Abstract
The Shape from Shading Problem is mathematically equivalent to a non-linear first order PDE. Horn[10] first solved this equation with a variational approach. We design an extended version by adding a smoothing term and present selected test results with synthetic and real images. The results are compared with the results of the original Horn approach.
Preview
Unable to display preview. Download preview PDF.
References
Ascher, U., Carter, M., A Multigrid Method for Shape from Shading, SIAM J. Numerical Analysis, Februar 1993.
Brandt, A., Dinar, N., Multigrid Solutions to elliptic flow problems, Numerical Methods for Partial Differential Equations, S. Parter, ed., Proceedings, Oktober 1978, Madison, WI, Academic Press, NY, 1979.
Brandt, A., Guide to Multigrid Development, Multigrid Methods, ed. W. Hackbusch and U. Trottenberg, Proceedings of Conference on Multigrid Methods, Köln-Porz, 1981.
Brooks, Chojnacki, N., MultigridSolutions to Elliptic Flow Problems, Multigrid Methods for Partial Differential Equations, ed. S.Parter, Academic Press, 1979.
Courant, R., Hilbert, D., Methods of Mathematical Physics, Interscience, 1953.
Chabrowski, J., Zhang, K., On variational approach to photometric stereo, Annales H Poincare 1994
Hackbusch, W., Multigrid Methods and Applications, Springer Verlag 1985.
Horn, B., Brooks, M., A Variational Approach to Shape from Shading, Computer Vision, Graphics and Image Processing, 1986.
Horn, B., Brooks, M., Shape from Shading, MIT Press, Boston, MA, 1989.
Horn, B., Robot Vision MIT Press, Boston, MA, 1986.
Kozera, R., A Note on Existence and Uniqueness in Shape from Shading, IEEE Conference on Computer Vision and Pattern Recognition, 1993.
Kozera, R., On Shape Recovery from two shading patterns, Intern. Jour. of Pattern Rec. and Artifficial Intelligence, 6 (4), 1992.
Leclerc, Y.G., Bobick, A.F., The direct computation of Height from shading, CVPR 1991
Lions, P., Rouy, E., Tourin, A., Shape From Shading, Viscosity Solutions and Edges, Numerische Mathematik, 64 (3), 1993.
Rouy, E., Tourin, A., A Viscosity Solutions Approach to Shape from Shading, SIAM J. Numer. Anal., Juni 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag London Limited
About this paper
Cite this paper
Ulich, G. (1996). A new variational technique for Shape from Shading. In: Berger, MO., Deriche, R., Herlin, I., Jaffré, J., Morel, JM. (eds) ICAOS '96. Lecture Notes in Control and Information Sciences, vol 219. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-76076-8_138
Download citation
DOI: https://doi.org/10.1007/3-540-76076-8_138
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76076-4
Online ISBN: 978-3-540-40945-8
eBook Packages: Springer Book Archive