Skip to main content
SpringerLink
Log in

Path Space Filtering

  • Conference paper
  • First Online:
Monte Carlo and Quasi-Monte Carlo Methods

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 163))

Abstract

We improve the efficiency of quasi-Monte Carlo integro-approximation by using weighted averages of samples instead of the samples themselves. The proposed deterministic algorithm is constructed such that it converges to the solution of the given integro-approximation problem. The improvements and wide applicability of the consistent method are demonstrated by visual evidence in the setting of light transport simulation for photorealistic image synthesis, where the weighted averages correspond to locally smoothed contributions of path space samples.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ernst, M., Stamminger, M., Greiner, G.: Filter importance sampling. In: Proceedings of the IEEE/EG Symposium on Interactive Ray Tracing, pp. 125–132 (2006)

    Google Scholar 

  2. Gautron, P., Droske, M., Wächter, C., Kettner, L., Keller, A., Binder, N., Dahm, K.: Path space similarity determined by Fourier histogram descriptors. In: ACM SIGGRAPH 2014 Talks, SIGGRAPH’14, pp. 39:1–39:1. ACM (2014)

    Google Scholar 

  3. Georgiev, I., Křivánek, J., Davidovič, T., Slusallek, P.: Light transport simulation with vertex connection and merging. ACM Trans. Graph. (TOG) 31(6), 192:1–192:10 (2012)

    Article  Google Scholar 

  4. Hachisuka, T., Jensen, H.: Stochastic progressive photon mapping. In: SIGGRAPH Asia’09: ACM SIGGRAPH Asia Papers, pp. 1–8. ACM (2009)

    Google Scholar 

  5. Hachisuka, T., Ogaki, S., Jensen, H.: Progressive photon mapping. ACM Trans. Graph. 27(5), 130:1–130:8 (2008)

    Article  Google Scholar 

  6. Hachisuka, T., Pantaleoni, J., Jensen, H.: A path space extension for robust light transport simulation. ACM Trans. Graph. (TOG) 31(6), 191:1–191:10 (2012)

    Article  Google Scholar 

  7. Jensen, H.: Realistic Image Synthesis Using Photon Mapping. AK Peters, Natick (2001)

    Book  MATH  Google Scholar 

  8. Jensen, H., Buhler, J.: A rapid hierarchical rendering technique for translucent materials. ACM Trans. Graph. 21(3), 576–581 (2002)

    Article  Google Scholar 

  9. Keller, A.: Instant radiosity. In: SIGGRAPH’97: Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, pp. 49–56 (1997)

    Google Scholar 

  10. Keller, A.: Quasi-Monte Carlo Methods for Photorealistic Image Synthesis. Ph.D. thesis, University of Kaiserslautern, Germany (1998)

    Google Scholar 

  11. Keller, A.: Quasi-Monte Carlo image synthesis in a nutshell. In: Dick, J., Kuo, F., Peters, G., Sloan, I. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2012, pp. 203–238. Springer, Heidelberg (2013)

    Google Scholar 

  12. Keller, A., Binder, N.: Deterministic consistent density estimation for light transport simulation. In: Dick, J., Kuo, F., Peters, G., Sloan, I. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2012, pp. 467–480. Springer, Heidelberg (2013)

    Google Scholar 

  13. Keller, A., Droske, M., Grünschloß, L., Seibert, D.: A divide-and-conquer algorithm for simultaneous photon map queries. Poster at High-Performance Graphics in Vancouver. http://www.highperformancegraphics.org/previous/www_2011/media/Posters/HPG2011_Posters_Keller1_abstract.pdf (2011)

  14. Knauer, E., Bärz, J., Müller, S.: A hybrid approach to interactive global illumination and soft shadows. Vis. Comput.: Int. J. Comput. Graph. 26(6–8), 565–574 (2010)

    Article  Google Scholar 

  15. Kollig, T., Keller, A.: Efficient bidirectional path tracing by randomized quasi-Monte Carlo integration. In: Niederreiter, H., Fang, K., Hickernell, F. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2000, pp. 290–305. Springer, Berlin (2002)

    Google Scholar 

  16. Kontkanen, J., Räsänen, J., Keller, A.: Irradiance filtering for Monte Carlo ray tracing. In: Talay, D., Niederreiter, H. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2004, pp. 259–272. Springer, Berlin (2004)

