International Journal of Computer Vision

, Volume 6, Issue 3, pp 173–195 | Cite as

Shape from interreflections

  • Shree K. Nayar
  • Katsushi Ikeuchi
  • Takeo Kanade
Article

Abstract

Shape-from-intensity methods assume that points in a scene are only illuminated by the sources of light. This assumption is valid only when the scene consists of a single convex surface. Most scenes consist of concave surfaces where points reflect light among themselves. In the presence of these interreflections, shape-from-intensity methods produce erroneous (pseudo) estimates of shape and reflectance. This article shows that, for Lambertian surfaces, the pseudo shape and reflectance are unique and can be mathematically related to the actual shape and reflectance of the surface. We present an iterative algorithm that simultaneously recovers the actual shape and reflectance from the pseudo estimates. The general behavior of the algorithm and its convergence properties are discussed. Simulations as well as experimental results are included to demonstrate the accuracy and robustness of the algorithm.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bajesy, R., Lee, S.W., and Leonardis, A., 1989. Image segmentation with detection of highlights and interreflections using color. GRASP LAB 182 MS-CIS-89-39, University of Pennsylvania, Dept. of Computer and Info. Science, June.Google Scholar
  2. Brill, M.H., 1989. Object-based segmentation and color recognition in multispectral images. Proc. SPIE-SPSE Meeting, January, Paper 1076-11.Google Scholar
  3. Cohen, M.F., and Greenberg, D.P., 1985. The hemi-cube: a radiosity solution for complex environments. SIGGRAPH 1985 19: 31–40.Google Scholar
  4. Drew, M.S., and Funt, B.V., 1990. Calculating surface reflectance using a single-bounce model of mutual reflection. Proc. 3rd Intern. Conf. Comput. Vision, pp. 394–399.Google Scholar
  5. Forsyth, D., and Zisserman, A., 1989. Mutual illumination. Proc. Conf. Comput. Vision Patt. Recog., San Diego, pp. 466–473.Google Scholar
  6. Forsyth, D., and Zisserman, A., 1990. Shape from shading in the light of mutual illumination. Image and Vision Comput. 8 (1): 42–49.Google Scholar
  7. Gilchrist, A.L., 1979. The perception of surface blacks and whites. Scientific American 240: 112–124.Google Scholar
  8. Horn, B.K.P., 1970. Shape from shading: A method for obtaining the shape of a smooth opaque object from one view. MIT Project MAC Internal Report TR-79 and MIT AI Laboratory Technical Report 232, November.Google Scholar
  9. Horn, B.K.P., 1975. Image intensity understanding. MIT AI Lab. Memo-335, August.Google Scholar
  10. Horn, B.K.P., 1977. Image intensity understanding. Artificial Intelligence 8 (2): 201–231.Google Scholar
  11. Horn, B.K.P., 1986. Robot Vision, MIT PRESS, Cambridge, MA.Google Scholar
  12. Jacquez, J.A., and Kuppenheim, H.F., 1955. Theory of the integrating sphere. Opt. Soc. Amer. 45: 460–470.Google Scholar
  13. Koenderink, J.J., and vanDoorn, A.J., 1983. Geometrical modes as a general method to treat diffuse interreflections in radiometry. Opt. Soc. Amer. 73(6): 843–850.Google Scholar
  14. Koenderink, J.J., and vanDoorn, A.J., 1981. Photometric invariants related to solld shapes. Optica Acta 27: 981–996.Google Scholar
  15. Nayar, S.K., Ikeuchi, K., Kanade, T., 1990. Determining shape and reflectance of hybrid surfaces by photometric sampling. IEEE Trans. Robot. Autom. 6 (4): 418–431.Google Scholar
  16. Nayar, S.K., Ikeuchi, K., Kanade, T., 1990. Shape from interreflections. Proc. 3rd Intern. Conf. Comput. Vision. December. pp. 2–11.Google Scholar
  17. Nayar, S.K., Shape Recovery using physical models of reflection and interreflection. Ph.D. dissertation, Department of Electrical and Computer Engineering, Carnegie Mellon University, December.Google Scholar
  18. Nicodemus, F.E., Richmond, J.C., Hsia, J.J., Ginsberg, I.W., and Limperis, T., 1977. Geometrical considerations and nomenclature of reflectance. NBS Monograph 160, National Bureau of Standards, October.Google Scholar
  19. Novak, C., 1990. Ph.D. thesis proposal. Department of Computer Science, Carnegie Mellon University, August.Google Scholar
  20. Woodham, R.J., 1978. Photometric stereo: A reflectance map technique for determining surface orientation from image intensity. Proc. SPIE 155: 136–143.Google Scholar

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Shree K. Nayar
    • 1
  • Katsushi Ikeuchi
    • 2
  • Takeo Kanade
    • 2
  1. 1.Department of Computer ScienceColumbia UniversityNew York
  2. 2.The Roboties InstituteCarnegie Mellon UniversityPittsburgh

Personalised recommendations