“On-line learning of parametric mixture models for light transport simulation” by Vorba, Karlík, Šik, Ritschel and Křivánek

  • ©Jiří Vorba, Ondřej Karlík, Martin Šik, Tobias Ritschel, and Jaroslav Křivánek



Session Title:

    Light Transport


    On-line learning of parametric mixture models for light transport simulation




    Monte Carlo techniques for light transport simulation rely on importance sampling when constructing light transport paths. Previous work has shown that suitable sampling distributions can be recovered from particles distributed in the scene prior to rendering. We propose to represent the distributions by a parametric mixture model trained in an on-line (i.e. progressive) manner from a potentially infinite stream of particles. This enables recovering good sampling distributions in scenes with complex lighting, where the necessary number of particles may exceed available memory. Using these distributions for sampling scattering directions and light emission significantly improves the performance of state-of-the-art light transport simulation algorithms when dealing with complex lighting.


    1. Arvo, J., and Kirk, D. 1990. Particle transport and image synthesis. In Proc. SIGGRAPH ’90, ACM, 63–66. Google ScholarDigital Library
    2. Bashford-Rogers, T., Debattista, K., and Chalmers, A. 2012. A significance cache for accelerating global illumination. Computer Graphics Forum 31, 6, 1837–51. Google ScholarDigital Library
    3. Bashford-Rogers, T., Debattista, K., and Chalmers, A. 2013. Importance driven environment map sampling. IEEE Transactions on Visualization and Computer Graphics 19.Google Scholar
    4. Bingham, C. 1974. An antipodally symmetric distribution on the sphere. The Annals of Statistics 2, 6, pp. 1201–1225.Google ScholarCross Ref
    5. Bishop, C. M. 2006. Pattern Recognition and Machine Learning. Springer. Google Scholar
    6. Booth, T. 1985. A sample problem for variance reduction in MCNP. Tech. rep., Los Alamos National Laboratory, Los Alamos, New Mexico 87545.Google Scholar
    7. Booth, T. E. 2012. Common misconceptions in Monte Carlo particle transport. Applied Radiation and Isotopes 70, 7.Google ScholarCross Ref
    8. Budge, B. C., Anderson, J. C., and Joy, K. I. 2008. Caustic forecasting: Unbiased estimation of caustic lighting for global illumination. Computer Graphics Forum 27, 7, 1963–70.Google ScholarCross Ref
    9. Cappé, O. 2011. Online Expectation Maximisation. John Wiley & Sons, Ltd, 31–53.Google Scholar
    10. Cline, D., Talbot, J., and Egbert, P. 2005. Energy redistribution path tracing. ACM Trans. Graph. 24, 3. Google ScholarDigital Library
    11. Cline, D., Adams, D., and Egbert, P. 2008. Table-driven adaptive importance sampling. Computer Graphics Forum 27. Google ScholarDigital Library
    12. Dempster, A. P., Laird, N. M., and Rubin, D. B. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B 39, 1, 1–38.Google ScholarCross Ref
    13. Dutré, P., and Willems, Y. 1994. Importance-driven Monte Carlo light tracing. In Eurographics Workshop on Rendering.Google Scholar
    14. Dutré, P., and Willems, Y. 1995. Potential-driven Monte Carlo particle tracing for diffuse environments with adaptive probability density functions. In EG Workshop on Rendering.Google Scholar
    15. Dutré, P., Bala, K., and Bekaert, P. 2006. Advanced Global Illumination, 2nd ed. A. K. Peters. Google ScholarDigital Library
    16. Fisher, R. 1953. Dispersion on a sphere. Proc. Royal Society of London. Series A. Math. Phys. 217, 1130, 295–305.Google Scholar
    17. Gauvain, J., and Lee, C.-H. 1994. Maximum a posteriori estimation for multivariate Gaussian mixture observations of Markov chains. IEEE Trans Audio Speech Lang Processing 2, 2, 291–298.Google ScholarCross Ref
    18. Georgiev, I., Křivánek, J., Popov, S., and Slusallek, P. 2012. Importance caching for complex illumination. Computer Graphics Forum 31, 2pt3, 701–10. Proc. of Eurographics. Google ScholarDigital Library
    19. Georgiev, I., Křivánek, J., Davidovič, T., and Slusallek, P. 2012. Light transport simulation with vertex connection and merging. ACM Trans. Graph. 31, 6. Google ScholarDigital Library
    20. Georgiev, I. 2012. Implementing vertex connection and merging. Tech. rep., Saarland University.Google Scholar
    21. Hachisuka, T., Ogaki, S., and Jensen, H. W. 2008. Progressive photon mapping. ACM Trans. Graph. 27, 5 (Dec.). Google ScholarDigital Library
    22. Hachisuka, T., Pantaleoni, J., and Jensen, H. W. 2012. A path space extension for robust light transport simulation. ACM Trans. Graph. 31, 6. Google ScholarDigital Library
    23. Haghighat, A., and Wagner, J. C. 2003. Monte Carlo variance reduction with deterministic importance functions. Progress in Nuclear Energy 42, 1, 25–53.Google ScholarCross Ref
    24. Hey, H., and Purgathofer, W. 2002. Importance sampling with hemispherical particle footprints. In SCCG. Google ScholarDigital Library
