OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 18, Iss. 8 — Aug. 1, 2001
  • pp: 1882–1896

Generality of matched filtering and minimum Euclidean distance projection for optical pattern recognition

Richard D. Juday  »View Author Affiliations


JOSA A, Vol. 18, Issue 8, pp. 1882-1896 (2001)
http://dx.doi.org/10.1364/JOSAA.18.001882


View Full Text Article

Enhanced HTML    Acrobat PDF (270 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Matched filtering followed by a minimum Euclidean distance projection onto realizable filter values was previously shown to optimize the signal-to-noise ratio for single training images in optical correlation pattern recognition. The algorithm is now shown to solve the combination of (1) standard statistical pattern-recognition metrics with multiple training images, (2) additive input noise of known power spectral density and also additive detection noise that is irreducible by the filter, (3) the building of the filter on arbitrary subsets of the complex unit disk, and (4) the use of observable correlator outputs only. The criteria include the Fisher ratio, the Bayes error and Bayes cost, the Chernoff and Bhattacharyya bounds, the population entropy and expected information, versions of signal-to-noise ratio that use other than second power in their norm, and the area under the receiver operating characteristic curve. Different criteria are optimized by different complex scalar weights.

© 2001 Optical Society of America

OCIS Codes
(070.4550) Fourier optics and signal processing : Correlators
(070.5010) Fourier optics and signal processing : Pattern recognition
(100.6740) Image processing : Synthetic discrimination functions

History
Original Manuscript: November 27, 2000
Revised Manuscript: January 24, 2001
Manuscript Accepted: January 24, 2001
Published: August 1, 2001

Citation
Richard D. Juday, "Generality of matched filtering and minimum Euclidean distance projection for optical pattern recognition," J. Opt. Soc. Am. A 18, 1882-1896 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-8-1882


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992). [CrossRef]
  2. B. V. K. Vijaya Kumar, R. D. Juday, P. K. Rajan, “Saturated filters,” J. Opt. Soc. Am. A 9, 405–412 (1992). [CrossRef]
  3. B. F. Draayer, G. W. Carhart, M. K. Giles, “Optimum classification of correlation-plane data by Bayesian decision theory,” Appl. Opt. 33, 3034–3049 (1994). [CrossRef] [PubMed]
  4. See any statistical pattern recognition text. The example followed in this paper is from Keinosuke Fukunaga, Introduction to Statistical Pattern Recognition, 2nd ed. (Academic, New York, 1990).
  5. R. D. Juday, R. S. Barton, S. E. Monroe, “Experimental optical results with MEDOF, coupled modulators, and quadratic metrics,” Opt. Eng. 38, 302–312 (1999). [CrossRef]
  6. J. W. Goodman, Statistical Optics (Wiley, New York, 2000).
  7. B. Javidi, F. Parchekani, G. Zhang, “Minimum-mean-square-error filters for detecting a noisy target in background noise,” Appl. Opt. 35, 6964–6975 (1996). [CrossRef] [PubMed]
  8. C. Soutar, S. E. Monroe, J. Knopp, “Complex characterization of the Epson liquid crystal television,” Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 269–277 (1993). [CrossRef]
  9. L. G. Neto, D. Roberge, Y. Sheng, “Programmable optical phase-mostly holograms with coupled-mode modulation liquid-crystal television,” Appl. Opt. 34, 1944–1950 (1995). [CrossRef] [PubMed]
  10. R. D. Juday, “Optimal realizable filters and the minimum Euclidean distance principle,” Appl. Opt. 32, 5100–5111 (1993). [CrossRef] [PubMed]
  11. E.g., the function BESSELI(0,x,1) in Matlab Version 5 (The Mathworks, Inc., Natick MA); the function bessi0(x) from Numerical Recipes in C, 2nd ed. [Cambridge U. Press, New York (1992)]; Section 9.8 of Handbook of Mathematical Functions, M. Abramowitz, I. A. Stegun, eds., National Bureau of Standards publication AMS 55, U.S. Government Printing Office, Washington, D.C. (1964).
  12. R. D. Juday, “Generalized Rayleigh quotient approach to filter optimization,” J. Opt. Soc. Am. A 15, 777–790 (1998). [CrossRef]
  13. R. D. Juday, “A philosophy for optical filter optimization,” in 1999 Euro-American Workshop on Optoelectronic Information Processing, P. Réfrégier, B. Javidi, eds., Vol. CR74 of SPIE Critical Review Series (SPIE Optical Engineering Press, Bellingham, Wash., 1999), pp. 227–240.
  14. N. Towghi, B. Javidi, “lp-norm optimum filters for image recognition. Part I. Algorithms,” J. Opt. Soc. Am. A 16, 1928–1935 (1999). [CrossRef]
  15. D. A. Jared, D. J. Ennis, “Inclusion of filter modulation in synthetic discriminant function construction,” Appl. Opt. 28, 232–239 (1989). [CrossRef] [PubMed]
  16. M. Montes-Usátegui, J. Campos, I. Juvells, “Computation of arbitrarily constrained synthetic discriminant function filters,” Appl. Opt. 34, 3904–3914 (1995). [CrossRef]
  17. R. D. Juday, B. V. K. Vijaya Kumar, P. K. Rajan, “Optimal real correlation filters,” Appl. Opt. 30, 520–522 (1991). [CrossRef] [PubMed]
  18. C. F. Hester, D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980). [CrossRef] [PubMed]
  19. B. V. K. Vijaya Kumar, D. W. Carlson, A. Mahalanobis, “Optimal trade-off synthetic discriminant function filters for arbitrary devices,” Opt. Lett. 19, 1556–1558 (1994). [CrossRef]
  20. P. C. Miller, M. Royce, P. Virgo, M. Fiebig, G. Hamlyn, “Evaluation of an optical correlator automatic target recognition system for acquisition and tracking in densely cluttered natural scenes,” Opt. Eng. 38, 1814–1825 (1999). [CrossRef]
  21. J. M. Rollins, R. D. Juday, S. E. Monroe, “Laboratory results for the optimized Fisher ratio,” in Optical Pattern Recognition XI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE4043, 182–191 (2000). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited