Abstract

A procedure is presented for generating a small bank of optical correlation filters that can recognize a large number of perspective views of an object. The method applies to general kinds of image distortions in addition to those generated by different perspective views. The holographic filters are also invariant to image intensity and position (translation invariance). The method of design is to decompose the entire set of object variations into a set of eigenimages. These eigenimages contain complete information about the target set. An iterative procedure combines the eigenimages with different relative phases, so that complete target information can be extracted in an optical implementation. An example illustrates that a set of only 20 holographic filters recognizes a three-dimensional target over a continuous range of viewing angles.

© 1988 Optical Society of America

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1987 (2)

1986 (4)

1985 (1)

1984 (1)

1982 (4)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef] [PubMed]

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

Y. Yang, Y.-N. Hsu, H. H. Arsenault, “Optimum circular symmetrical filters and their uses in optical pattern recognition,” Opt. Acta 29, 627–644 (1982).
[CrossRef]

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

1980 (1)

1979 (1)

1975 (1)

A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,”IEEE Trans. Circuits Syst. CAS-22, 735–742 (1975).
[CrossRef]

1974 (1)

R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

1973 (1)

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1971 (1)

R. W. Gerchberg, W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik 34, 275–283 (1971).

1964 (1)

A. Vander Lugt, “Signal detection by complex spatial filtering,”IRE Trans. Inform. Theory IT-10, 139–145 (1964).
[CrossRef]

Arsenault, H. H.

Braunecker, B.

Casasent, D.

See for example, D. Casasent, W.-T. Chang, “Correlation synthetic discriminant functions,” Appl. Opt. 25, 2343–2350 (1986), and the many references contained therein.
[CrossRef] [PubMed]

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

D. Casasent, D. Psaltis, “Deformation invariant, space-variant optical pattern recognition,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 289–356.

D. Casasent, S. A. Liebowitz, A. Mahalanobis, “Parameter selection for iconic and symbolic pattern recognition filters,” in Optical and Digital Pattern Recognition, P. S. Schenker, H. Liu, eds., Proc. Soc. Photo-Opt. Instrum. Eng.754, 284–303 (1987).

Caulfield, H. J.

Chang, W.-T.

Fienup, J. R.

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef] [PubMed]

J. R. Fienup, “Reconstruction and synthesis applications of an iterative algorithm,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fienup, B. E. A. Saleh, eds., Proc. Soc. Photo-Opt. Instrum. Eng.373, 147–160 (1981).

Gallagher, N. C.

Gantmacher, F. R.

F. R. Gantmacher, The Theory of Matrices (Chelsea, New York, 1959), Vol. I.

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

Gerchberg, R. W.

R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

R. W. Gerchberg, W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik 34, 275–283 (1971).

Hauck, R.

Hirsch, P. M.

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object dependent diffuser,” U.S. Patent3,619,022 (November9, 1971).

Hsu, Y. N.

Hsu, Y.-N.

Y. Yang, Y.-N. Hsu, H. H. Arsenault, “Optimum circular symmetrical filters and their uses in optical pattern recognition,” Opt. Acta 29, 627–644 (1982).
[CrossRef]

Jordan, J. A.

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object dependent diffuser,” U.S. Patent3,619,022 (November9, 1971).

Lesem, L. B.

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object dependent diffuser,” U.S. Patent3,619,022 (November9, 1971).

Liebowitz, S. A.

D. Casasent, S. A. Liebowitz, A. Mahalanobis, “Parameter selection for iconic and symbolic pattern recognition filters,” in Optical and Digital Pattern Recognition, P. S. Schenker, H. Liu, eds., Proc. Soc. Photo-Opt. Instrum. Eng.754, 284–303 (1987).

Liu, B.

Lohmann, A. W.

Mahalanobis, A.

