Advertisement

A 5D Tree to Reduce the Variance of Monte Carlo Ray Tracing

  • Eric P. Lafortune
  • Yves D. Willems
Part of the Eurographics book series (EUROGRAPH)

Abstract

In this paper we present a 5D tree structure to cache illumination information gained during Monte Carlo ray tracing. The structure is elegant and simple to use. It is adaptive and makes abstraction of the complexity of the input scene automatically.

We then show how the information in this structure can be used to reduce the variance of the Monte Carlo process. Unlike earlier approaches the techniques presented here do not introduce a bias in the results.

Keywords

Probability Density Function Importance Sampling Incoming Radiance Global Illumination Input Scene 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Kalos and P. Whitlock, Monte Carlo Methods. Wiley & Sons, 1986.MATHCrossRefGoogle Scholar
  2. 2.
    J. Hammersly and D. Handscomb, Monte Carlo Methods. Chapman and Hall, 1964.Google Scholar
  3. 3.
    M. Lee, R. Redner, and S. Uselton, “Statistically optimized sampling for distributed ray tracing,” Computer Graphics, vol. 19, pp. 61 - 67, July 1985.CrossRefGoogle Scholar
  4. 4.
    R Shirley, Physically Based Lighting Calculations for Computer Graphics. PhD thesis, University of Illinois, Nov. 1990.Google Scholar
  5. 5.
    B. Lange, “The simulation of radiant light transfer with stochastic ray-tracing,” in Proceedings of the Second Eurographics Workshop on Rendering, ( Barcelona, Spain ), May 1991.Google Scholar
  6. 6.
    G. Ward, “Adaptive shadow testing for ray tracing,” in Proceedings of the Second Eurographics Workshop on Rendering, ( Barcelona, Spain ), May 1991.Google Scholar
  7. 7.
    S. Pattanaik, Computational Methods for Global Illumination and Visualisation of Complex 3D Environments. PhD thesis, Birla Institute of Technology & Science, Pilani, India, Feb. 1993.Google Scholar
  8. 8.
    E. Lafortune and Y. Willems, “A theoretical framework for physically based rendering,” Computer Graphics Forum, vol. 13, pp. 97–107, June 1994.CrossRefGoogle Scholar
  9. 9.
    P. Shirley, C. Wang, and K. Zimmerman, “Monte carlo techniques for direct lighting calculations,” ACM Transactions on Graphics, to appear.Google Scholar
  10. 10.
    E. Lafortune and Y. Willems, “Reducing the number of shadow rays in bidirectional path tracing,” in Proceedings of WSCG 95, (Pilsen, Czech Republic), pp. 384–392, Feb. 1995.Google Scholar
  11. 11.
    G. Ward, F. Rubinstein, and R. Clear, “A ray tracing solution for diffuse inter-reflection,” Computer Graphics, vol. 22, pp. 85–92, July 1988.CrossRefGoogle Scholar
  12. 12.
    G. Ward and P. Heckbert, “Irradiance gradients,” in Proceedings of the Third Eurographics Workshop on Rendering, (Bristol, UK), pp. 85 - 98, May 1992.Google Scholar
  13. 13.
    D. Immel, M. Cohen, and D. Greenberg, “A radiosity method for non-diffuse environments,” Computer Graphics, vol. 20, pp. 133 - 142, Aug. 1986.CrossRefGoogle Scholar
  14. 14.
    F. Sillion, J. Arvo, S. Westin, and D. Greenberg, “A global illumination solution for general reflectance distributions,” Computer Graphics, vol. 25, pp. 187 - 196, July 1991.CrossRefGoogle Scholar
  15. 15.
    C. Patmore, “Illumination of dense foliage models,” in Proceedings of the Fourth Eurographics Workshop on Rendering, (Paris, France), pp. 63 - 71, June 1993.Google Scholar
  16. 16.
    E. Languénou, K. Bouatouch, and M. Chelle, “Global illumination in presence of participating media with general properties,” in Proceedings of the Fifth Eurographics Workshop on Rendering, (Darmstadt, Germany), pp. 69–85, June 1994.Google Scholar
  17. 17.
    N. Max, “Efficient light propagation for multiple anisotropic volume scattering,” in Proceedings of the Fifth Eurographics Workshop on Rendering, (Darmstadt, Germany), pp. 87–104, June 1994.Google Scholar
  18. 18.
    F. Sillion, “Clustering and volume scattering for hierarchical radiosity calculations,” in Proceedings of the Fifth Eurographics Workshop on Rendering, (Darmstadt, Germany), pp. 105–117, June 1994.Google Scholar
  19. 19.
    E. Lafortune and Y. Willems, “Using the modified phong brdf for physically based rendering,” Technical Report CW197, Department of Computer Science, Katholieke Universiteit Leuven, Leuven, Belgium, Nov. 1994.Google Scholar
  20. 20.
    J. Halton, “On the relative merits of correlated and importance sampling for monte carlo integration,” Proceedings of the Cambridge Philisophical Society, vol. 61, pp. 497 - 498, 1965.MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    E. Lafortune and Y. Willems, “The ambient term as a variance reducing technique for monte carlo ray tracing,” in Proceedings of the Fifth Eurographics Workshop on Rendering, (Darmstadt, Germany), pp. 163 - 171, June 1994.Google Scholar
  22. 22.
    E. Lafortune and Y. Willems, “Bi-directional path tracing,” in Proceedings of Computer Graphics, (Alvor, Portugal), pp. 145 - 153, Dec. 1993.Google Scholar
  23. 23.
    E. Veach and L. Guibas, “Bidirectional estimators for light transport,” in Proceedings of the Fifth Eurographics Workshop on Rendering, (Darmstadt, Germany), pp. 147–162, June 1994.Google Scholar
  24. 24.
    Ph. Dutré and Y. Willems, “Potential-driven monte carlo particle tracing for dif-fuse environments with adaptive probability density functions,” in Proceedings of the Sixth Eurographics Workshop on Rendering, ( Dublin, Ireland ), June 1995.Google Scholar
  25. 25.
    H. Jensen, “Importance driven path tracing using the photon map,” in Proceedings of the Sixth Eurographics Workshop on Rendering, ( Dublin, Ireland ), June 1995.Google Scholar

Copyright information

© Springer-Verlag/Wien 1995

Authors and Affiliations

  • Eric P. Lafortune
    • 1
  • Yves D. Willems
    • 1
  1. 1.Department of Computer ScienceKatholieke Universiteit LeuvenHeverleeBelgium

Personalised recommendations