“Efficient BRDF importance sampling using a factored representation” by Lawrence, Rusinkiewicz and Ramamoorthi

  • ©Jason Lawrence, Szymon Rusinkiewicz, and Ravi Ramamoorthi




    Efficient BRDF importance sampling using a factored representation



    High-quality Monte Carlo image synthesis requires the ability to importance sample realistic BRDF models. However, analytic sampling algorithms exist only for the Phong model and its derivatives such as Lafortune and Blinn-Phong. This paper demonstrates an importance sampling technique for a wide range of BRDFs, including complex analytic models such as Cook-Torrance and measured materials, which are being increasingly used for realistic image synthesis. Our approach is based on a compact factored representation of the BRDF that is optimized for sampling. We show that our algorithm consistently offers better efficiency than alternatives that involve fitting and sampling a Lafortune or Blinn-Phong lobe, and is more compact than sampling strategies based on tabulating the full BRDF. We are able to efficiently create images involving multiple measured and analytic BRDFs, under both complex direct lighting and global illumination.


    1. AGARWAL, S., RAMAMOORTHI, R., BELONGIE, S., AND JENSEN, H. W. 2003. Structured importance sampling of environment maps. In SIGGRAPH 03, 605–612.]] Google ScholarDigital Library
    2. ASHIKHMIN, M., AND SHIRLEY, P. 2000. An anisotropic Phong BRDF model. Journal of Graphics Tools: JGT 5, 2, 25–32.]] Google ScholarDigital Library
    3. BLINN, J. F. 1977. Models of light reflection for computer synthesized pictures. In SIGGRAPH 77, 192–198.]] Google ScholarDigital Library
    4. CHEN, W.-C., BOUGUET, J.-Y., CHU, M. H., AND GRZESZCZUK, R. 2002. Light field mapping: efficient representation and hardware rendering of surface light fields. In SIGGRAPH 02, 447–456.]] Google ScholarDigital Library
    5. COOK, R. L., AND TORRANCE, K. E. 1982. A reflectance model for computer graphics. ACM Trans. Graph. 1, 1, 7–24.]] Google ScholarDigital Library
    6. COOK, R. L. 1986. Stochastic sampling in computer graphics. ACM Transactions on Graphics 5, 1, 51–72.]] Google ScholarDigital Library
    7. DANA, K. J., VAN GINNEKEN, B., NAYAR, S. K., AND KOENDERINK, J. J. 1999. Reflectance and texture of real-world surfaces. ACM Trans. Graph. 18, 1, 1–34.]] Google ScholarDigital Library
    8. GREENBERG, D. P., TORRANCE, K. E., SHIRLEY, P., ARVO, J., LAFORTUNE, E., FERWERDA, J. A., WALTER, B., TRUMBORE, B., PATTANAIK, S., AND FOO, S.-C. 1997. A framework for realistic image synthesis. In SIGGRAPH 97, 477–494.]] Google ScholarDigital Library
    9. HAPKE, B. 1963. A theoretical photometric function for the lunar surface. Journal of Geophysical Research 68, 15.]]Google ScholarCross Ref
    10. HE, X. D., TORRANCE, K. E., SILLION, F. X., AND GREENBERG, D. P. 1991. A comprehensive physical model for light reflection. In SIGGRAPH 91, 175–186.]] Google ScholarDigital Library
    11. KAJIYA, J. T. 1985. Anisotropic reflection models. In SIGGRAPH 85, 15–21.]] Google ScholarDigital Library
    12. KAJIYA, J. T. 1986. The rendering equation. In SIGGRAPH 86, 143–150.]] Google ScholarDigital Library
    13. KAUTZ, J., AND MCCOOL, M. D. 1999. Interactive rendering with arbitrary BRDFs using separable approximations. In Proceedings of the 10th Eurographics Workshop on Rendering, 281–292.]]Google ScholarDigital Library
    14. KOENDERINK, J., AND VAN DOORN, A. 1998. Phenomenological description of bidirectional surface reflection. JOSA A 15, 11, 2903–2912.]]Google ScholarCross Ref
