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.
This research was supported in part by National Science Foundation grants DMS-9115762, IRI-9113690, and CDA-822572.
Chapter PDF
References
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.
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.
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.
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.
B. K. P. Horn and M.J. Brooks (eds.) Shape from Shading. MIT Press: Cambridge, MA, 1989.
H. J. Kushner and P. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, Springer-Verlag: New York, 1992.
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.
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.
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.
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.
J. Oliensis, “Uniqueness in Shape From Shading,” The International Journal of Computer Vision, Vol. 6 no. 2, pp. 75–104, 1991.
R. T. Rockafellar, Convex Analysis, Princeton University Press: Princeton, 1970.
E. Rouy, A. Tourin, “A Viscosity Solutions Approach To Shape-From-Shading,” SIAM J. on Numerical Analysis 29:867–884, 1992.
E. Rouy, A. Tourin, “A Viscosity Solutions Approach To Shape-From-Shading,” unpublished report.
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.
B. V. H. Saxberg, “A Modern Differential Geometric Approach to Shape from Shading,” MIT Artificial Intelligence Laboratory, TR 1117, 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dupuis, P., Oliensis, J. (1994). Shape from shading: Provably convergent algorithms and uniqueness results. In: Eklundh, JO. (eds) Computer Vision — ECCV '94. ECCV 1994. Lecture Notes in Computer Science, vol 801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028359
Download citation
DOI: https://doi.org/10.1007/BFb0028359
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57957-1
Online ISBN: 978-3-540-48400-4
eBook Packages: Springer Book Archive