Recovering shading from color images

  • Brian V. Funt
  • Mark S. Drew
  • Michael Brockington
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 588)


Existing shape-from-shading algorithms assume constant reflectance across the shaded surface. Multi-colored surfaces are excluded because both shading and reflectance affect the measured image intensity. Given a standard RGB color image, we describe a method of eliminating the reflectance effects in order to calculate a shading field that depends only on the relative positions of the illuminant and surface. Of course, shading recovery is closely tied to lightness recovery and our method follows from the work of Land [10, 9], Horn [7] and Blake [1]. In the luminance image, R+G+B, shading and reflectance are confounded. Reflectance changes are located and removed from the luminance image by thresholding the gradient of its logarithm at locations of abrupt chromaticity change. Thresholding can lead to gradient fields which are not conservative (do not have zero curl everywhere and are not integrable) and therefore do not represent realizable shading fields. By applying a new curl-correction technique at the thresholded locations, the thresholding is improved and the gradient fields are forced to be conservative. The resulting Poisson equation is solved directly by the Fourier transform method. Experiments with real images are presented.


Color Image Gradient Image Color Edge Reflectance Change Threshold Image 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    A. Blake. Boundary conditions for lightness computation in Mondrian world. Computer Vision, Graphics, and Image Processing, 32:314–327, 1985.Google Scholar
  2. 2.
    P. T. Eliason, L. A. Soderblom, and P. S. Chavez Jr. Extraction of topographic and spectral albedo information from multispectral images. Photogrammetric Engineering and Remote Sensing, 48:1571–1579, 1981.Google Scholar
  3. 3.
    R. T. Frankot and R. Chellappa. A method for enforcing integrability in shape from shading algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10:439–451, 1988.Google Scholar
  4. 4.
    B. V. Funt and M.S. Drew. Color constancy computation in near-Mondrian scenes using a finite dimensional linear model. In Computer Vision and Pattern Recognition Proceedings, pages 544–549. IEEE Computer Society, June 1988.Google Scholar
  5. 5.
    R. C. Gonzalez and P. Wintz. Digital Image Processing. Addison/Wesley, 2nd edition, 1987.Google Scholar
  6. 6.
    G. Healey. Using color for geometry-insensitive segmentation. J. Opt. Soc. Am. A, 6:920–937, 1989.Google Scholar
  7. 7.
    B. K. P. Horn. Determining lightness from an image. Computer Vision, Graphics, and Image Processing, 3:277–299, 1974.Google Scholar
  8. 8.
    A. Hurlbert. Formal connections between lightness algorithms. J. Opt. Soc. Am. A, 3:1684–1692, 1986.PubMedGoogle Scholar
  9. 9.
    E.H. Land. Recent advances in retinex theory. Vision Res., 26:7–21, 1986.PubMedGoogle Scholar
  10. 10.
    E.H. Land and J.J. McCann. Lightness and retinex theory. J. Opt. Soc. Amer., 61:1–11, 1971.Google Scholar
  11. 11.
    A. P. Pentland. Linear shape from shading. Int. J. Comput. Vision, 4:153–162, 1990.Google Scholar
  12. 12.
    T. Poggio. Mit progress in understanding images. In DARPA Image Understanding Work-shop, pages 56–74, 1989.Google Scholar
  13. 13.
    T. Simchony, R. Chellappa, and M. Shao. Direct analytical methods for solving Poisson equations in computer vision problems. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12:435–445, 1990.Google Scholar
  14. 14.
    D. Terzopoulos. Image analysis using multigrid relaxation methods. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8:129–139, 1986.Google Scholar
  15. 15.
    G. Wyszecki and W.S. Stiles. Color Science: Concepts and Methods, Quantitative Data and Formulas. Wiley, New York, 2nd edition, 1982.Google Scholar
  16. 16.
    Q. Zheng and R. Chellappa. Estimation of illuminant direction, albedo, and shape from shading. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13:680–702, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Brian V. Funt
    • 1
  • Mark S. Drew
    • 1
  • Michael Brockington
    • 1
  1. 1.School of Computing ScienceSimon Fraser UniversityVancouverCanada

Personalised recommendations