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. 14, Iss. 4 — Apr. 1, 1997
  • pp: 779–791

Robust quadrature filters

J. L. Marroquin, J. E. Figueroa, and M. Servin  »View Author Affiliations


JOSA A, Vol. 14, Issue 4, pp. 779-791 (1997)
http://dx.doi.org/10.1364/JOSAA.14.000779


View Full Text Article

Enhanced HTML    Acrobat PDF (596 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We deal with the relation between two well-known topics in signal processing and computational vision: quadrature filters (QF’s) and Bayesian estimation with Markov random fields (MRF’s) as prior models. We present a new class of complex-valued MRF models such that the optimal estimators obtained with them correspond to the output of QF’s tuned at particular frequencies. It is shown that the machinery that has proven to be effective in classical (real-valued) MRF modeling may be generalized to the complex case in a straightforward way. To illustrate the power of this technique, we present complex MRF models that implement robust QF’s that exhibit good performance in situations in which ordinary linear, shift-invariant filters fail. These include robust filters that are relatively insensitive to edge effects and missing data and that can reliably estimate the local phase in singularity neighborhoods; we also present models for the specification of piecewise-smooth QF’s. Examples of applications to fringe pattern analysis, phase-based stereo reconstruction, and texture segmentation are presented as well.

© 1997 Optical Society of America

History
Original Manuscript: March 4, 1996
Revised Manuscript: November 8, 1996
Manuscript Accepted: November 12, 1996
Published: April 1, 1997

Citation
J. L. Marroquin, J. E. Figueroa, and M. Servin, "Robust quadrature filters," J. Opt. Soc. Am. A 14, 779-791 (1997)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-14-4-779


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. S. Geman, D. Geman, “Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 721–741 (1984). [CrossRef]
  2. J. Marroquin, S. Mitter, T. Poggio, “Probabilistic solution of ill-posed problems in computational vision,” J. Am. Stat. Assoc. 82, 76–89 (1987). [CrossRef]
  3. A. Blake, A. Zisserman, Visual Reconstruction (MIT Press, Cambridge, Mass., 1987).
  4. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978).
  5. D. Gabor, “Theory of communication,” J. Inst. Electr. Eng. 93, 429–457 (1946).
  6. D. J. Fleet, A. D. Jepson, M. R. M. Jenkin, “Phase-based disparity measurement,” Comput. Vision Graphics Image Process. 53, 198–210 (1991).
  7. T. Sanger, “Stereo disparity computation using Gabor filters,” Biol. Cybern. 59, 405–418 (1988). [CrossRef]
  8. M. Takeda, H. Ina, S. Kobayashi, “Fourier transform methods of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
  9. M. Turner, “Texture discrimination by Gabor functions,” Biol. Cybern. 55, 71–82 (1986). [PubMed]
  10. J. Beck, A. Sutter, R. Ivry, “Spatial frequency channels and perceptual grouping in texture segregation,” Comput. Vision Graphics and Image Process. 37, 299–325 (1987). [CrossRef]
  11. J. Bergen, E. Adelson, “Early vision and texture perception,” Nature (London) 333, 363–364 (1988). [CrossRef]
  12. I. Fogel, D. Sagi, “Gabor filters for texture discrimination,” Biol. Cybern. 61, 103–113 (1989). [CrossRef]
  13. E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985). [CrossRef] [PubMed]
  14. D. J. Heeger, “A model for the extraction of image flow,” J. Opt. Soc. Am. A 4, 1455–1471 (1987). [CrossRef] [PubMed]
  15. J. Besag, “Spatial interaction and the statistical analysis of lattice systems,” J. R. Stat. Soc. B 36, 192–326 (1974).
  16. G. H. Golub, C. F. Van Loan, Matrix Computations (Johns Hopkins U., Baltimore, 1990).
  17. J. L. Marroquin, M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. Am. A 12, 2393–2400 (1995). [CrossRef]
  18. J. L. Marroquin, “Deterministic interactive particle models for image processing and computer graphics,” Comput. Vision Graphics Image Process. 55, 408–417 (1993).
  19. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–393.
  20. D. Malacara, ed., Optical Shop Testing (Wiley, New York, 1992).
  21. A. N. Thikonov, V. Y. Arsenin, Solutions to Ill-posed Problems (Winston and Sons, Washington, D.C., 1977).
  22. M. Bertero, T. Poggio, V. Torre, “Ill-posed problems in early vision,” Proc. IEEE 76, 869–887 (1988). [CrossRef]
  23. W. E. L. Grimson, “A computational theory of visual surface interpolation,” Philos. Trans. R. Soc. London, Ser. B 298, 395–427 (1982). [CrossRef] [PubMed]
  24. D. Geman, G. Reynolds, “Constrained restoration and the recovery of discontinuities,” IEEE Trans. Pattern Anal. Machine Intell. 14, 367–383 (1992). [CrossRef]
  25. J. L. Marroquin, “Probabilistic solution of inverse problems,” (Massachusetts Institute of Technology, Cambridge, Mass., 1985).
  26. J. L. Marroquin, “The adaptive ICM algorithm,” , Centro de Investigación en Matematicas, Guonajuato, Mexico, 1996).
  27. T. Poggio, H. Voorhees, A. Yuille, “A regularized solution to edge detection,” (Massachusetts Institute of Technology, Cambridge, Mass., 1985).
  28. G. Wahba, Spline Models for Observational Data (Society for Industrial and Applied Mathematics, Philadelphia, 1990).

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