, “Modified composite filter for pattern recognition in the presence of noise with non-zero mean,” Opt. Commun. 63, 15–20 (1987).
[CrossRef]

Butler, S.

J. Riggins, S. Butler, “Simulation of synthetic discriminant function optical implementation,” Opt. Eng. 23, 721–726 (1984).

Caelli, T. M.

T. M. Caelli, Z. Q. Liu, “On the minimum number of templates required for shift, rotation and size invariant pattern recognition” Patt. Recog. 21, 205–216 (1988).
[CrossRef]

Campos, J.

J. Campos, H. H. Arsenault, “Optimum sidelobe-reducing invariant matched filters for pattern recognition,” in Optical Computing ’88, P. Chavel, J. W. Goodman, G. Robin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.963, 298–303 (1988).
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Carayannis, G.

N. Kalouptsidis, G. Carayannis, D. Manolakis, “On block matrices with elements of special structure,” in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1982), pp. 1744–1747.

Casasent, D.

D. Casasent, G. Ravichandran, “Advanced distortion-invariant MACE filters,” Appl. Opt. 31, 1109–1116 (1992).
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G. Ravichandran, D. Casasent, “Minimum noise and correlation energy (MINACE) optical correlation filter,” Appl. Opt. 31, 1823–1833 (1992).
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D. Casasent, G. Ravichandran, S. Bollapraggada, “Gaussian MACE correlation filters,” Appl. Opt. 30, 5176–5181 (1991).
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G. Ravichandran, D. Casasent, “Generalized in-plane rotation-invariant minimum average correlation energy filter,” Opt. Eng. 30, 1601–1607 (1991).
[CrossRef]

D. Casasent, A. Iyer, G. Ravichandran, “Circular harmonic function MACE filters,” Appl. Opt. 30, 5169–5175 (1991).
[CrossRef] [PubMed]

B. V. K. Vijaya Kumar, D. Casasent, A. Mahalanobis, “Correlation filters for target in a Markov model background clutter,” Appl. Opt. 28, 3112–3119 (1989).
[CrossRef]

D. Casasent, A. Mahalanobis, “Rule-based symbolic processor for object recognition,” Appl. Opt. 26, 4795–4802 (1987).
[CrossRef] [PubMed]

S. Leibowitz, D. Casasent, “Error-correction coding in an associative processor,” Appl. Opt. 26, 999–1006 (1987).
[CrossRef]

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

A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Spatial-temporal correlation filter for inplane distortion invariance,” Appl. Opt. 25, 4466–4472 (1986).
[CrossRef] [PubMed]

D. Casasent, W. T. Chang, “Correlation synthetic discriminant functions,” Appl. Opt. 25, 2343–2350 (1986).
[CrossRef] [PubMed]

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

D. Casasent, “Computer generated holograms for pattern recognition: a review,” Opt. Eng. 23, 1620–1627 (1984).

D. Casasent, “Unified synthetic discriminant function computation formulation” Appl. Opt. 23, 1620–1627 (1984).
[CrossRef] [PubMed]

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

Caulfield, H. J.

Chang, C. C.

Chang, W. T.

Cheung, K. F.

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 ratios,” Opt. Eng. 29, 994–1001 (1990).
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B. V. K. Vijaya Kumar, A. Lee, J. M. Connelly, “Estimating object rotation and scale using correlation filters,” Opt. Eng. 28, 474–481 (1989).

J. M. Connelly, “Designing filters for an acousto-optic based two-dimensional correlator,” Ph.D. dissertation (Carnegie Mellon University, Pittsburgh, Pa., 1990).

Costello, D. J.

S. Lin, D. J. Costello, Error Control Coding Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1983).

Daiuto, B. J.

R. D. Juday, B. J. Daiuto, “Relaxation method of compensation in an optical correlator,” Opt. Eng. 26, 1094–1101 (1987).

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 ratios,” Opt. Eng. 29, 994–1001 (1990).
[CrossRef]

F. M. Dickey, B. D. Hansche, “Quad-phase correlation filters for pattern recognition,” Appl. Opt. 28, 1611–1613 (1989).
[CrossRef] [PubMed]

Downie, J. D.

