Advertisement

On the classification of singular points for the global shape from shading problem: A study of the constraints imposed by isophotes

  • Takayuki Okatani
  • Koichiro Deguchi
Session T1B: Physics-Based Vision
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1351)

Abstract

This paper concerns with the global surface reconstruction from a shaded image. It is known that the key to the global reconstruction lies in classifying singular points in the image into three categories—convex, concave or saddle classes. Several methods have been proposed for this problem. All of them require explicit solution of the shape from shading equation. Therefore the results may suffer from image noise and modeling errors of the surface reflecting properties and illumination. If the classification of singular points without such an explicit solution of the equation would have been possible, then the global reconstruction could have been made much more precise. The present work aims towards developing a classification technique where such a explicit solution is not required. Our first step is to show that isophotes (lines of equal brightness) provide some information on the types of singulax points; if two isophotes exist which evolve from two singular points and meet each other, then the one of the two singular points is elliptic and the other is hyperbolic. This is derived from intrinsic properties of a smooth (twice differentiable) surface.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. K. P. Horn, “Shape from shading: a method for obtaining the shape of a smooth opaque object from one view,” Tech. Rep. MAC-TR-79, MIT, Cambridge, MA, 1970.Google Scholar
  2. 2.
    K. Ikeuchi and B. K. P. Horn, “Numerical shape from shading and occluding boundaries,” Artificial Intelligence, vol. 17, no. 3, pp. 141–184, 1981.Google Scholar
  3. 3.
    B. K. P. Horn and M. J. Brooks, Shape from shading. Cambridge, MA: MIT Press, 1989.Google Scholar
  4. 4.
    A. Blake, A. Zisserman, and G. Knowles, “Surface descriptions from stereo and shading,” Image and Vision Computing, vol. 3, no. 4, pp. 183–191, 1985.Google Scholar
  5. 5.
    B. V. H. Saxberg, “A modern differential geometric approach to shape from shading,” Tech. Rep. 1117, MIT Al Laboratory, 1989.Google Scholar
  6. 6.
    J. Oliensis, “Uniqueness in shape from shading,” IJCV, vol. 6, no. 2, pp. 75–104, 1991.Google Scholar
  7. 7.
    J. Oliensis, “Shape from shading as a partially well-constructed problem,” CVGIP, vol. 54, pp. 163–183, September 1991.Google Scholar
  8. 8.
    J. Oliensis and P. Dupuis, “A global algorithm for shape from shading,” in 4th ICCV Conference, Berlin, pp. 692–701, 1993.Google Scholar
  9. 9.
    R. Kimmel and A. M. Bruckstein, “Global shape from shading,” Computer Vision and Image Understanding, vol. 62, no. 3, pp. 360–369, 1995.Google Scholar
  10. 10.
    D. Forsyth and A. Zisserman, “Reflections on Shading,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 13, no. 7, pp. 671–679, 1991.Google Scholar
  11. 11.
    B. K. P. Horn, Robot Vision. MIT Press: Cambridge, MA; and McGraw-Hill: New York, 1986.Google Scholar
  12. 12.
    R. Kimmel and A. M. Bruckstein, “Tracking level sets by level sets: A method for solving the shape from shading problem,” Computer Vision and Image Understanding, vol. 62, pp. 47–58, July 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Takayuki Okatani
    • 1
  • Koichiro Deguchi
    • 1
  1. 1.Faculty of EngineeringUniversity of TokyoBunkyo-ku, TokyoJapan

Personalised recommendations