    25. Jakob, W., and Marschner, S. 2012. Manifold exploration: A Markov chain Monte Carlo technique for rendering scenes with difficult specular transport. ACM Trans. Graph. 31, 4 (July). Google ScholarDigital Library
    26. Jakob, W., Regg, C., and Jarosz, W. 2011. Progressive expectation-maximization for hierarchical volumetric photon mapping. Computer Graphics Forum 30, 4, 1287–1297. Google ScholarDigital Library
    27. Jakob, W., 2010. Mitsuba renderer. http://mitsuba-renderer.org.Google Scholar
    28. Jensen, H. W. 1995. Importance driven path tracing using the photon map. In Eurographics Workshop Rendering, 326–335.Google ScholarCross Ref
    29. Karlík, O., 2009. Corona Renderer. http://corona-renderer.com.Google Scholar
    30. Kelemen, C., Szirmay-Kalos, L., Antal, G., and Csonka, F. 2002. A simple and robust mutation strategy for the Metropolis light transport algorithm. Comp. Graph. Forum (Proc. of Eurographics) 21, 3, 531–540.Google ScholarCross Ref
    31. Kent, J. T. 1982. The Fisher-Bingham distribution on the sphere. Journal of the Royal Statistical Society. Series B 44, 1, 71–80.Google Scholar
    32. Křivánek, J., Gautron, P., Pattanaik, S., and Bouatouch, K. 2005. Radiance caching for efficient global illumination computation. IEEE Trans. Vis. Comp. Graph. 11, 5. Google ScholarDigital Library
    33. Křivánek, J., Bouatouch, K., Pattanaik, S. N., and Žára, J. 2006. Making radiance and irradiance caching practical: Adaptive caching and neighbor clamping. In Eurographics Symposium on Rendering, 127–138. Google ScholarDigital Library
    34. Lafortune, E. P., and Willems, Y. D. 1995. A 5D tree to reduce the variance of Monte Carlo ray tracing. In Eurographics Workshop on Rendering. 11–20.Google Scholar
    35. Lehtinen, J., Karras, T., Laine, S., Aittala, M., Durand, F., and Aila, T. 2013. Gradient-domain Metropolis light transport. ACM Trans. Graph. 32, 4. Google ScholarDigital Library
    36. Lepage, G. P. 1978. A new algorithm for adaptive multidimensional integration. Journal of Comp. Physics 27, 192–203.Google ScholarCross Ref
    37. Liang, P., and Klein, D. 2009. Online EM for unsupervised models. In Human Language Technologies (NAACL ’09), Association for Computational Linguistics, 611–619. Google ScholarDigital Library
    38. Pegoraro, V., Brownlee, C., Shirley, P. S., and Parker, S. G. 2008. Towards interactive global illumination effects via sequential Monte Carlo adaptation. In IEEE Symposium on Interactive Ray Tracing, 107–114.Google Scholar
    39. Pegoraro, V., Wald, I., and Parker, S. G. 2008. Sequential Monte Carlo adaptation in low-anisotropy participating media. Computer Graphics Forum 27, 4, 1097–1104. Google ScholarDigital Library
    40. Peter, I., and Pietrek, G. 1998. Importance driven construction of photon maps. In Rendering Techniques, 269–80.Google Scholar
    41. Pharr, M., and Humphreys, G. 2010. Physically Based Rendering, Second Edition: From Theory To Implementation, 2nd ed. Morgan Kaufmann Publishers Inc., San Francisco, CA. Google ScholarDigital Library
    42. Sato, M.-A., and Ishii, S. 2000. On-line EM algorithm for the normalized Gaussian network. Neural Comput. 12, 2 (Feb.). Google ScholarDigital Library
    43. Shirley, P., and Chiu, K. 1997. A low distortion map between disk and square. J. Graph. Tools 2, 3 (Dec.), 45–52. Google ScholarDigital Library
    44. Silverman, B. W. 1986. Density Estimation for Statistics and Data Analysis. Chapman & Hall, London.Google Scholar
    45. Steinhurst, J., and Lastra, A. 2006. Global importance sampling of glossy surfaces using the photon map. In IEEE Symposium on Interactive Ray Tracing, 133–138.Google Scholar
    46. Tsai, Y.-T., Chang, C.-C., Jiang, Q.-Z., and Weng, S.-C. 2008. Importance sampling of products from illumination and BRDF using spherical radial basis functions. The Visual Computer 24, 7. Google ScholarDigital Library
    47. Veach, E., and Guibas, L. J. 1997. Metropolis light transport. In SIGGRAPH ’97. Google ScholarDigital Library
    48. Veach, E. 1997. Robust Monte Carlo methods for light transport simulation. PhD thesis, Stanford University. Google ScholarDigital Library
    49. Verbeek, J. J., Nunnink, J. R., and Vlassis, N. 2006. Accelerated EM-based clustering of large data sets. Data Mining and Knowledge Discovery 13, 3, 291–307. Google ScholarDigital Library
    50. Ward, G. J., Rubinstein, F. M., and Clear, R. D. 1988. A ray tracing solution for diffuse interreflection. In SIGGRAPH ’88, no. 4, ACM, 85–92. Google ScholarDigital Library
    51. Ward, G. J. 1992. Measuring and modeling anisotropic reflection. In SIGGRAPH ’92, ACM, 265–272. Google ScholarDigital Library
    52. Xu, K., Sun, W.-L., Dong, Z., Zhao, D.-Y., Wu, R.-D., and Hu, S.-M. 2013. Anisotropic spherical Gaussians. ACM Transactions on Graphics 32, 6, 209:1–209:11. Google ScholarDigital Library

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