Skip to main content

A new variational technique for Shape from Shading

  • Image Restoration
  • Conference paper
  • First Online:
ICAOS '96

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 219))

  • 215 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ascher, U., Carter, M., A Multigrid Method for Shape from Shading, SIAM J. Numerical Analysis, Februar 1993.

    Google Scholar 

  2. 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.

    Google Scholar 

  3. Brandt, A., Guide to Multigrid Development, Multigrid Methods, ed. W. Hackbusch and U. Trottenberg, Proceedings of Conference on Multigrid Methods, Köln-Porz, 1981.

    Google Scholar 

  4. Brooks, Chojnacki, N., MultigridSolutions to Elliptic Flow Problems, Multigrid Methods for Partial Differential Equations, ed. S.Parter, Academic Press, 1979.

    Google Scholar 

  5. Courant, R., Hilbert, D., Methods of Mathematical Physics, Interscience, 1953.

    Google Scholar 

  6. Chabrowski, J., Zhang, K., On variational approach to photometric stereo, Annales H Poincare 1994

    Google Scholar 

  7. Hackbusch, W., Multigrid Methods and Applications, Springer Verlag 1985.

    Google Scholar 

  8. Horn, B., Brooks, M., A Variational Approach to Shape from Shading, Computer Vision, Graphics and Image Processing, 1986.

    Google Scholar 

  9. Horn, B., Brooks, M., Shape from Shading, MIT Press, Boston, MA, 1989.

    Google Scholar 

  10. Horn, B., Robot Vision MIT Press, Boston, MA, 1986.

    Google Scholar 

  11. Kozera, R., A Note on Existence and Uniqueness in Shape from Shading, IEEE Conference on Computer Vision and Pattern Recognition, 1993.

    Google Scholar 

  12. Kozera, R., On Shape Recovery from two shading patterns, Intern. Jour. of Pattern Rec. and Artifficial Intelligence, 6 (4), 1992.

    Google Scholar 

  13. Leclerc, Y.G., Bobick, A.F., The direct computation of Height from shading, CVPR 1991

    Google Scholar 

  14. Lions, P., Rouy, E., Tourin, A., Shape From Shading, Viscosity Solutions and Edges, Numerische Mathematik, 64 (3), 1993.

    Google Scholar 

  15. Rouy, E., Tourin, A., A Viscosity Solutions Approach to Shape from Shading, SIAM J. Numer. Anal., Juni 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Marie-Odile Berger Rachid Deriche Isabelle Herlin Jérome Jaffré Jean-Michel Morel

Rights and permissions

Reprints 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

Publish with us

Policies and ethics