A New Framework for Grayscale and Colour Non-lambertian Shape-from-Shading

  • William A. P. Smith
  • Edwin R. Hancock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4844)


In this paper we show how arbitrary surface reflectance properties can be incorporated into a shape-from-shading scheme, by using a Riemannian minimisation scheme to minimise the brightness error. We show that for face images an additional regularising constraint on the surface height function is all that is required to recover accurate face shape from single images, the only assumption being of a single light source of known direction. The method extends naturally to colour images, which add additional constraints to the problem. For our experimental evaluation we incorporate the Torrance and Sparrow surface reflectance model into our scheme and show how to solve for its parameters in conjunction with recovering a face shape estimate. We demonstrate that the method provides a realistic route to non-Lambertian shape-from-shading for both grayscale and colour face images.


Face Image Surface Gradient Photometric Stereo View Synthesis Radiance Function 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ahmed, A.H., Farag, A.A.: A new formulation for shape from shading for non-lambertian surfaces. In: Proc. CVPR, vol. 2, pp. 1817–1824 (2006)Google Scholar
  2. 2.
    Georghiades, A.: Recovering 3-d shape and reflectance from a small number of photographs. In: Eurographics Symposium on Rendering, pp. 230–240 (2003)Google Scholar
  3. 3.
    Christensen, P.H., Shapiro, L.G.: Three-dimensional shape from color photometric stereo. Int. J. Comput. Vision 13, 213–227 (1994)CrossRefGoogle Scholar
  4. 4.
    Ononye, A.E., Smith, P.W.: Estimating the shape of a surface with non-constant reflectance from a single color image. In: Proc. BMVC, pp. 163–172 (2002)Google Scholar
  5. 5.
    Torrance, K., Sparrow, E.: Theory for off-specular reflection from roughened surfaces. J. Opt. Soc. Am. 57, 1105–1114 (1967)CrossRefGoogle Scholar
  6. 6.
    Horn, B.K.P., Brooks, M.J.: The variational approach to shape from shading. Comput. Vis. Graph. Image Process 33, 174–208 (1986)CrossRefGoogle Scholar
  7. 7.
    Worthington, P.L., Hancock, E.R.: New constraints on data-closeness and needle map consistency for shape-from-shading. IEEE Trans. Pattern Anal. Mach. Intell. 21, 1250–1267 (1999)CrossRefGoogle Scholar
  8. 8.
    Zhang, F., Hancock, E.R.: A riemannian weighted filter for edge-sensitive image smoothing. In: Proc. ICPR, pp. 594–598 (2006)Google Scholar
  9. 9.
    Frankot, R.T., Chellappa, R.: A method for enforcing integrability in shape from shading algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 10, 439–451 (1988)zbMATHCrossRefGoogle Scholar
  10. 10.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990)CrossRefGoogle Scholar
  11. 11.
    Georghiades, A., Belhumeur, P., Kriegman, D.: From few to many: Illumination cone models for face recognition under variable lighting and pose. IEEE Trans. Pattern Anal. Mach. Intell. 23, 643–660 (2001)CrossRefGoogle Scholar
  12. 12.
    Sim, T., Baker, S., Bsat, M.: The cmu pose, illumination, and expression database. IEEE Trans. Pattern Anal. Mach. Intell. 25, 1615–1618 (2003)CrossRefGoogle Scholar
  13. 13.
    USF HumanID 3D Face Database, Courtesy of Sudeep. Sarkar, University of South Florida, Tampa, FLGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • William A. P. Smith
    • 1
  • Edwin R. Hancock
    • 1
  1. 1.Department of Computer Science, The University of York 

Personalised recommendations