A Light Scattering Model for Layered Rough Surfaces

  • Hossein Ragheb
  • Edwin R. Hancock
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4142)


We develop a new model for the scattering of light from layered rough surfaces. The model contains a surface scattering component together with a subsurface scattering component. The former component corresponds to the roughness on the upper surface boundary and is modeled using the modified Beckmann model. The latter component accounts for both refraction due to Fresnel transmission through the layer and rough (Beckmann) scattering at the lower layer boundary. Depending on the type of surface, the contributions of the two scattering components to the total outgoing radiance can vary dramatically for different materials. This behavior is conveniently captured by allowing a balance parameter in the model. Our experiments with BRDF data from several types of surface and with different scales of roughness confirm that the new model outperforms alternative variants of the Beckmann model together with several alternative reflectance models.


Balance Parameter Bread Sample Outgoing Radiance Subsurface Scattering Exponential Correlation 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.
    Beckmann, P., Spizzichino, A.: The Scattering of Electromagnetic Waves from Rough Surfaces. Pergamon, New York (1963)MATHGoogle Scholar
  2. 2.
    Beckmann, P.: Scattering of Light by Rough Surfaces. In: Wolf, E. (ed.) Progress in Optics, vol. VI, pp. 55–69 (1967)Google Scholar
  3. 3.
    Caron, J., Lafait, J., Andraud, C.: Scalar Kirchhoff’s Model for Light Scattering from Dielectric Random Rough Surfaces. Optics Com. 207, 17–28 (2002)CrossRefGoogle Scholar
  4. 4.
    Chandrasekhar, S.: Radiative Transfer. Dover, New York (1960)Google Scholar
  5. 5.
  6. 6.
    Dana, K.J., Nayar, S.K., van Ginneken, B., Koenderink, J.J.: Reflectance and Texture of Real-World Surfaces. In: Proc. IEEE CVPR, pp. 151–157 (1997)Google Scholar
  7. 7.
    Hanrahan, P., Krueger, W.: Reflectance from Layered Surfaces due to Subsurface Scattering. In: Computer Graphics, SIGGRAPH 1993 Proceedings, pp. 165–174 (1993)Google Scholar
  8. 8.
    He, X.D., Torrance, K.E., Sillion, F.X., Greenberg, D.P.: A Comprehensive Physical Model for Light Reflection. Computer Graphics 25, 175–186 (1991)CrossRefGoogle Scholar
  9. 9.
    Jensen, H.W., Marschner, S., Levoy, M., Hanrahan, P.: A Practical Model for Subsurface Light Transport. In: Proceedings of SIGGRAPH, pp. 511–518 (2001)Google Scholar
  10. 10.
    Lu, R., Koenderink, J., Kappers, A.: Optical properties of shot fabric. Applied Optics 39, 5785–5795 (2000)CrossRefGoogle Scholar
  11. 11.
    Kubelka, P.: New Contribution to the Optics of Intensely Light-Scattering Materials: Part I. J. Opt. Soc. Am. 38(5), 448–457 (1948)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Lafortune, E.P.F., Foo, S., Torrance, K.E., Greenberg, D.P.: Non-linear Approximation of Reflectance Functions. In: Proceedings of SIGGRAPH, pp. 117–126 (1997)Google Scholar
  13. 13.
    Matusik, W., Pfister, H., Brand, M., McMillan, L.: A Data-Driven Reflectance Model. ACM Transactions on Graphics 22(3), 759–769 (2003)CrossRefGoogle Scholar
  14. 14.
    Oren, M., Nayar, S.K.: Generalization of the Lambertian Model and Implications for Machine Vision. Int’l J. Computer Vision 14(3), 227–251 (1995)CrossRefGoogle Scholar
  15. 15.
    Ragheb, H., Hancock, E.: Testing New Variants of the Beckmann-Kirchhoff Model against Radiance Data. Computer Vision and Image Understanding 102(2), 145–168 (2006)CrossRefGoogle Scholar
  16. 16.
    Stam, J.: An Illumination Model for a Skin Layer Bounded by Rough Surfaces. In: Proc. Eurographics Workshop on Rendering, pp. 39–52 (2001)Google Scholar
  17. 17.
    Torrance, K.E., Sparrow, E.M.: Theory for Off-Specular Reflection from Roughened Surfaces. J. Opt. Soc. Am. 57(9), 1105–1114 (1967)CrossRefGoogle Scholar
  18. 18.
    Vernold, C.L., Harvey, J.E.: A Modified Beckmann-Kirchoff Scattering Theory for Non-paraxial Angles. In: Proceedings of the SPIE, vol. 3426, pp. 51–56 (1998)Google Scholar
  19. 19.
    Wolff, L.B.: Diffuse Reflectance Model for Smooth Dielectric Surfaces. J. Opt. Soc. Am. A 11(11), 2956–2968 (1994)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hossein Ragheb
    • 1
  • Edwin R. Hancock
    • 2
  1. 1.Department of Computer EngineeringBu-Ali Sina UniversityHamedanIran
  2. 2.Department of Computer ScienceUniversity of YorkYorkUK

Personalised recommendations