Abstract

Utilizing the phase-coded optical processor, the least-squares linear mapping technique (LSLMT) has been optically implemented to classify large-dimensional images. The LSLMT is useful for performing a transform from large-dimensional observation or feature space to small-dimensional decision space for separating multiple image classes by maximizing the interclass differences while minimizing the intraclass variations. As an example, the classifier designed for handwritten letters was studied. The performance of the LSLMT was compared also with those of a matched filter and an average filter.

© 1982 Optical Society of Americ

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  1. A. Vander Lugt, "Signal detection by complex spatial filtering," IEEE Trans. Inf. Theory IT-10, 139–145 (1964); A. Vander Lugt, F. B. Rotz, and A. Klooster, "Character reading by optical spatial filtering," in Optical and Electrooptical Information Processing, J. T. Tippet et al., eds. (MIT Press, Cambridge, Mass., 1965), p. 125.
  2. A. D. Gara, "Real-time tracking of moving objects by optical correlation," Appl. Opt. 18, 172–174 (1979).
  3. S. P. Almeida and J. K. T. Eu, "Water pollution monitoring using matched spatial filters," Appl. Opt. 15, 510–515 (1976).
  4. D. Casasent and D. Psaltis, "Position, rotation, and scale invariant optical correlation," Appl. Opt. 15, 1795–1799 (1976).
  5. C. F. Hester and D. Casasent, "Optical pattern recognition using average filters to produce discriminant hypersurfaces," Proc. Soc. Photo-Opt. Instrumen. Eng. 201, 77–82 (1979).
  6. H. J. Caufield, R. Haimes, and D. Casasent, "Beyond matched filtering," Opt. Eng. 19, 152–156 (1980).
  7. J. R. Leger and S. H. Lee, "A hybrid optical processor for pattern recognition and classification using a generalized set of pattern functions," Appl. Opt. 21, 274–287 (1982).
  8. J. Duvernoy, "Optical pattern recognition and clustering: Karhunen-Loéve analysis," Appl. Opt. 15, 1584–1590 (1976).
  9. J. R. Leger and S. H. Lee, "Image classification by an optical implementation of Fukunaga-Koontz transform," J. Opt. Soc. Am. 72, 556–564 (1982).
  10. N. Ahmed and K. R. Rao, Orthogonal Transforms for Digital Signal Processing (Springer-Verlag, New York, 1975), pp. 225–253.
  11. K. Fukunaga, Introduction to Statistical Pattern Recognition (Academic, New York, 1972), pp. 40–42.
  12. J. R. Leger and S. H. Lee, "Coherent optical implementation of generalized two-dimensional transforms," Opt. Eng. 18, 518–523 (1979).
  13. C. P. Leibel, Change Your Handwriting, Change Your Life (Stein and Day, New York, 1972), pp. 87–101.
  14. J. Cederquist and S. H. Lee, "Coherent optical feedback for the analog solution of partial differential equations," J. Opt. Soc. Am. 70, 944–953 (1980).
  15. J. R. Leger, J. Cederquist, and S. H. Lee,"Micro-computer based hybrid processor at UCSD," Opt. Eng. (to be published, May/June 1982).
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 179–181.

1982 (2)

1980 (2)

J. Cederquist and S. H. Lee, "Coherent optical feedback for the analog solution of partial differential equations," J. Opt. Soc. Am. 70, 944–953 (1980).

H. J. Caufield, R. Haimes, and D. Casasent, "Beyond matched filtering," Opt. Eng. 19, 152–156 (1980).

1979 (3)

J. R. Leger and S. H. Lee, "Coherent optical implementation of generalized two-dimensional transforms," Opt. Eng. 18, 518–523 (1979).

C. F. Hester and D. Casasent, "Optical pattern recognition using average filters to produce discriminant hypersurfaces," Proc. Soc. Photo-Opt. Instrumen. Eng. 201, 77–82 (1979).

A. D. Gara, "Real-time tracking of moving objects by optical correlation," Appl. Opt. 18, 172–174 (1979).

1976 (3)

Ahmed, N.

N. Ahmed and K. R. Rao, Orthogonal Transforms for Digital Signal Processing (Springer-Verlag, New York, 1975), pp. 225–253.

Almeida, S. P.

Casasent, D.

H. J. Caufield, R. Haimes, and D. Casasent, "Beyond matched filtering," Opt. Eng. 19, 152–156 (1980).

C. F. Hester and D. Casasent, "Optical pattern recognition using average filters to produce discriminant hypersurfaces," Proc. Soc. Photo-Opt. Instrumen. Eng. 201, 77–82 (1979).

