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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 1 — Jan. 1, 1999
  • pp: 85–96

Decision regions of Fourier-plane nonlinear filtering for image recognition

B. Javidi, N. Towghi, and J. Li  »View Author Affiliations

JOSA A, Vol. 16, Issue 1, pp. 85-96 (1999)

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In image recognition applications, complex decision regions in the image space are needed. Linear filtering forms the decision regions by hyperplanes in the image space. We determine the decision region formed by Fourier-plane nonlinear filtering. In the case in which power law nonlinearity is applied in the Fourier plane, the decision region turns out to be approximately an n-dimensional parabola that opens toward the direction of the reference vector. That is, the intersection of the decision region with any plane (two-dimensional vector space) not containing any vector parallel to the reference vector is a bounded convex region enclosed by a closed curve. The size of the convex region depends on the filter nonlinearity, which determines the distortion robustness and discrimination capability of the filter. It can be adjusted by choosing different Fourier-plane nonlinearities and/or different threshold values at the output plane. These types of regions are desirable and well suited in image recognition. Analytical and numerical solutions are provided.

© 1999 Optical Society of America

OCIS Codes
(070.4340) Fourier optics and signal processing : Nonlinear optical signal processing
(070.5010) Fourier optics and signal processing : Pattern recognition

Original Manuscript: February 23, 1998
Revised Manuscript: June 26, 1998
Manuscript Accepted: September 11, 1998
Published: January 1, 1999

B. Javidi, N. Towghi, and J. Li, "Decision regions of Fourier-plane nonlinear filtering for image recognition," J. Opt. Soc. Am. A 16, 85-96 (1999)

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  1. M. Nadler, E. P. Smith, Pattern Recognition Engineering (Wiley, New York, 1993).
  2. R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).
  3. J. T. Tou, R. C. Gonzalez, Pattern Recognition Principles (Addison-Wesley, Reading, Mass., 1974).
  4. H. J. Caufield, W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 8, 2354–2356 (1969). [CrossRef]
  5. D. L. Flannery, J. L. Horner, “Fourier optical signal processor,” Proc. IEEE 1511, 77 (1989).
  6. P. Refregier, “Filter design for optical image recognition: multicriteria optimization approach,” Opt. Lett. 15, 854–856 (1990). [CrossRef] [PubMed]
  7. A. Mahalonobis, “Review of correlation filters and their application scene matching,” in Optoelectronic Devices and Systems for Processing, B. Javidi, K. M. Johnson, eds., Vol. CR65 of Critical Review Series (SPIE Press, Bellingham, Wash., 1996), pp. 240–260.
  8. H.-Y. Li, Y. Qiao, D. Psaltis, “Optical network for real-time face recognition,” Appl. Opt. 32, 5026–5035 (1993). [CrossRef] [PubMed]
  9. P. Refregier, F. Goudaul, “A decision theoretical approach to nonlinear joint-transform correlation,” J. Opt. Soc. Am. A 15, 61–67 (1998). [CrossRef]
  10. Y.-N. Hsu, H. H. Arsenault, G. April, “Rotation-invariant image recognition using circular harmonic expansion,” Appl. Opt. 21, 4012–4015 (1982). [CrossRef] [PubMed]
  11. D. Weber, D. Casasent, “Quadratic filters for object classification and detection,” in Optical Pattern Recognition, D. Casasent, T. Chao, eds., Proc. SPIE3073, 2–13 (1997). [CrossRef]
  12. B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989). [CrossRef] [PubMed]
  13. B. Javidi, J. Wang, A. Fazlolahi, “Performance of the nonlinear joint transform correlator for signals with low-pass characteristics,” Appl. Opt. 33, 834–848 (1994). [CrossRef] [PubMed]
  14. K. H. Fielding, J. L. Horner, “1-f binary joint transform correlator,” Opt. Eng. 29, 1081–1087 (1990). [CrossRef]
  15. Ph. Réfrégier, V. Laude, B. Javidi, “Nonlinear joint-transform correlation: an optimal solution for adaptive image discrimination and input noise robustness,” Opt. Lett. 19, 405–407 (1994). [PubMed]
  16. B. Javidi, D. Painchaud, “Distortion-invariant image recognition using Fourier-plane nonlinear filters,” Appl. Opt. 35, 318–331 (1996). [CrossRef] [PubMed]
  17. W. B. Hahn, D. L. Flannery, “Design elements of binary joint transform correlation and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992). [CrossRef]
  18. B. Javidi, J. Li, Q. Tang, “Optical implementation of neural networks for face recognition by the use of nonlinear joint transform correlators,” Appl. Opt. 34, 3950–3962 (1995). [CrossRef] [PubMed]
  19. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967).
  20. D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984). [CrossRef]
  21. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984). [CrossRef] [PubMed]
  22. B. Javidi, J. Li, A. H. Fazlollahi, J. Horner, “Binary nonlinear joint transform correlator performance with different thresholding methods under unknown illumination conditions,” Appl. Opt. 34, 886–896 (1995). [CrossRef] [PubMed]

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