    Google Scholar 

  17. Křivánek, J.: Radiance caching for global illumination computation on glossy surfaces. Ph.D. thesis, Université de Rennes 1 and Czech Technical University in Prague (2005)

    Google Scholar 

  18. Křivánek, J., Gautron, P.: Practical Global Illumination with Irradiance Caching. Synthesis lectures in computer graphics and animation. Morgan & Claypool, San Rafael (2009)

    Google Scholar 

  19. Lafortune, E.: Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering. Ph.D. thesis, Katholieke Universiteit Leuven, Belgium (1996)

    Google Scholar 

  20. Lehtinen, J., Aila, T., Chen, J., Laine, S., Durand, F.: Temporal light field reconstruction for rendering distribution effects. ACM Trans. Graph. 30(4), 55:1–55:12 (2011)

    Article  Google Scholar 

  21. Lehtinen, J., Aila, T., Laine, S., Durand, F.: Reconstructing the indirect light field for global illumination. ACM Trans. Graph. 31(4), 51 (2012)

    Article  Google Scholar 

  22. Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia (1992)

    Book  MATH  Google Scholar 

  23. Powell, M., Swann, J.: Weighted uniform sampling - a Monte Carlo technique for reducing variance. IMA J. Appl. Math. 2(3), 228–236 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  24. Schwenk, K.: Filtering techniques for low-noise previews of interactive stochastic ray tracing. Ph.D. thesis, Technische Universität Darmstadt (2013)

    Google Scholar 

  25. Shepard, D.: A two-dimensional interpolation function for irregularly-spaced data. In: Proceedings of the 23rd ACM National Conference, pp. 517–524. ACM (1968)

    Google Scholar 

  26. Silverman, B.: Density Estimation for Statistics and Data Analysis. Chapman & Hall/CRC, London (1986)

    Book  MATH  Google Scholar 

  27. Spanier, J., Maize, E.: Quasi-random methods for estimating integrals using relatively small samples. SIAM Rev. 36(1), 18–44 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  28. Suykens, F., Willems, Y.: Adaptive filtering for progressive Monte Carlo image rendering. In: WSCG 2000 Conference Proceedings (2000)

    Google Scholar 

  29. Teschner, M., Heidelberger, B., Müller, M., Pomeranets, D., Gross, M.: Optimized spatial hashing for collision detection of deformable objects. In: Proceedings of VMV’03, pp. 47–54. Munich, Germany (2003)

    Google Scholar 

  30. Veach, E.: Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. thesis, Stanford University (1997)

    Google Scholar 

  31. Wald, I., Kollig, T., Benthin, C., Keller, A., Slusallek, P.: Interactive global illumination using fast ray tracing. In: Debevec, P., Gibson, S. (eds.) Rendering Techniques (Proceedings of the 13th Eurographics Workshop on Rendering), pp. 15–24 (2002)

    Google Scholar 

  32. Ward, G., Rubinstein, F., Clear, R.: A ray tracing solution for diffuse interreflection. Comput. Graph. 22, 85–90 (1988)

    Article  Google Scholar 

  33. Wyman, C., Sloan, P., Shirley, P.: Simple analytic approximations to the CIE XYZ color matching functions. J. Comput. Graph. Tech. (JCGT) 2, 1–11 (2013). http://jcgt.org/published/0002/02/01/

Download references

Author information

Authors and Affiliations

  1. NVIDIA, Fasanenstr. 81, 10623, Berlin, Germany

    Alexander Keller, Ken Dahm & Nikolaus Binder

Authors
  1. Alexander Keller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ken Dahm
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nikolaus Binder
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Keller .

Editor information

Editors and Affiliations

  1. Department of Computer Science, KU Leuven, Heverlee, Belgium

    Ronald Cools

  2. Department of Computer Science, KU Leuven, Heverlee, Belgium

    Dirk Nuyens

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Keller, A., Dahm, K., Binder, N. (2016). Path Space Filtering. In: Cools, R., Nuyens, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods. Springer Proceedings in Mathematics & Statistics, vol 163. Springer, Cham. https://doi.org/10.1007/978-3-319-33507-0_21

Download citation

Publish with us

Policies and ethics

Search

Navigation