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Shape from shading: Provably convergent algorithms and uniqueness results

  • Paul Dupuis
  • John Oliensis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 801)

Abstract

An explicit representation for the surface corresponding to a shaded image is presented and proven to be correct (under standard conditions). Uniqueness of the surface is an immediate consequence. Using this representation, various iterative algorithms for shape reconstruction are derived. It has been proven that all these algorithms converge monotonically to the correct surface reconstruction, and they have been shown experimentally to be fast and robust. Some of the results of this paper extend previous ones to the case of illumination from a general direction.

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References

  1. 1.
    M. Bichsel, A. P. Pentland, “A Simple Algorithm for Shape from Shading,” Proc. IEEE Conference on Computer Vision and Pattern Recognition, Champaign, Illinois, pp. 459–465, June 1992.Google Scholar
  2. 2.
    A. R. Bruss, “The Eikonal Equation: Some Results Applicable to Computer Vision,” Journal of Mathematical Physics, Vol. 23, No. 5, pp. 890–896, May 1982.Google Scholar
  3. 3.
    P. Dupuis and J. Oliensis, “An Optimal Control Formulation and Related Numerical Methods for a Problem in Shape Reconstruction,” to appear in Annals of Applied Probability.Google Scholar
  4. 4.
    P. Dupuis and J. Oliensis, “Direct Method for Reconstructing Shape from Shading,” in IEEE Computer Vision and Pattern Recognition, Champaign, Illinois, June 1992, pp. 453–458.Google Scholar
  5. 5.
    B. K. P. Horn and M.J. Brooks (eds.) Shape from Shading. MIT Press: Cambridge, MA, 1989.Google Scholar
  6. 6.
    H. J. Kushner and P. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, Springer-Verlag: New York, 1992.Google Scholar
  7. 7.
    J. Oliensis and P. Dupuis, “A Global Algorithm for Shape from Shading,” long paper, Proc. of the Fourth International Conference on Computer Vision, Berlin, Germany 1993, pp. 692–701.Google Scholar
  8. 8.
    J. Oliensis and P. Dupuis, “Direct Method for Reconstructing Shape from Shading,” in Physics-Based Vision: Principles and Practice, Shape Inference Volume, L. Wolff, S. Shafer, G. Healey, editors, Jones and Bartlett, Boston, June 1992, pp. 17–28.Google Scholar
  9. 9.
    J. Oliensis and Paul Dupuis, “Direct method for reconstructing shape from shading,” Proc. SPIE Conf. 1570 on Geometric Methods in Computer Vision, San Diego, California, July 1991, pp. 116–128.Google Scholar
  10. 10.
    J. Oliensis, “Shape from Shading as a Partially Well-Constrained Problem,” Computer Vision, Graphics, and Image Processing: Image Understanding, Vol. 54, No. 2, September 1991, pp. 163–183.Google Scholar
  11. 11.
    J. Oliensis, “Uniqueness in Shape From Shading,” The International Journal of Computer Vision, Vol. 6 no. 2, pp. 75–104, 1991.Google Scholar
  12. 12.
    R. T. Rockafellar, Convex Analysis, Princeton University Press: Princeton, 1970.Google Scholar
  13. 13.
    E. Rouy, A. Tourin, “A Viscosity Solutions Approach To Shape-From-Shading,” SIAM J. on Numerical Analysis 29:867–884, 1992.Google Scholar
  14. 14.
    E. Rouy, A. Tourin, “A Viscosity Solutions Approach To Shape-From-Shading,” unpublished report.Google Scholar
  15. 15.
    B. V. H. Saxberg, “An Application of Dynamical Systems Theory to Shape From Shading,” in Proc. DARPA Image Understanding Workshop, Palo Alto, CA, pp. 1089–1104, May 1989.Google Scholar
  16. 16.
    B. V. H. Saxberg, “A Modern Differential Geometric Approach to Shape from Shading,” MIT Artificial Intelligence Laboratory, TR 1117, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Paul Dupuis
    • 1
  • John Oliensis
    • 2
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of Computer ScienceUniversity of Massachusetts at AmherstAmherstUSA

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