OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 36, Iss. 35 — Dec. 10, 1997
  • pp: 9212–9224

Application of nonlinearity to wavelet-transformed images to improve correlation filter performance

Lamia S. Jamal-Aldin, Rupert C. D. Young, and Chris R. Chatwin  »View Author Affiliations

Applied Optics, Vol. 36, Issue 35, pp. 9212-9224 (1997)

View Full Text Article

Enhanced HTML    Acrobat PDF (2222 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A useful filter for pattern recognition must strike a compromise between the conflicting requirements of in-class distortion tolerance and out-of-class discrimination. Such a filter will be bandpass in nature, the high-frequency response being attenuated to provide less sensitivity to in-class variations, while the low frequencies must be removed, since they compromise the discrimination ability of the filter. A convenient bandpass is the difference of Gaussian (DOG) function, which provides a close approximation to the Laplacian of Gaussian. We describe the effect of a preprocessing operation applied to a DOG filtered image. This operation is shown to result in greater tolerance to in-class variation while maintaining an excellent discrimination ability. Additionally, the introduction of nonlinearity is shown to provide greater robustness in the filter response to noise and background clutter in the input scene.

© 1997 Optical Society of America

Original Manuscript: April 28, 1997
Revised Manuscript: August 7, 1997
Published: December 10, 1997

Lamia S. Jamal-Aldin, Rupert C. D. Young, and Chris R. Chatwin, "Application of nonlinearity to wavelet-transformed images to improve correlation filter performance," Appl. Opt. 36, 9212-9224 (1997)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. C. D. Young, C. R. Chatwin, “Design and simulation of a synthetic discriminant function filter for implementation in an up-dateable photorefractive correlator,” in Optical Pattern Recognition III, D. Casasent, T.-H. Chao, eds., Proc. SPIE1701, 239–263 (1992). [CrossRef]
  2. X. J. Lu, A. Katz, E. G. Kanterakis, N. P. Caviris, “Joint transform correlator that uses wavelet transforms,” Opt. Lett. 17, 1700–1702 (1992). [CrossRef] [PubMed]
  3. Y. L. Sheng, D. Roberge, H. Szu, T. W. Lu, “Optical wavelet matched filters for shift-invariant pattern recognition,” Opt. Lett. 18, 299–301 (1993). [CrossRef] [PubMed]
  4. M. W. Wen, S. H. Yin, P. Purwardi, F. T. S. Yu, “Wavelet matched filtering using a photorefractive crystal,” Opt. Commun. 99, 325–330 (1993). [CrossRef]
  5. R. C. D. Young, C. R. Chatwin, B. F. Scott, “High-speed hybrid optical digital correlator system,” Opt. Eng. 32, 2608–2615 (1993). [CrossRef]
  6. B. Javidi, “Non-linear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989). [CrossRef] [PubMed]
  7. B. Javidi, “Generalization of the linear matched filter concept to nonlinear matched filters,” Appl. Opt. 29, 1215–1224 (1990). [CrossRef] [PubMed]
  8. B. Javidi, G. Zhang, “Experiments on non-linearly transformed matched filters,” Opt. Eng. 31, 934–938 (1992). [CrossRef]
  9. B. Javidi, D. Painchaud, “Distortion-invariant pattern recognition with Fourier-plane nonlinear filters,” Appl. Opt. 35, 318–331 (1996). [CrossRef] [PubMed]
  10. K. Chalasinska-Macukow, R. Kotynski, K. Styczynski, F. Turon, J. Campos, M. J. Yzuel, E. Ahouzi, C. Gorecki, “Pure phase correlation. Application to optical pattern recognition,” in Euro-American Workshop on Optical Pattern Recognition, B. Javidi, P. Réfrégier, eds. (SPIE Optical Engineering Press, Bellingham, Washington, 1994), pp. 275–292.
  11. A. Grossmann, J. Morlet, “Decomposition of Hardy functions into square integrable wavelets of constant shape,” SIAM J. Math. Anal. 15, 723–736 (1984). [CrossRef]
  12. I. Daubechies, “The wavelet transform, time frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36, 961–1005 (1990). [CrossRef]
  13. S. Mallat, “A theory of multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Machine Intell. 31, 674–693 (1989). [CrossRef]
  14. I. Daubechies, Ten Lectures on Wavelets (Academic, San Diego, Calif., 1992). [CrossRef]
  15. C. K. Chui, An Introduction to Wavelets (Academic, San Diego, Calif., 1992).
  16. Y. Meyer, Waveletsand Operators (Cambridge U. Press, Cambridge, UK, 1992).
  17. D. Marr, E. Hildreth, “Theory of edge detection,” Proc. RT. Soc. London Ser. B 207, 187–217 (1980). [CrossRef]
  18. B. V. K. Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990). [CrossRef] [PubMed]
  19. J. L. Horner, “Light utilization in optical correlators,” Appl. Opt. 21, 4511–4514 (1982). [CrossRef] [PubMed]
  20. P. Refregier, “Filter design for optical pattern recognition: multicriteria optimization approach,” Opt. Lett. 15, 854–856 (1990). [CrossRef] [PubMed]
  21. D. Flannery, “Optimal trade-off distortion-tolerant constrained-modulation correlation filters,” J. Opt. Soc. Am. A 12, 66–72 (1995). [CrossRef]
  22. A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, S. R. F. Sims, J. Epperson, “Unconstrained correlation filters,” Appl. Opt. 33, 3751–3759 (1994). [CrossRef] [PubMed]

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