D. Casasent and D. Psaltis, "Position, rotation, and scale invariant optical correlation," Appl. Opt. 15, 1795–1799 (1976).

Caufield, H. J.

H. J. Caufield, R. Haimes, and D. Casasent, "Beyond matched filtering," Opt. Eng. 19, 152–156 (1980).

Cederquist, J.

J. Cederquist and S. H. Lee, "Coherent optical feedback for the analog solution of partial differential equations," J. Opt. Soc. Am. 70, 944–953 (1980).

J. R. Leger, J. Cederquist, and S. H. Lee,"Micro-computer based hybrid processor at UCSD," Opt. Eng. (to be published, May/June 1982).

Duvernoy, J.

Eu, J. K. T.

Fukunaga, K.

K. Fukunaga, Introduction to Statistical Pattern Recognition (Academic, New York, 1972), pp. 40–42.

Gara, A. D.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 179–181.

Haimes, R.

H. J. Caufield, R. Haimes, and D. Casasent, "Beyond matched filtering," Opt. Eng. 19, 152–156 (1980).

Hester, C. F.

C. F. Hester and D. Casasent, "Optical pattern recognition using average filters to produce discriminant hypersurfaces," Proc. Soc. Photo-Opt. Instrumen. Eng. 201, 77–82 (1979).

Lee, S. H.

Leger, J. R.

J. R. Leger and S. H. Lee, "A hybrid optical processor for pattern recognition and classification using a generalized set of pattern functions," Appl. Opt. 21, 274–287 (1982).

J. R. Leger and S. H. Lee, "Image classification by an optical implementation of Fukunaga-Koontz transform," J. Opt. Soc. Am. 72, 556–564 (1982).

J. R. Leger and S. H. Lee, "Coherent optical implementation of generalized two-dimensional transforms," Opt. Eng. 18, 518–523 (1979).

J. R. Leger, J. Cederquist, and S. H. Lee,"Micro-computer based hybrid processor at UCSD," Opt. Eng. (to be published, May/June 1982).

Leibel, C. P.

C. P. Leibel, Change Your Handwriting, Change Your Life (Stein and Day, New York, 1972), pp. 87–101.

Psaltis, D.

Rao, K. R.

N. Ahmed and K. R. Rao, Orthogonal Transforms for Digital Signal Processing (Springer-Verlag, New York, 1975), pp. 225–253.

Vander Lugt, A.

A. Vander Lugt, "Signal detection by complex spatial filtering," IEEE Trans. Inf. Theory IT-10, 139–145 (1964); A. Vander Lugt, F. B. Rotz, and A. Klooster, "Character reading by optical spatial filtering," in Optical and Electrooptical Information Processing, J. T. Tippet et al., eds. (MIT Press, Cambridge, Mass., 1965), p. 125.

Appl. Opt. (5)

J. Opt. Soc. Am. (2)

Opt. Eng. (2)

H. J. Caufield, R. Haimes, and D. Casasent, "Beyond matched filtering," Opt. Eng. 19, 152–156 (1980).

J. R. Leger and S. H. Lee, "Coherent optical implementation of generalized two-dimensional transforms," Opt. Eng. 18, 518–523 (1979).

Proc. Soc. Photo-Opt. Instrumen. Eng. (1)

C. F. Hester and D. Casasent, "Optical pattern recognition using average filters to produce discriminant hypersurfaces," Proc. Soc. Photo-Opt. Instrumen. Eng. 201, 77–82 (1979).

Other (6)

A. Vander Lugt, "Signal detection by complex spatial filtering," IEEE Trans. Inf. Theory IT-10, 139–145 (1964); A. Vander Lugt, F. B. Rotz, and A. Klooster, "Character reading by optical spatial filtering," in Optical and Electrooptical Information Processing, J. T. Tippet et al., eds. (MIT Press, Cambridge, Mass., 1965), p. 125.

N. Ahmed and K. R. Rao, Orthogonal Transforms for Digital Signal Processing (Springer-Verlag, New York, 1975), pp. 225–253.

K. Fukunaga, Introduction to Statistical Pattern Recognition (Academic, New York, 1972), pp. 40–42.

C. P. Leibel, Change Your Handwriting, Change Your Life (Stein and Day, New York, 1972), pp. 87–101.

J. R. Leger, J. Cederquist, and S. H. Lee,"Micro-computer based hybrid processor at UCSD," Opt. Eng. (to be published, May/June 1982).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 179–181.

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