Radiance Function Estimation for Object Classification

  • Antonio Robles-Kelly
  • Edwin R. Hancock
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3287)


This paper describes a simple method for estimating the surface radiance function from single images of smooth surfaces made of materials whose reflectance function is isotropic and monotonic. The method makes use of an implicit mapping of the Gauss map between the surface and a unit sphere. By assuming the material brightness is monotonic with respect to the angle between the illuminant direction and the surface normal, we show how the radiance function can be represented by a polar function on the unit sphere. Under conditions in which the light source direction and the viewer direction are identical, we show how the recovery of the radiance function may be posed as that of estimating a tabular representation of this polar function. A simple differential geometry analysis shows how the tabular representation of the radiance function can be obtained using the cumulative distribution of image gradients. We illustrate the utility of the tabular representation of the radiance function for purposes of material classification.


Unit Sphere Zenith Angle Polar Function Image Gradient Viewer Direction 
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.
    Beckmann, P., Spizzochino, A.: The Scattering of Electromagnetic Waves from Rough Surfaces. Pergamon, New York (1963)zbMATHGoogle Scholar
  2. 2.
    Vernold, C.L., Harvey, J.E.: A modified beckmann-kirchoff scattering theory for non-paraxial angles. In: Scattering and Surface Roughness. Proc. of the SPIE, vol. 3426, pp. 51–56 (1998)Google Scholar
  3. 3.
    Cook, R.L., Torrance, K.E.: A reflectance model for computer graphics. ACM Trans. on Graphics 1(1), 7–24 (1982)CrossRefGoogle Scholar
  4. 4.
    Phong, B.T.: Illumination for computer generated pictures. Communications of the ACM 18(6), 311–317 (1975)CrossRefGoogle Scholar
  5. 5.
    Wolff, L.B.: On the relative brightness of specular and diffuse reflection. In: Int. Conf. on Comp. Vision and Patt. Recognition, pp. 369–376 (1994)Google Scholar
  6. 6.
    Nayar, S.K., Oren, M.: Visual appearance of matte surfaces. SCIENCE 267, 1153–1156 (1995)CrossRefGoogle Scholar
  7. 7.
    Westin, S., Arvo, J., Torrance, K.: Predicting reflectance functions from complex surfaces. In: SIGGRAPH 1992 Conference Proceedings, pp. 255–264 (1992)Google Scholar
  8. 8.
    He, X., Heynen, P., Phillips, R., Torrance, K., Salesin, D., Greenberg, D.: A fast and accurate light reflection model. In: Siggraph 1992 Conference Proceedings, vol. 26, pp. 253–254 (1992)Google Scholar
  9. 9.
    Ward, G.J.: Measuring and modeling anisotropic reflection. Computer Graphics 26(2), 265–272 (1992)CrossRefGoogle Scholar
  10. 10.
    Lafortune, E.P.F., Foo, S.-C., Torrance, K.E., Greenberg, D.P.: Nonlinear approximation of reflectance functions. In: SIGGRAPH 1997 Conference Proceedings, pp. 117–126 (1997)Google Scholar
  11. 11.
    Dana, K.J., Nayar, S.K.: Correlation model for 3d texture. In: Int. Conf. on Comp. Vision, pp. 1061–1066 (1999)Google Scholar
  12. 12.
    Marschner, S.R., Westin, S.H., Lafortune, E.P.F., Torrance, K.E., Greenberg, D.P.: Image-based brdf measurement including human skin. In: 10th Eurographics Rendering Workshop (1999)Google Scholar
  13. 13.
    Debevec, P., Hawkins, T., Tchou, C., Duiker, H.-P., Sarokin, W., Sagar, M.: Acquiring the reflectance field of a human face. In: SIGGRAPH 2000, pp. 145–156 (2000)Google Scholar
  14. 14.
    Hertzmann, A., Seitz, S.M.: Shape and materials by example: A photometric stereo approach. In: Int. Conf. on Comp. Vision and Patt. Recognition, pp. 533–540 (2003)Google Scholar
  15. 15.
    Borg, I., Groenen, P.: Modern Multidimensional Scaling, Theory and Applications. Series in Statistics. Springer, Heidelberg (1997)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Antonio Robles-Kelly
    • 1
  • Edwin R. Hancock
    • 1
  1. 1.Department of Computer ScienceUniversity of YorkYorkUK

Personalised recommendations