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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 4 — Apr. 1, 1998
  • pp: 777–790

Generalized Rayleigh quotient approach to filter optimization

Richard D. Juday  »View Author Affiliations


JOSA A, Vol. 15, Issue 4, pp. 777-790 (1998)
http://dx.doi.org/10.1364/JOSAA.15.000777


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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

OCIS Codes
(100.4550) Image processing : Correlators
(100.5010) Image processing : Pattern recognition
(120.2440) Instrumentation, measurement, and metrology : Filters

History
Original Manuscript: May 29, 1997
Revised Manuscript: October 27, 1997
Manuscript Accepted: November 13, 1997
Published: April 1, 1998

Citation
Richard D. Juday, "Generalized Rayleigh quotient approach to filter optimization," J. Opt. Soc. Am. A 15, 777-790 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-4-777

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