Abstract

Through the Rayleigh quotient (the ratio of intensity responses of a filter to different objects) we may generalize a great number of metrics used in optical pattern recognition. The Rayleigh quotient has been optimized in linear digital systems under the constraint of unit-energy filters. In optical pattern recognition at least two considerations violate the conditions under which the quotient has been digitally optimized: the noise background of the measurement invokes nonlinearity, and filters are constrained other than to unit energy. I show a solution that optimizes the ratio of biased measurements, subject to constraining filter values to arbitrary subsets of the complex plane. Previous solutions are discussed as special cases. A metric’s numerator and denominator may now both include the objects’ phase.

© 1998 Optical Society of America

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1996 (1)

1994 (2)

1993 (2)

1992 (2)

1989 (4)

1984 (1)

Bahri, Z.

Carlson, D. W.

Duda, O.

O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Farn, M. W.

Gianino, P. D.

Goodman, J. W.

Hart, P. E.

O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Horner, J. L.

Javidi, B.

Juday, R. D.

Karivaratha Rajan, P.

Laude, V.

Mahalanobis, A.

Parchekani, F.

Réfrégier, Ph.

Therrien, C. W.

For example, C. W. Therrien, Discrete Random Signals and Statistical Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1992), Sec. 5.4.

Vijaya Kumar, B. V. K.

Willett, P.

Yaroslavsky, L. P.

L. P. Yaroslavsky, “Is [sic] the phase-only filter and its modifications optimal in terms of the discrimination capability in pattern recognition?” Appl. Opt. 31, 1677–1679 (1992).
[CrossRef] [PubMed]

L. P. Yaroslavsky, “The theory of optimal methods for localization of objects in pictures,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1993), Vol. XXXII, pp. 145–201.

Zhang, G.

Appl. Opt. (9)

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

Opt. Lett. (2)

Other (4)

O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

For example, C. W. Therrien, Discrete Random Signals and Statistical Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1992), Sec. 5.4.

L. P. Yaroslavsky, “The theory of optimal methods for localization of objects in pictures,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1993), Vol. XXXII, pp. 145–201.

R. D. Juday, “Optical correlation with a cross-coupled spatial light modulator,” in Spatial Light Modulators and Applications, Vol. 8 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988).

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