    15. KOLLIG, T., AND KELLER, A. 2003. Efficient illumination by high dynamic range images. In Eurographics Symposium on Rendering 03, 45–51.]] Google ScholarDigital Library
    16. LAFORTUNE, E. P. F., FOO, S.-C., TORRANCE, K. E., AND GREENBERG, D. P. 1997. Non-linear approximation of reflectance functions. In SIGGRAPH 97, 117–126.]] Google ScholarDigital Library
    17. LEE, D. D., AND SEUNG, H. S. 2000. Algorithms for non-negative matrix factorization. In NIPS, 556–562.]]Google Scholar
    18. MARSCHNER, S., WESTIN, S., LAFORTUNE, E., TORRANCE, K., AND GREENBERG, D. 1999. Image-based BRDF measurement including human skin. In Proceedings of 10th Eurographics Workshop on Rendering, 139–152.]] Google ScholarDigital Library
    19. MATUSIK, W., PFISTER, H., BRAND, M., AND MCMILLAN, L. 2003. A data-driven reflectance model. In SIGGRAPH 03, 759–769.]] Google ScholarDigital Library
    20. MATUSIK, W. 2003. A Data-Drive Reflectance Model. PhD thesis, Massachusettes Institute of Technology.]] Google ScholarDigital Library
    21. MCCOOL, M. D., ANG, J., AND AHMAD, A. 2001. Homomorphic factorization of BRDFs for high-performance rendering. In SIGGRAPH 01, 185–194.]] Google ScholarDigital Library
    22. NICODEMUS, F. E., RICHMOND, J. C., HSIA, J. J., GINSBERG, I. W., AND LIMPERIS, T. 1977. Geometric Considerations and Nomenclature for Reflectance. National Bureau of Standards (US).]]Google Scholar
    23. OREN, M., AND NAYAR, S. K. 1994. Generalization of Lambert’s reflectance model. In SIGGRAPH 94, 239–246.]] Google ScholarDigital Library
    24. PHONG, B. T. 1975. Illumination for computer generated pictures. Commun. ACM 18, 6, 311–317.]] Google ScholarDigital Library
    25. POULIN, P., AND FOURNIER, A. 1990. A model for anisotropic reflection. In SIGGRAPH 90, 273–282.]] Google ScholarDigital Library
    26. RUSINKIEWICZ, S. 1998. A new change of variables for efficient BRDF representation. In Eurographics Rendering Workshop ’98, 11–22.]]Google ScholarCross Ref
    27. SHIRLEY, P. 1990. Physically Based Lighting Calculations for Computer Graphics. PhD thesis, University of Illinois at Urbana Champaign.]] Google ScholarDigital Library
    28. SILLION, F. X., ARVO, J. R., WESTIN, S. H., AND GREENBERG, D. P. 1991. A global illumination solution for general reflectance distributions. In Proceedings of the 18th annual conference on Computer graphics and interactive techniques, ACM Press, 187–196.]] Google ScholarDigital Library
    29. SUYKENS, F., VOM BERGE, K., LAGAE, A., AND DUTRE, P. 2003. Interactive rendering with bidirectional texture functions. EUROGRAPHICS 2003, Computer Graphics Forum 22, 3.]]Google Scholar
    30. TORRANCE, K. E., AND SPARROW, E. M. 1967. Theory for off-specular reflection from roughened surfaces. Journal of the Optical Society of America 57.]]Google ScholarCross Ref
    31. VEACH, E., AND GUIBAS, L. 1995. Optimally combining sampling techniques for Monte Carlo rendering. In SIGGRAPH 95, 419–428.]] Google ScholarDigital Library
    32. WARD, G. J. 1992. Measuring and modeling anisotropic reflection. In SIGGRAPH 92, 265–272.]] Google ScholarDigital Library
    33. WESTIN, S. H., ARVO, J. R., AND TORRANCE, K. E. 1992. Predicting reflectance functions from complex surfaces. In Proceedings of the 19th annual conference on Computer graphics and interactive techniques, ACM Press, 255–264.]] Google ScholarDigital Library

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