Ennis, D.

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

D. Jared, D. Ennis, “Learned distortion-invariant pattern recognition using synthetic discriminant functions,” in Hybrid Image Processing, D. P. Casasent, A. G. Tescher, eds., Proc. Soc. Photo-Opt. Instrum. Eng.638, 91–101 (1986).

Epperson, J.

B. V. K. Vijaya Kumar, A. Mahalanobis, S. Song, S. R. F. Sims, J. Epperson, “Minimum squared error synthetic discriminant functions,” Opt. Eng. (to be published).

Farn, M. W.

M. W. Farn, J. W. Goodman, “Optimal maximum correlation filters for arbitrarily constrained devices,” Appl. Opt. 28, 3326–3366 (1989).

Feigin, G.

Feldman, M. R.

Ferreira, C.

Fielding, K. H.

K. H. Fielding, S. K. Rogers, M. Kabrisky, J. P. Mills, “Position, scale and rotation invariant halographic associative memory,” Opt. Eng. 28, 849–853 (1989).

Figue, J.

Ph.Refregier Refregier, J. Figue, “Optimal trade-off filter for pattern recognition and their comparison with Wiener approach,” Opt. Comput. Process. 1, 3–10 (1991).

Flannery, D. L.

Flavin, M.

M. Flavin, J. L. Horner, “Amplitude encoded binary phase-only filter,” in Digital and Optical Shape Representation and Pattern Recognition, R. D. Juday, ed., Proc. Soc. Photo-Opt. Instrum. Eng.938, 261–265 (1988).

Fleisher, M.

Florence, J. M.

S. E. Monroe, R. D. Juday, J. M. Florence, “Laboratory results using the synthetic estimation filter, in Aerospace Pattern Recognition, M. R. Weathersby, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1098, 190–197 (1989).

J. M. Florence, “Design considerations for phase-only correlation filters,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1151, 195–202 (1989).

Fu, K. S.

J. K. Mui, K. S. Fu, “Automated classification of nucleated blood cells using a binary tree classifier,” IEEE Trans. Pattern Anal. Mach. Intell. 2, 429–443 (1980).

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Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik (Stuttgart) 34, 2758 (1982).

Gheen, G.

G. Gheen, “Optimal distortion invariant quadratic filters,” in Optical Information Processing Systems and Architectures III, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1564, 112–120 (1991).

G. Gheen, “Maximum mean square projection filters,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1151, 278–283 (1989).

Gianino, P. D.

Giles, M.

T. Walsh, M. Giles, “Statistical filtering of time-sequenced peak correlation responses for distortion-invariant recognition of multiple input objects,” Opt. Eng. 29, 1052–1064 (1990).
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Goodman, J. W.

M. W. Farn, J. W. Goodman, “Optimal maximum correlation filters for arbitrarily constrained devices,” Appl. Opt. 28, 3326–3366 (1989).

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Hassebrook, L.

L. Hassebrook, B. V. K. Vijaya Kumar, L. Hostetler, “Linear phase coefficient composite filter banks for distortion-invariant optical pattern recognition,” Opt. Eng. 29, 1033–1043 (1990).
[CrossRef]

B. V. K. Vijaya Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
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L. Hassebrook, B. V. K. Vijaya Kumar, L. Hostetler, “Linear phase coefficient composite filters for optical pattern recognition,” in Optical Pattern Recognition, H. Liu, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1053, 218–226 (1989).

L. Hassebrook, “Design of distortion-invariant linear phase response filters and filter banks,” Ph.D. dissertation (Carnegie Mellon University, Pittsburgh, Pa, 1990).

Hauck, R. W.

Hester, C. F.

C. F. Hester, D. Casasent, “Multivariant technique for multiclass pattern recognition.” Appl. Opt. 19, 1758–1761 (1980).
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J. Brasher, C. F. Hester, D. W. Lawson, S. R. F. Sims, “Multi-state higher-order filters,” in Hybrid Image and Signal Processing II, D. P. Casasent, A. G. Tescher, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1297, 103–109 (1990).

