Abstract
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.
Keywords
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 is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Faure, H.: Discrépance de suites associées à un système de numération (en dimension s). Acta Arith. 41(4), 337–351 (1982)
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)
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)
Hachisuka, T., Ogaki, S., Jensen, H.: Progressive photon mapping. ACM Transactions on Graphics 27(5), 130:1–130:8 (2008)
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)
Hlawka, E., Mück, R.: Über eine Transformation von gleichverteilten Folgen II. Computing 9, 127–138 (1972)
Jensen, H.: Realistic Image Synthesis Using Photon Mapping. AK Peters (2001)
Keller, A.: Quasi-Monte Carlo Methods for Photorealistic Image Synthesis. Ph.D. thesis, University of Kaiserslautern, Germany (1998)
Keller, A.: Strictly Deterministic Sampling Methods in Computer Graphics. SIGGRAPH 2003 Course Notes, Course #44: Monte Carlo Ray Tracing (2003)
Keller, A.: Myths of computer graphics. In: H. Niederreiter (ed.) Monte Carlo and Quasi-Monte Carlo Methods 2004, pp. 217–243. Springer (2006)
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)
Knaus, C., Zwicker, M.: Progressive photon mapping: A probabilistic approach. ACM Transactions on Graphics (TOG) 30(3) (2011)
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)
Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia (1992)
Shirley, P.: Realistic Ray Tracing. AK Peters, Ltd. (2000)
Silverman, B.: Density Estimation for Statistics and Data Analysis. Chapman & Hall/CRC (1986)
Sobol’, I.: Uniformly Distributed Sequences with an additional Uniform Property. Zh. vychisl. Mat. mat. Fiz. 16(5), 1332–1337 (1976)
Veach, E.: Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. thesis, Stanford University (1997)
Wächter, C.: Quasi-Monte Carlo Light Transport Simulation by Efficient Ray Tracing. Ph.D. thesis, Universität Ulm (2008)
Woźniakowski, H.: Average case complexity of multivariate integration. Bull. Amer. Math. Soc. 24, 185–194 (1991)
Acknowledgements
This work has been dedicated to Jerry Spanier’s 80th birthday.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Keller, A., Grünschloß, L., Droske, M. (2012). Quasi-Monte Carlo Progressive Photon Mapping. In: Plaskota, L., Woźniakowski, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2010. Springer Proceedings in Mathematics & Statistics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27440-4_28
Download citation
DOI: https://doi.org/10.1007/978-3-642-27440-4_28
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27439-8
Online ISBN: 978-3-642-27440-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)