Quasi-Monte Carlo Progressive Photon Mapping

  • Alexander Keller
  • Leonhard Grünschloß
  • Marc Droske
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 23)


The simulation of light transport often involves specular and transmissive surfaces, which are modeled by functions that are not square integrable. However, in many practical cases unbiased Monte Carlo methods are not able to handle such functions efficiently and consistent Monte Carlo methods are applied. Based on quasi-Monte Carlo integration, a deterministic alternative to the stochastic approaches is introduced. The new method for deterministic consistent functional approximation uses deterministic consistent density estimation.


Smooth Particle Hydrodynamic Query Point Initial Radius Smooth Particle Hydrodynamic Path Space 
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.



This work has been dedicated to Jerry Spanier’s 80th birthday.


  1. 1.
    Faure, H.: Discrépance de suites associées à un système de numération (en dimension s). Acta Arith. 41(4), 337–351 (1982)Google Scholar
  2. 2.
    Grünschloß, L., Raab, M., Keller, A.: Enumerating quasi-Monte Carlo point sequences in elementary intervals. In: H. Woźniakowski, L. Plaskota (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2010, pp. 399–408 in this volume. Springer (2012)Google Scholar
  3. 3.
    Hachisuka, T., Jensen, H.: Stochastic progressive photon mapping. In: SIGGRAPH Asia ’09: ACM SIGGRAPH Asia 2009 papers, pp. 1–8. ACM, New York, NY, USA (2009)Google Scholar
  4. 4.
    Hachisuka, T., Ogaki, S., Jensen, H.: Progressive photon mapping. ACM Transactions on Graphics 27(5), 130:1–130:8 (2008)Google Scholar
  5. 5.
    Hickernell, F., Hong, H., L’Ecuyer, P., Lemieux, C.: Extensible lattice sequences for quasi-Monte Carlo quadrature. SIAM J. Sci. Comput. 22, 1117–1138 (2001)Google Scholar
  6. 6.
    Hlawka, E., Mück, R.: Über eine Transformation von gleichverteilten Folgen II. Computing 9, 127–138 (1972)Google Scholar
  7. 7.
    Jensen, H.: Realistic Image Synthesis Using Photon Mapping. AK Peters (2001)Google Scholar
  8. 8.
    Keller, A.: Quasi-Monte Carlo Methods for Photorealistic Image Synthesis. Ph.D. thesis, University of Kaiserslautern, Germany (1998)Google Scholar
  9. 9.
    Keller, A.: Strictly Deterministic Sampling Methods in Computer Graphics. SIGGRAPH 2003 Course Notes, Course #44: Monte Carlo Ray Tracing (2003)Google Scholar
  10. 10.
    Keller, A.: Myths of computer graphics. In: H. Niederreiter (ed.) Monte Carlo and Quasi-Monte Carlo Methods 2004, pp. 217–243. Springer (2006)Google Scholar
  11. 11.
    Keller, A., Grünschloß, L.: Parallel quasi-Monte Carlo methods. In: L. Plaskota, H. Woźniakowski (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2010, pp. 489–500 in this volume. Springer (2012)Google Scholar
  12. 12.
    Knaus, C., Zwicker, M.: Progressive photon mapping: A probabilistic approach. ACM Transactions on Graphics (TOG) 30(3) (2011)Google Scholar
  13. 13.
    Kollig, T., Keller, A.: Efficient bidirectional path tracing by randomized quasi-Monte Carlo integration. In: H. Niederreiter, K. Fang, F. Hickernell (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2000, pp. 290–305. Springer (2002)Google Scholar
  14. 14.
    Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia (1992)Google Scholar
  15. 15.
    Shirley, P.: Realistic Ray Tracing. AK Peters, Ltd. (2000)Google Scholar
  16. 16.
    Silverman, B.: Density Estimation for Statistics and Data Analysis. Chapman & Hall/CRC (1986)Google Scholar
  17. 17.
    Sobol’, I.: Uniformly Distributed Sequences with an additional Uniform Property. Zh. vychisl. Mat. mat. Fiz. 16(5), 1332–1337 (1976)Google Scholar
  18. 18.
    Veach, E.: Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. thesis, Stanford University (1997)Google Scholar
  19. 19.
    Wächter, C.: Quasi-Monte Carlo Light Transport Simulation by Efficient Ray Tracing. Ph.D. thesis, Universität Ulm (2008)Google Scholar
  20. 20.
    Woźniakowski, H.: Average case complexity of multivariate integration. Bull. Amer. Math. Soc. 24, 185–194 (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexander Keller
    • 1
  • Leonhard Grünschloß
    • 2
  • Marc Droske
    • 1
  1. 1.NVIDIA ARC GmbHBerlinGermany
  2. 2.Rendering Research Weta DigitalWellingtonNew Zealand

Personalised recommendations