Horner, J. L.

D. L. Flannery, J. L. Horner, “Fourier optical processors,” Proc. IEEE 77, 1511–1527 (1989).
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J. L. Horner, P. D. Gianino, “Applying the phase-only filter concept to synthetic discriminant function correlation filter,” Appl. Opt. 24, 851–855 (1985).
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J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
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J. L. Horner, “Light utilization in optical correlators,” Appl. Opt. 21, 4511–4514 (1982).
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M. Flavin, J. L. Horner, “Amplitude encoded binary phase-only filter,” in Digital and Optical Shape Representation and Pattern Recognition, R. D. Juday, ed., Proc. Soc. Photo-Opt. Instrum. Eng.938, 261–265 (1988).

Hostetler, L.

L. Hassebrook, B. V. K. Vijaya Kumar, L. Hostetler, “Linear phase coefficient composite filter banks for distortion-invariant optical pattern recognition,” Opt. Eng. 29, 1033–1043 (1990).
[CrossRef]

L. Hassebrook, B. V. K. Vijaya Kumar, L. Hostetler, “Linear phase coefficient composite filters for optical pattern recognition,” in Optical Pattern Recognition, H. Liu, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1053, 218–226 (1989).

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D. Jared, D. Ennis, “Inclusion of filter modulation in synthetic discriminant function construction,” Appl. Opt. 28, 232–239 (1989).
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D. Jared, D. Ennis, “Learned distortion-invariant pattern recognition using synthetic discriminant functions,” in Hybrid Image Processing, D. P. Casasent, A. G. Tescher, eds., Proc. Soc. Photo-Opt. Instrum. Eng.638, 91–101 (1986).

Jenkins, E. L.

E. L. Jenkins, J. W. Morris, S. R. F. Sims, “Synthetic discriminant functions for target correlation,” in Infrared Image Processing and Enhancement, M. R. Weathersby, ed., Proc. Soc. Photo-Opt. Instrum. Eng.781, 140–147 (1987).

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R. D. Juday, “Correlation with a spatial light modulator having phase and amplitude cross coupling,” Appl. Opt. 28, 4865–4869 (1989).
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R. D. Juday, B. J. Daiuto, “Relaxation method of compensation in an optical correlator,” Opt. Eng. 26, 1094–1101 (1987).

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Figures (11)

Fig. 1
Fig. 1

Schematic of the frequency-plane correlator.

Fig. 2
Fig. 2

Output SNR as a function of input rotation for different N values where N is the number of training images. The image SBVP is 1000 (see Ref. 42 below).

Fig. 3
Fig. 3

Worst-case SNR as a function of N, the number of training images for different input SWBP’s (see Ref. 42 below).

Fig. 4
Fig. 4

Optimum SBWP as a function of training set size N (see Ref. 42 below).

Fig. 5
Fig. 5

Representation of the SDF equations using hyperplanes. Here the number of training images N = 2.

Fig. 6
Fig. 6

Optimal trade-off curves for filter design.

Fig. 7
Fig. 7

Probability-density functions of the output for a two-class, two-training image problem.

Fig. 8
Fig. 8

Illustration of the min–max approach used in Kallman’s filter design.

Fig. 9
Fig. 9

Simple illustration of the design of quadratic filters (N = 5, d = 2).

Fig. 10
Fig. 10

Example of multilinked decision structure for filter selection (see Ref. 103).

Fig. 11
Fig. 11

Hierarchical tree structure example for a four-class problem.

