Bidirectional Estimators for Light Transport

  • Eric Veach
  • Leonidas Guibas
Part of the Focus on Computer Graphics book series (FOCUS COMPUTER)


Most of the research on the global illumination problem in computer graphics has been concentrated on finite-element (radiosity) techniques. Monte Carlo methods are an intriguing alternative which are attractive for their ability to handle very general scene descriptions without the need for meshing. In this paper we study techniques for reducing the sampling noise inherent in pure Monte Carlo approaches to global illumination. Every light energy transport path from a light source to the eye can be generated in a number of different ways, according to how we partition the path into an initial portion traced from a light source, and a final portion traced from the eye. Each partitioning gives us a different unbiased estimator, but some partitionings give estimators with much lower variance than others. We give examples of this phenomenon and describe its significance. We also present work in progress on the problem of combining these multiple estimators to achieve near-optimal variance, with the goal of producing images with less noise for a given number of samples.


Monte Carlo Computer Graphic Filter Function Transport Path Bidirectional Reflectance Distribution 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.
    J. Hammersley, D. Handscomb, Monte Carlo Methods, Chapman and Hall, 1964.Google Scholar
  2. 2.
    M. Kalos, P. Whitlock, Monte Carlo Methods, Volume I: Basics. J. Wiley, New York, 1986.MATHCrossRefGoogle Scholar
  3. 3.
    R. Cook, T. Porter, L. Carpenter, Distributed ray tracing. Computer Graphics (Siggraph ’84), 18, 137–146 (1984).CrossRefGoogle Scholar
  4. 4.
    J. Arvo, D. Kirk, Particle transport and image synthesis, Computer Graphics (Siggraph ’90), 24, 63–66 (1990).CrossRefGoogle Scholar
  5. 5.
    P. Shirley, C. Wang, Luminaire sampling in distribution ray tracing. Technical Report 343, CS Dept., Indiana University, Jan 1992. Also appears in: Siggraph ’93 Global Illumination Course Notes.Google Scholar
  6. 6.
    J. Kajiya, The rendering equation. Computer Graphics (Siggraph ’86), 20, 143–150 (1986).CrossRefGoogle Scholar
  7. 7.
    D. Kirk, J. Arvo, Unbiased sampling techniques for image synthesis, Computer Graphics (SIGGRAPH ’91), 25, 153–156 (1991).CrossRefGoogle Scholar
  8. 8.
    F. Sillion, J. Arvo, S. Westin, D. Greenberg, A global illumination solution for general reflectance distributions. Computer Graphics (SIGGRAPH ’91), 25, 187–196 (1991).CrossRefGoogle Scholar
  9. 9.
    D. Baum, S. Mann, K. Smith, J. Winget, Making radiosity usable: automatic pre-processing and meshing techniques for the generation of accurate radiosity solutions. Computer Graphics (SIGGRAPH ’91), 25, 51–60 (1991).CrossRefGoogle Scholar
  10. 10.
    D. Lischinski, F. Tampieri, D. Greenberg, Combining hierarchical radiosity and discontinuity meshing. Computer Graphics (SIGGRAPH ’93), 27, 199–208 (1993).Google Scholar
  11. 11.
    S. Pattanaik, S. Mudur, Efficient potential equation solutions for global illumination computation. Computers and Graphics, 17 (4), 387–396 (1993).CrossRefGoogle Scholar
  12. 12.
    S. Chen, H. Rushmeier, G. Miller, D. Turner, A progressive multi-pass method for global illumination. Computer Graphics (SIGGRAPH ’91), 25, 165–174 (1991).CrossRefGoogle Scholar
  13. 13.
    M. Watt, Light-water interaction using backward beam tracing. Computer Graphics (SIGGRAPH ’90), 24, 377–385 (1990).CrossRefGoogle Scholar
  14. 14.
    P. Shirley, A ray tracing method for illumination calculation in diffuse-specular scenes. Graphics Interface ’90, 205–212 (1990).Google Scholar
  15. 15.
    J. Arvo, Backward ray tracing. SIGGRAPH ’86 “Developments in Ray Tracing” course notes (1986).Google Scholar
  16. 16.
    P. Heckbert, Adaptive radiosity textures for bidirectional ray tracing. Computer Graphics (SIGGRAPH ’90), 24, 145–154 (1990).CrossRefGoogle Scholar
  17. 17.
    P. Shirley, Time complexity of Monte-Carlo radiosity. Eurographics ’91 Proceedings, 459–465 (1991).Google Scholar
  18. 18.
    P. Shirley, K. Sung, W. Brown, A ray tracing framework for global illumination. Graphics Interface ’91, 117–128 (1991).Google Scholar
  19. 19.
    B. Lesaec, C. Schlick, A progressive ray-tracing based radiosity with general reflectance functions. Eurographics Workshop on Photo simulation, Realism, and Physics in Computer Graphics, 1990.Google Scholar
  20. 20.
    G. Ward, F. Rubinstein, R. Clear, A ray tracing solution for diffuse interreflection. Computer Graphics (SIGGRAPH ’88), 22, 85–92 (1988).CrossRefGoogle Scholar
  21. 21.
    E. Lafortune, Y. Willems, Bidirectional path tracing. Compu Graphics Proceedings (Alvor, Portugal), 145–153 (Dec. 1993).Google Scholar
  22. 22.
    M. Cohen, J. Wallace, Radiosity and Realistic Image Synthesis. Academic Press, 1993.Google Scholar
  23. 23.
    Lewins, Jeffery, Importancef The Adjoint Function: The Physical Basis of Variational and Perturbation Theory in Transport and Diffusion Problems. Pergamon Press, New York, 1965.Google Scholar
  24. 24.
    J. Spanier, E. Gelbard, Monte Carlo Principles and Neutron Transport Problems, Addison-Wesley, 1969.Google Scholar
  25. 25.
    P. Christensen, D. Salesin, T. DeRose, A continuous adjoint formulation for ra-diance transport. Fourth Eurographics Workshop on Rendering, 1993.Google Scholar
  26. 26.
    S. Pattanaik, S. Mudur, The Potential Equation and Importance in Illumination Computations. Computer Graphics Forum, 12 (2), 131–136 (1993).CrossRefGoogle Scholar
  27. 27.
    B. Smits, J. Arvo, D. Salesin, An importance-driven radiosity algorithm. Computer Graphics (SIGGRAPH ’92), 26, 273–282 (1992).CrossRefGoogle Scholar

Copyright information

© EUROGRAPHICS The European Association for Computer Graphics 1995

Authors and Affiliations

  • Eric Veach
    • 1
  • Leonidas Guibas
    • 1
  1. 1.Computer Science DepartmentStanford UniversityUSA

Personalised recommendations