OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 9 — Sep. 1, 2001
  • pp: 2054–2071

Noise robustness of nonlinear filters for image recognition

Nasser Towghi, Luting Pan, and Bahram Javidi  »View Author Affiliations

JOSA A, Vol. 18, Issue 9, pp. 2054-2071 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (348 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We analyze the performance of the Fourier plane nonlinear filters in terms of signal-to-noise ratio (SNR). We obtain a range of nonlinearities for which SNR is robust to the variations in input-noise bandwidth. This is shown both by analytical estimates of the SNR for nonlinear filters and by experimental simulations. Specifically, we analyze the SNR when Fourier plane nonlinearity is applied to the input signal. Using the Karhunen–Loève series expansion of the noise process, we obtain precise analytic expressions of the SNR for Fourier plane nonlinear filters in the presence of various types of additive-noise processes. We find a range of nonlinearities that need to be applied that keep the output SNR of the filter stable relative to changes in the noise bandwidth.

© 2001 Optical Society of America

OCIS Codes
(100.5010) Image processing : Pattern recognition

Original Manuscript: June 26, 2000
Revised Manuscript: November 27, 2000
Manuscript Accepted: November 27, 2000
Published: September 1, 2001

Nasser Towghi, Luting Pan, and Bahram Javidi, "Noise robustness of nonlinear filters for image recognition," J. Opt. Soc. Am. A 18, 2054-2071 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. L. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theory IT-6, 311–329 (1960). [CrossRef]
  2. A. Vanderlugt, “Signal detection by complex filters,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  3. D. Casasent, D. Psaltis, “Position, rotation, and scale-invariant optical correlation,” Appl. Opt. 15, 1795–1799 (1976). [CrossRef] [PubMed]
  4. A. Mahalanobis, B. V. K. V. Kumar, D. Casasent, “Minimum average correlation energy filters,” Appl. Opt. 26, 3633–3640 (1987). [CrossRef] [PubMed]
  5. H. J. Caufield, W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 8, 2354–2356 (1969). [CrossRef]
  6. D. L. Flannery, J. L. Horner, “Fourier optical signal processor,” Proc. IEEE 77, 1511–1527 (1989). [CrossRef]
  7. B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989). [CrossRef] [PubMed]
  8. 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]
  9. K. H. Fielding, J. L. Horner, “1-f binary joint transform correlator,” Opt. Eng. 29, 1081–1087 (1990). [CrossRef]
  10. 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]
  11. J. L. Horner, P. D. Gianino, “Phase-only matched filter,” Appl. Opt. 8, 812–816 (1984). [CrossRef]
  12. D. Casasent, “Unified synthetic discrimination function computational formulation,” Appl. Opt. 23, 1620–1627 (1984). [CrossRef]
  13. Ph. Réfrégier, J. Figue, “Optimal trade-off filters for pattern recognition and their comparison with Wiener approach,” Opt. Comput. Process. 1, 245–265 (1991).
  14. Ph. Réfrégier, “Optimal trade-off filters for noise robustness, sharpness of the correlation peak, and Horner efficiency,” Opt. Lett. 16, 829–831 (1991). [CrossRef] [PubMed]
  15. Ph. Réfrégier, “Filter design for optical pattern recognition: multicriteria approach,” Opt. Lett. 15, 854–856 (1990). [CrossRef]
  16. Ph. Refregier, “Optical pattern recognition: optimal trade-off circular harmonic filters,” Opt. Commun. 86, 113–118 (1991). [CrossRef]
  17. B. Javidi, D. Painchaud, “Distortion invariant pattern recognition using Fourier plane nonlinear filters,” Appl. Opt. 35, 318–331 (1996). [CrossRef] [PubMed]
  18. W. B. Hahn, D. L. Flannery, “Design elements of binary joint transform correlation and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992). [CrossRef]
  19. J. W. Goodman, Introduction to Fourier Optics (McGraw–Hill, New York, 1967).
  20. K. Fukunaga, Statistical Pattern Recognition, 2nd ed. (Academic, San Diego, Calif., 1990), p. 59.
  21. V. Gnedenko, The Theory of Probability (Mir, Moscow, 1976).

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