Equations (68)

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S ( u , v ) = s ( x , y ) exp [ - j 2 π ( u x + v y ) ] × d x d y ,
c ( τ x , τ y ) = F ( u , v ) H * ( u , v ) exp [ j 2 π ( u τ x + v τ y ) ] × d u d v = h * ( x , y ) f ( x + τ x , y + τ y ) d x d y = h ( x , y ) f ( x , y ) ,
h ( x , y ) s i ( x , y ) τ x = 0 , τ y = 0 = h * ( x , y ) s i ( x , y ) × d x d y = c ,             i = 1 , 2 , , N ,
h ( x , y ) = a 1 s 1 ( x , y ) + + a N s N ( x , y ) ,
i = 1 N a i * R i j = c ,             j = 1 , 2 , , N ,
R i j = s i * ( x , y ) s j ( x , y ) d x d y
h ( x , y ) p i ( x , y ) τ x = 0 , τ y = 0 = 0 ,             i = 1 , 2 , , N .
i = 1 N a i * R i j = c j ,             j = 1 , 2 , , N .
R a * = c .
h + s i = c i ,             i = 1 , 2 , , N ,
S + h = c * .
h = Sa ,
a = ( S + S ) - 1 c * .
h ECP = S ( S + S ) - 1 c * .
h = S ( S + S ) - 1 c * + [ I d - S ( S + S ) - 1 S + ] z ,
y = h + ( s i + n ) = c i + h + n ,
σ y 2 = E { h + n 2 } = E { h + n n + h } = h + Σ h .
h MVSDF = Σ - 1 S ( S + Σ - 1 S ) - 1 c * .
σ min 2 = [ Σ - 1 S ( S + Σ - 1 S ) - 1 c * ] + Σ [ Σ - 1 S ( S + Σ - 1 S ) - 1 c * ] = c T ( S + Σ - 1 S ) - 1 c * = c + ( S T Σ - 1 S * ) - 1 c .
c ( 0 , 0 ) = H * ( u , v ) F ( u , v ) d u d v = h ^ + f ^ ,
F ^ + h ^ = c * ,
S i ( u , v ) H * ( u , v ) d u d v = c i ,             i = 1 , 2 , , N .
E ave = 1 N i = 1 N c i ( τ x , τ y ) 2 d τ x d τ y = 1 N i = 1 N S i ( u , v ) 2 H ( u , v ) 2 d u d v ,
S ^ + h ^ = c * ,
E ave = h ^ + D ^ h ^ ,
h ^ MACE = D ^ - 1 S ^ ( S ^ + D ^ - 1 S ^ ) - 1 c * .
E min = c T ( S ^ + D ^ - 1 S ^ ) - 1 c * = c + ( S ^ T D ^ - 1 S ^ * ) - 1 c .
u i = [ s i ( 1 ) s i ( 2 ) s i ( d ) 0 s i ( 1 ) s i ( 2 ) s i ( d - 1 ) 0 0 0 0 s i ( 1 ) s i ( 2 ) 0 0 0 s i ( 1 ) ] [ h * ( 1 ) h * ( 2 ) h * ( d ) ] = S i h * ,
E ave = 1 N i = 1 N ( h T S i + S i h * ) = h T R h * ,
R = 1 N i = 1 N S i + S i .
h SMACE = R - 1 S ( S + R - 1 S ) - 1 c * ,
σ 2 = h + h = h ^ + h ^ ,
CM = E ave + α σ 2 = h ^ + D ^ h ^ + α h ^ + h ^ = h ^ + ( D ^ + α I d ) h ^ ,
h ^ = ( D ^ + α I d ) - 1 S ^ [ S ^ + ( D ^ + α I d ) - 1 S ^ ] - 1 c * .
σ min 2 = h + Σ h = c T ( S + Σ - 1 S ) - 1 S + Σ - 1 Σ Σ - 1 S ( S + Σ - 1 S ) - 1 c * = c + Bc ,
B = ( S T Σ - 1 S * ) - 1 .
σ min 2 = i = 1 N l = 1 N b i l c i * c l = i = l N l = 1 N b i l m i m l exp [ - j ( θ i - θ l ) ] = i = 1 N b i i m i 2 + 2 i = 1 ( N - 1 ) l = i + 1 N b i l m i m l cos [ ( θ i - θ l ) ] .
