Example-Based Face Shape Recovery Using the Zenith Angle of the Surface Normal

  • Mario Castelán
  • Ana J. Almazán-Delfín
  • Marco I. Ramírez-Sosa-Morán
  • Luz A. Torres-Méndez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4827)


We present a method for recovering facial shape using an image of a face and a reference model. The zenith angle of the surface normal is recovered directly from the intensities of the image. The azimuth angle of the reference model is then combined with the calculated zenith angle in order to get a new field of surface normals. After integration of the needle map, the recovered surface has the effect of mapped facial features over the reference model. Experiments demonstrate that for the lambertian case, surface recovery is achieved with high accuracy. For non-Lambertian cases, experiments suggest potential for face recognition applications.


Ground Truth Input Image Reference Model Zenith Angle Azimuth Angle 
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.
    Horn, B., Brooks, M.: Shape from Shading. MIT Press, Cambridge (1989)Google Scholar
  2. 2.
    Jognston, A., Hill, H., Carman, N.: Recognising faces: Effects of lightning direction, inversion and brightness reversal. Perception 21, 365–375 (1992)CrossRefGoogle Scholar
  3. 3.
    Atick, J., Griffin, P., Redlich, N.: Statistical approach to shape from shading: Reconstruction of three-dimensional face surfaces from single two-dimensional images. Neural Computation 8, 1321–1340 (1996)CrossRefGoogle Scholar
  4. 4.
    Blanz, V., Vetter, T.: Face recognition based on fitting a 3d morphable model. IEEE T. PAMI 25(9), 1063–1074 (2003)Google Scholar
  5. 5.
    Smith, W., Hancock, E.R.: Recovering facial shape and albedo using a statistical model of surface normal direction. In: Proc. IEEE ICCV 2005, pp. 588–595 (2005)Google Scholar
  6. 6.
    Castelán, M., Hancock, E.R.: Using cartesian models of faces with a data-driven and integrable fitting framework. In: Campilho, A., Kamel, M. (eds.) ICIAR 2006. LNCS, vol. 4142, pp. 134–145. Springer, Heidelberg (2006)Google Scholar
  7. 7.
    Worthington, P.L., Hancock, E.R.: New constraints on data-closeness and needle map consistency for shape-from-shading. IEEE T. PAMI 21(12), 1250–1267 (1999)Google Scholar
  8. 8.
    Kemelmacher, I., Basri, R.: Molding face shapes by example. In: Proc. European Conference in Computer Vision (2006)Google Scholar
  9. 9.
    Marr, D.: Vision: A Computational Investigation into the Human Representation and Processing of the Visual information. Freeman (1982)Google Scholar
  10. 10.
    Moses, Y., Adini, Y., Ullman, S.: Face recognition: the problem of compensating for changes in illumination direction. In: Proc. European Conference on Computer Vision, pp. 286–296 (1994)Google Scholar
  11. 11.
    Horn, B.: Understanding image intensities. Artificial Intelligence 8, 201–231 (1997)CrossRefGoogle Scholar
  12. 12.
    Erens, R., Kappers, A., Koenderink, J.: Perception of local shape from shading. Perception and Psychophysics 54(2), 145–156 (1993)Google Scholar
  13. 13.
    Blanz, V., Vetter, T.: A morphable model for the synthesis of 3d faces. In: SIGGRAPH 1999, pp. 187–194 (1999)Google Scholar
  14. 14.
    Frankot, R., Chellappa, R.: A method for enforcing integrability in shape from shading algorithms. IEEE T.PAMI 10, 438–451 (1988)Google Scholar
  15. 15.
    Young, F.W., H.R.M.: Theory and Applications of Multidimensional Scaling. Eribaum Associates, Hillsdale (1994)Google Scholar
  16. 16.
    Georghiades, A., Belhumeur, D., Kriegman, D.: From few to many: Illumination cone models for face recognition under variable lighting and pose. In: IEEE T. PAMI, pp. 634–660 (2001)Google Scholar
  17. 17.
    Basri, R., Jacobs, D.W.: Lambertian reflectance and linear subspaces. IEEE T. PAMI 25(2), 218–233 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Mario Castelán
    • 1
  • Ana J. Almazán-Delfín
    • 2
  • Marco I. Ramírez-Sosa-Morán
    • 3
  • Luz A. Torres-Méndez
    • 1
  1. 1.CINVESTAV Campus Saltillo, Ramos Arizpe 25900, CoahuilaMéxico
  2. 2.Universidad Veracruzana, Facultad de Física e Inteligencia Artificial, Xalapa 91000, VeracruzMéxico
  3. 3.ITESM, Campus Saltillo, Saltillo 25270, CoahuilaMéxico

Personalised recommendations