D. Casasent, S. A. Liebowitz, A. Mahalanobis, “Parameter selection for iconic and symbolic pattern recognition filters,” in Optical and Digital Pattern Recognition, P. S. Schenker, H. Liu, eds., Proc. Soc. Photo-Opt. Instrum. Eng.754, 284–303 (1987).

Naylor, A. W.

A. W. Naylor, G. R. Sell, Linear Operator Theory in Engineering and Science (Springer-Verlag, New York, 1982).

Ochoa, E.

Papoulis, A.

A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,”IEEE Trans. Circuits Syst. CAS-22, 735–742 (1975).
[CrossRef]

Pochapsky, E.

Psaltis, D.

D. Casasent, D. Psaltis, “Deformation invariant, space-variant optical pattern recognition,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 289–356.

Rao, C. R.

C. R. Rao, Linear Statistical Inference and Its Applications, 2nd ed. (Wiley, New York, 1973).

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

R. W. Gerchberg, W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik 34, 275–283 (1971).

Schils, G. F.

Sell, G. R.

A. W. Naylor, G. R. Sell, Linear Operator Theory in Engineering and Science (Springer-Verlag, New York, 1982).

Sheng, Y.

Sweeney, D. W.

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation, and Linear Modulation Theory, Part I (Wiley, New York, 1968).

Vander Lugt, A.

A. Vander Lugt, “Signal detection by complex spatial filtering,”IRE Trans. Inform. Theory IT-10, 139–145 (1964).
[CrossRef]

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. Imag. MI-1, 81–94 (1982).
[CrossRef]

Yang, Y.

Y. Yang, Y.-N. Hsu, H. H. Arsenault, “Optimum circular symmetrical filters and their uses in optical pattern recognition,” Opt. Acta 29, 627–644 (1982).
[CrossRef]

Youla, D. C.

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

Appl. Opt. (8)

IEEE Trans. Circuits Syst. (1)

A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,”IEEE Trans. Circuits Syst. CAS-22, 735–742 (1975).
[CrossRef]

IEEE Trans. Med. Imag. (1)

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

IRE Trans. Inform. Theory (1)

A. Vander Lugt, “Signal detection by complex spatial filtering,”IRE Trans. Inform. Theory IT-10, 139–145 (1964).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Opt. Soc. Am. A (3)

Opt. Acta (2)

Y. Yang, Y.-N. Hsu, H. H. Arsenault, “Optimum circular symmetrical filters and their uses in optical pattern recognition,” Opt. Acta 29, 627–644 (1982).
[CrossRef]

R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

Opt. Lett. (1)

Optik (2)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

R. W. Gerchberg, W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik 34, 275–283 (1971).

Other (10)

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object dependent diffuser,” U.S. Patent3,619,022 (November9, 1971).

A. W. Naylor, G. R. Sell, Linear Operator Theory in Engineering and Science (Springer-Verlag, New York, 1982).

F. R. Gantmacher, The Theory of Matrices (Chelsea, New York, 1959), Vol. I.

H. L. Van Trees, Detection, Estimation, and Linear Modulation Theory, Part I (Wiley, New York, 1968).

C. R. Rao, Linear Statistical Inference and Its Applications, 2nd ed. (Wiley, New York, 1973).

D. Casasent, D. Psaltis, “Deformation invariant, space-variant optical pattern recognition,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 289–356.

D. Casasent, S. A. Liebowitz, A. Mahalanobis, “Parameter selection for iconic and symbolic pattern recognition filters,” in Optical and Digital Pattern Recognition, P. S. Schenker, H. Liu, eds., Proc. Soc. Photo-Opt. Instrum. Eng.754, 284–303 (1987).

IMSL Library, fortran Subroutines for Mathematics and Statistics (IMSL, Houston, Tex., 1984).

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

J. R. Fienup, “Reconstruction and synthesis applications of an iterative algorithm,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fienup, B. E. A. Saleh, eds., Proc. Soc. Photo-Opt. Instrum. Eng.373, 147–160 (1981).

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