σ min 2 = i = 1 N l = 1 N b i l m i m l ,
DR = ( m 2 - m 1 ) 2 σ min 2 = ( m 2 - m 1 ) 2 b 11 m 1 2 + b 22 m 2 2 + ( b 12 + b 21 ) m 1 m 2 .
A s j ( i ) v i ,             i = 1 , 2 , , C ,             j = 1 , 2 , , N ,
= i = 1 C j = 1 N As j ( i ) - v i 2
A = [ i = 1 C j = 1 N v i s j ( i ) + ] [ i = 1 C j = 1 N s j ( i ) s j ( i ) + ] - 1 ,
peak = min 1 i N 0 [ max ( τ x , τ y ) box c i ( τ x , τ y ) ] ,
clutter = max { max 1 i N 0 [ max ( τ x , τ y ) box c i ( τ x , τ y ) ] , max ( N 0 + 1 ) i N [ max ( τ x , τ y ) c i ( τ x , τ y ) ] } .
s ( r , θ ) = m = - s m ( r ) exp ( j m θ ) ,
s m ( r ) = 1 2 π 0 2 π s ( r , θ ) exp ( - j m θ ) d θ .
h ( r , θ ) = m = - h m ( r ) exp ( j m θ ) .
E ( θ 0 ) = 0 0 2 π h * ( r , θ ) s ( r , θ - θ 0 ) r d θ d r = 0 r d r 0 2 π d θ m = - h m * ( r ) exp ( - j m θ ) × n = - s n ( r ) exp [ + j n ( θ - θ 0 ) ] = m = - n = - 0 r h m * ( r ) s n ( r ) d r · 0 2 π exp [ - j θ ( m - n ) ] exp ( - j n θ 0 ) d θ = m = - n = - 2 π δ m n × 0 r h m * ( r ) s n ( r ) d r · exp ( - j n θ 0 ) = 2 π n = - β n exp ( - j n θ 0 ) ,
β n = 0 r h n * ( r ) s n ( r ) d r .
P e = 1 - P r ( all four bits are correct ) = 1 - ( 1 - p ) 4 ,
P e = 1 - P r ( either no bits or one bit is incorrect ) = 1 - [ ( 1 - p ) 7 + 7 p ( 1 - p ) 6 ] .
ASP = 1 N i = 1 N h + s i 2 = h + R h ,
R = 1 N i = 1 N s i s i + .
R h = λ max h ,
I = h 1 T f 2 + h 2 T f 2 + h M T f 2 = f T h 1 h 1 T f + + f T h M h M T f = f T R h f ,
R h = i = 1 M h i h i T .
ϕ _ k = { 1 exp ( - j 2 π N k ) exp ( - j 4 π N k ) × exp [ - j 2 π ( N - 1 ) N ] k } T , k = 0 , 1 , 2 , , ( N - 1 ) .
h k ( x , y ) = n = 0 ( N - 1 ) exp ( - j 2 π N n k ) s n ( x , y ) , k = 0 , 1 , , ( N - 1 ) .
h k = S ϕ _ k ,
S T h k = S T S ϕ _ k = R ϕ _ k = λ k ϕ k ,             k = 0 , 1 , , ( N - 1 ) .
h k + h l = ϕ _ k + S T S ϕ l = ϕ k + R ϕ l = λ l ϕ k + ϕ l = { λ k N if k = l 0 if k l ,
s n ( x , y ) , F - 1 M [ H ( u , v ) ] = c n ,             n = 1 , 2 , , N ,
a i k + 1 = a i k + β ( c i - c 1 · c i k c 1 k ) ,             i = 1 , 2 , , N ,
S m ( ρ ) = 2 π ( - j ) m 0 s m ( r ) J m ( 2 π ρ r ) r d r ,
H m ( ρ , ϕ ) = exp { j [ θ m ( ρ ) + m ϕ ] } ,
overall entropy = entropy over desired class images - entropy over undesired class images .
γ = ( h , s 0 ) 2 max { ( h , f i , k ) 2 , ( h , s k ) 2 } ,
h + ( S - γ F i , k ) h 0 for all i , k , h + ( S - γ S k ) h 0 for all k 0

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