Subscribe

Issue No.08 - August (2011 vol.17)

pp: 1108-1121

Anthony Pajot , IRIT, Université Paul Sabatier IRIT-CNRS, Toulouse

Mathias Paulin , IRIT, Université Paul Sabatier IRIT-CNRS, Toulouse

Pierre Poulin , Universite de Montreal, Montreal

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2010.230

ABSTRACT

We present a general method enhancing the robustness of estimators based on multiple importance sampling (MIS) in a numerical integration context. MIS minimizes variance of estimators for a given sampling configuration, but when this configuration is less adapted to the integrand, the resulting estimator suffers from extra variance. We address this issue by introducing the notion of "representativity” of a sampling strategy, and demonstrate how it can be used to increase robustness of estimators, by adapting them to the integrand. We first show how to compute representativities using common rendering informations such as BSDF, photon maps, or caches in order to choose the best sampling strategy for MIS. We then give hints to generalize our method to any integration problem and demonstrate that it can be used successfully to enhance robustness in different common rendering algorithms.

INDEX TERMS

Monte-Carlo, three-dimensional graphics and realism.

CITATION

Anthony Pajot, Mathias Paulin, Pierre Poulin, "Representativity for Robust and Adaptive Multiple Importance Sampling",

*IEEE Transactions on Visualization & Computer Graphics*, vol.17, no. 8, pp. 1108-1121, August 2011, doi:10.1109/TVCG.2010.230REFERENCES

- [1] J.T. Kajiya, “The Rendering Equation,”
Proc. ACM SIGGRAPH, pp. 143-150, 1986.- [2] E. Veach and L.J. Guibas, “Optimally Combining Sampling Techniques for Monte Carlo Rendering,”
Proc. ACM SIGGRAPH, pp. 419-428, 1995.- [3] E.P. Lafortune and Y.D. Willems, “Using the Modified Phong Reflectance Model for Physically Based Rendering,” Technical Report CW197, 1994.
- [4] J. Lawrence, S. Rusinkiewicz, and R. Ramamoorthi, “Efficient BRDF Importance Sampling Using a Factored Representation,”
Proc. ACM SIGGRAPH, pp. 496-505, 2004.- [5] M. Ashikhmin and P. Shirley, “An Anisotropic Phong Light Reflection Model,”
J. Graphics Tools, vol. 5, pp. 25-32, 2000.- [6] B. Walter, S.R. Marschner, H. Li, and K.E. Torrance, “Microfacet Models for Refraction through Rough Surfaces,”
Proc. Eurographics Symp. Rendering (EGSR '07), pp. 195-206, 2007.- [7] S. Agarwal, R. Ramamoorthi, S. Belongie, and H.W. Jensen, “Structured Importance Sampling of Environment Maps,”
Proc. ACM SIGGRAPH, pp. 605-612, 2003.- [8] V. Ostromoukhov, C. Donohue, and P.-M. Jodoin, “Fast Hierarchical Importance Sampling with Blue Noise Properties,”
Proc. ACM SIGGRAPH, pp. 488-495, 2004.- [9] M. Pharr and G. Humphreys,
Physically Based Rendering: From Theory to Implementation. Morgan Kaufmann Publishers, 2004.- [10] H. Jensen, “Global Illumination Using Photon Maps,”
Proc. Eurographics Workshop Rendering (EGWR '96), pp. 21-30, 1996.- [11] H.W. Jensen, “Importance Driven Path Tracing Using the Photon Map,”
Proc. Eurographics Workshop Rendering (EGWR '05), pp. 326-335, 1995.- [12] H. Hey and W. Purgathofer, “Importance Sampling with Hemispherical Particle Footprints,”
Proc. Spring Conf. Computer Graphics (SCCG '02), pp. 107-114, 2002.- [13] M. Pharr, “Extended Photon Map Implementation,” http://www.pbrt.org/pluginsexphotonmap.pdf , 2010.
- [14] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller, “Equations of State Calculations by Fast Computing Machines,”
J. Chemical Physics, vol. 21, pp. 1087-1092, 1953.- [15] J.F. Talbot, “Importance Resampling for Global Illumination,” master's thesis, Brigham Young Univ., 2005.
- [16] D. Burke, A. Ghosh, and W. Heidrich, “Bidirectional Importance Sampling for Direct Illumination,”
Proc. Eurographics Symp. Rendering (EGSR '05), pp. 147-156, 2005.- [17] P. Clarberg, W. Jarosz, T. Akenine-Möller, and H.W. Jensen, “Wavelet Importance Sampling: Efficiently Evaluating Products of Complex Functions,”
Proc. ACM SIGGRAPH, pp. 1166-1175, 2005.- [18] P. Clarberg and T. Akenine-Möller, “Practical Product Importance Sampling for Direct Illumination,”
Proc. Eurographics '08, pp. 681-690, 2008.- [19] R. Wang and O. Akerlund, “Bidirectional Importance Sampling for Unstructured Illumination,”
Proc. Eurographics '09, pp. 269-278, 2009.- [20] F. Rousselle, P. Clarberg, L. Leblanc, V. Ostromoukhov, and P. Poulin, “Efficient Product Sampling Using Hierarchical Thresholding,”
Proc. Computer Graphics Int'l (CGI '08), pp. 465-474, 2008.- [21] C. Lemieux,
Monte Carlo and Quasi-Monte Carlo Sampling. Springer, 2009.- [22] A. Keller, “Quasi-Monte Carlo Methods in Computer Graphics,”
Zeitschrift fur Angewandte Mathematik und Mechanik, vol. 76, no. 3, pp. 109-112, citeseer.ist.psu.edu/articleheinrich94quasimonte. html , 1996.- [23] D.E. Knuth,
The Art of Computer Programming : Seminumerical Algorithms, vol. 2, ch. 3, p. 232, Addison-Wesley, 1998.- [24] M. Donikian, B. Walter, K. Bala, S. Fernandez, and D.P. Greenberg, “Accurate Direct Illumination Using Iterative Adaptive Sampling,”
IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 3, pp. 353-364, May/June 2006.- [25] E. Veach and L.J. Guibas, “Bidirectional Estimators for Light Transport,”
Proc. Fifth Eurographics Workshop Rendering (EGWR '94), pp. 147-162, 1994.- [26] E.P. Lafortune and Y.D. Willems, “Bi-Directional Path Tracing,”
Proc. Compugraphics, pp. 145-153, 1993.- [27] E. Veach and L.J. Guibas, “Metropolis Light Transport,”
Proc. ACM SIGGRAPH, pp. 65-76, 1997.- [28] H.S. Wilf,
Algorithms and Complexity. AK Peters, 2003. |