An Illumination Model for a Skin Layer Bounded by Rough Surfaces

  • Jos Stam
Part of the Eurographics book series (EUROGRAPH)


In this paper we present a novel illumination model that takes into account multiple anisotropic scattering in a layer bounded by two rough surfaces. We compute the model by a discrete-ordinate solution of the equation of radiative transfer. This approach is orders of magnitude faster than a Monte Carlo simulation and does not suffer from any noisy artifacts. By fitting low order splines to our results we are able to build analytical shaders. This is highly desirable since animators typically want to texture map the parameters of such a shader for higher realism. We apply our model to the important problem of rendering human skin. Our model does not seem to have appeared before in the optics literature. Most previous models did not handle rough surfaces at the skin’s boundary. Also we introduce a simple analytical bidirectional transmittance distribution function (BTDF) for an isotropic rough surface by generalizing the Cook-Torrance model.


Radiative Transfer Phase Function Skin Layer Global Illumination Cosine Series 
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.


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  1. 1.
    P. Beckmann and A. Spizzichino. The Scattering of Electromagnetic Waves from Rough Surfaces. Pergamon, New York, 1963.MATHGoogle Scholar
  2. 2.
    M. Born and E. Wolf. Principles of Optics. Sixth (corrected) Edition. Cambridge University Press, Cambridge, U.K., 1997.Google Scholar
  3. 3.
    S. Chandrasekhar. Radiative Transfer. Dover, New York, 1960.Google Scholar
  4. 4.
    R. L. Cook and K. E. Torrance. A Reflectance Model for Computer Graphics. ACM Computer Graphics (SIGGRAPH ’81),15(3):307–316, August 1981.CrossRefGoogle Scholar
  5. 5.
    P. Hanrahan and W. Krueger. Reflection from Layered Surfaces due to Subsurface Scattering. In Proceedings of SIGGRAPH ’93, pages 165–174. Addison-Wesley Publishing Company, August 1993.Google Scholar
  6. 6.
    J. E. Hansen and L. D. Travis. Light Scattering in Planetary Atmospheres. Space Science Reviews, 16:527–610, 1974.CrossRefGoogle Scholar
  7. 7.
    X. D. He. Physically-Based Modelsfor the Reflection, Transmission and Subsurface Scattering of Light by Smooth and Rough Surfaces, with Applications to Realistic Image Synthesis. PhD thesis, Cornell University, Ithaca, New York, 1993.Google Scholar
  8. 8.
    H. W. Jensen, S. R. Marschner, M. Levoy, and P. Hanrahan. A Practical Model for Subsurface Light Transport. In Computer Graphics Proceedings, Annual Conference Series, 2001, page (to appear), August 2001.Google Scholar
  9. 9.
    Z. Jin and K. Stamnes. Radiative transfer in nonuniformly refracting layered media: atmosphere-ocean system. Applied Optics, 33(3):431–442, January 1994.CrossRefGoogle Scholar
  10. 10.
    J. T. Kajiya and B. P. von Herzen. Ray Tracing Volume Densities. ACM Computer Graphics (SJGGRAPH’ 84),18(3):165–174, July 1984.CrossRefGoogle Scholar
  11. 11.
    E. P. F. Lafortune, S-C. Foo, K. E. Torrance, and D. P. Greenberg. Non-Linear Approximation of Reflectance Functions. In Computer Graphics Proceedings, Annual Conference Series, 1997, pages 117–126, August 1997.Google Scholar
  12. 12.
    E. Languénou, K. Bouatouch, and M. Chelle. Global illumination in presence of participating media with general properties. In Proceedings of the 5th Eurographics Workshop on Rendering, pages 69–85, Darmstadt, Germany, June 1994.Google Scholar
  13. 13.
    S. R. Marschner, S. H. Westin, E. P. F. Lafortune, K. E. Torrance, and D. P. Greenberg. Image-based brdf measurement including human skin. Eurographics Workshop on Rendering, 1999.Google Scholar
  14. 14.
    N. Max. Efficient light propagation for multiple anisotropic volume scattering. In Proceedings of the 5th Eurographics Workshop on Rendering, pages 87–104, Darmstadt, Germany, June 1994.Google Scholar
  15. 15.
    C. D. Mobley. A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces. Limnology and Oceanography, 34(8):1473–1483, 1989.CrossRefGoogle Scholar
  16. 16.
    S. K. Nayar, K. Ikeuchi, and T. Kanade. Surface Reflection: Physical and Geometrical Perspectives. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(7):611–634, July 1991.CrossRefGoogle Scholar
  17. 17.
    NETLIB. The code is publicly available from Scholar
  18. 18.
    M. Pharr and P. Hanrahan. Monte Carlo Evaluation of Non-Linear Scattering Equations for Subsurface Reflection. In Computer Graphics Proceedings, Annual Conference Series, 2000, pages 75–84, July 2000.Google Scholar
  19. 19.
    G. N. Plass, G. W. Kattawar, and F. E. Catchings. Matrix operator theory of radiative transfer. 1: Rayleigh scattering. Applied Optics, 12(2):314–329, February 1973.CrossRefGoogle Scholar
  20. 20.
    A. A. Prahl, M. J. C. van Gernert,, and A. J. Welch. Determining the optical properties of turbid media by using the adding-doubling method. Applied Optics, 32:559–568, 1993.CrossRefGoogle Scholar
  21. 21.
    K. Stamnes and P. Conklin. A New Multi-Layer Discrete Ordinate Approach to Radiative Transfer in Vertically Inhomogeneous Atmospheres. Journal of Quantum Spectroscopy and Radiative Transfer, 31(3):273–282, 1984.CrossRefGoogle Scholar
  22. 22.
    K. E. Torrance and E. M. Sparrow. Theory for Off-Specular Reflection From Roughened Surfaces. Journal of the Optical Society of America, 57(9): 1105–1114, September 1967.CrossRefGoogle Scholar
  23. 23.
    V. V. Tuchin. Light scattering study of tissue. Physics — Uspekhi, 40(5):495–515, 1997.CrossRefGoogle Scholar
  24. 24.
    M. J. C. van Gernert, S. L. Jacques, H. J. C. M. Sterenborg, and W. M. Star. Skin optics. IEEE Transactions on Biomedical Engineering, 36(12):1146–1154, December 1989.CrossRefGoogle Scholar
  25. 25.
    B. van Ginneken, M. Stavridi, and J. J. Koenderink. Diffuse and specular reflectance from rough surfaces. Applied Optics, 37(1):130–139, January 1998.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Jos Stam
    • 1
  1. 1.Alias | wavefrontSeattleUSA

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