“Continuous multiple importance sampling” by West, Georgiev, Gruson and Hachisuka
Conference:
Type:
Title:
- Continuous multiple importance sampling
Session/Category Title: Monte Carlo and Perception
Presenter(s)/Author(s):
Abstract:
Multiple importance sampling (MIS) is a provably good way to combine a finite set of sampling techniques to reduce variance in Monte Carlo integral estimation. However, there exist integration problems for which a continuum of sampling techniques is available. To handle such cases we establish a continuous MIS (CMIS) formulation as a generalization of MIS to uncountably infinite sets of techniques. Our formulation is equipped with a base estimator that is coupled with a provably optimal balance heuristic and a practical stochastic MIS (SMIS) estimator that makes CMIS accessible to a broad range of problems. To illustrate the effectiveness and utility of our framework, we apply it to three different light transport applications, showing improved performance over the prior state-of-the-art techniques.
References:
1. Anonymous. “Two random variables were talking in a bar. They thought they were being discrete but I heard their chatter continuously”. Annals of Statistical Jokes.Google Scholar
2. Pablo Bauszat, Victor Petitjean, and Elmar Eisemann. 2017. Gradient-Domain Path Reusing. ACM Trans. Graph. 36, 6, Article Article 229 (Nov. 2017), 9 pages. Google ScholarDigital Library
3. Philippe Bekaert, Mateu Sbert, and John Halton. 2002. Accelerating Path Tracing by Re-Using Paths. In Proceedings of the 13th Eurographics Workshop on Rendering. Eurographics Association, 125–134.Google Scholar
4. T. E. Booth. 2007. Unbiased Monte Carlo Estimation of the Reciprocal of an Integral. 156, 3 (2007), 403–407. https://doi.org/10/gfzq76Google Scholar
5. Robert L. Cook. 1986. Stochastic Sampling in Computer Graphics. 5, 1 (Jan. 1986), 51–72. https://doi.org/10/cqwhccGoogle Scholar
6. Robert L. Cook, Thomas Porter, and Loren Carpenter. 1984. Distributed Ray Tracing. 18, 3 (July 1984), 137–145. https://doi.org/10/c9thc3Google Scholar
7. Xi Deng, Shaojie Jiao, Benedikt Bitterli, and Wojciech Jarosz. 2019. Photon surfaces for robust, unbiased volumetric density estimation. ACM Transactions on Graphics (Proceedings of SIGGRAPH) 38, 4 (jul 2019). Google ScholarDigital Library
8. Victor Elvira, Luca Martino, David Luengo, and Mónica Bugallo. 2015. Generalized Multiple Importance Sampling. Statist. Sci. 34 (11 2015). Google ScholarCross Ref
9. H.B. Enderton. Elements of Set Theory. Elsevier Science.Google Scholar
10. Iliyan Georgiev and Marcos Fajardo. 2016. Blue-Noise Dithered Sampling. 35:1–35:1. https://doi.org/10/gfznbxGoogle Scholar
11. Iliyan Georgiev, Jaroslav Křivánek, Stefan Popov, and Philipp Slusallek. 2012. Importance Caching for Complex Illumination. 31, 2 (June 2012), 701–710. https://doi.org/10/gbbdccGoogle Scholar
12. Pascal Grittmann, Iliyan Georgiev, Philipp Slusallek, and Jaroslav Křivánek. 2019. Variance-Aware Multiple Importance Sampling. ACM Trans. Graph. (SIGGRAPH Asia 2019) 38, 6 (2019), 9. Google ScholarDigital Library
13. Vlastimil Havran and Mateu Sbert. 2014. Optimal combination of techniques in multiple importance sampling. 141–150. Google ScholarDigital Library
14. Yuanzhen He and Boxin Tang. 2014. A Characterization of Strong Orthogonal Arrays of Strength Three. 42, 4 (2014), 1347–1360. https://doi.org/10/gfznb4Google Scholar
15. Eric Heitz and Laurent Belcour. 2019. Distributing Monte Carlo Errors as a Blue Noise in Screen Space by Permuting Pixel Seeds Between Frames. Computer Graphics Forum (2019). Google ScholarCross Ref
16. Binh-Son Hua, Adrien Gruson, Victor Petitjean, Matthias Zwicker, Derek Nowrouzezahrai, Elmar Eisemann, and Toshiya Hachisuka. 2019. A Survey on Gradient-Domain Rendering. Computer Graphics Forum 38 (05 2019), 455–472. Google ScholarCross Ref
17. Wenzel Jakob and Johannes Hanika. 2019. A Low-Dimensional Function Space for Efficient Spectral Upsampling. Computer Graphics Forum (Proceedings of Eurographics) 38, 2 (March 2019).Google ScholarCross Ref
18. J. L. W. V. Jensen. 1906. Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Math. 30 (1906), 175–193. Google ScholarCross Ref
19. James T. Kajiya. 1986. The Rendering Equation. 20, 4 (Aug. 1986), 143–150. https://doi.org/10/cvf53jGoogle Scholar
20. Ondřej Karlík, Martin Šik, Petr Vévoda, Tomáš Skřivan, and Jaroslav Křivánek. 2019. MIS Compensation: Optimizing Sampling Techniques in Multiple Importance Sampling. ACM Trans. Graph. (SIGGRAPH Asia 2019) 38, 6 (2019), 12. Google ScholarDigital Library
21. Alexander Keller, Ken Dahm, and Nikolaus Binder. 2014. Path Space Filtering (SIGGRAPH ’14). ACM, 68:1–68:1. https://doi.org/10/gfz6mrGoogle Scholar
22. Ivo Kondapaneni, Petr Vévoda, Pascal Grittmann, Tomas Skrivan, Philipp Slusallek, and Jaroslav Krivanek. 2019. Optimal Multiple Importance Sampling. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2019) 38, 4 (July 2019), 37:1–37:14. Google ScholarDigital Library
23. Jaroslav Křivánek, Pascal Gautron, Sumanta Pattanaik, and Kadi Bouatouch. 2005. Radiance Caching for Efficient Global Illumination Computation. 11, 5 (2005), 550–561. https://doi.org/10/csf2swGoogle Scholar
24. Jaroslav Křivánek, Iliyan Georgiev, Toshiya Hachisuka, Petr Vévoda, Martin Šik, Derek Nowrouzezahrai, and Wojciech Jarosz. 2014. Unifying Points, Beams, and Paths in Volumetric Light Transport Simulation. 33, 4 (July 2014), 103:1–103:13. https://doi.org/10/f6cz72Google Scholar
25. Morgan McGuire. 2017. Computer Graphics Archive. https://casual-effects.com/dataGoogle Scholar
26. Anthony Pajot, Loic Barthe, Mathias Paulin, and Pierre Poulin. 2011. Representativity for Robust and Adaptive Multiple Importance Sampling. 17, 8 (2011), 1108–1121. https://doi.org/10/dpg3dnGoogle Scholar
27. Stefan Popov, Ravi Ramamoorthi, Fredo Durand, and George Drettakis. 2015. Probabilistic Connections for Bidirectional Path Tracing. Comput. Graph. Forum 34, 4 (July 2015), 75–86.Google Scholar
28. Mateu Sbert and Vlastimil Havran. 2017. Adaptive multiple importance sampling for general functions. The Visual Computer 33, 6 (01 Jun 2017), 845–855. Google ScholarDigital Library
29. Mateu Sbert, Vlastimil Havran, and László Szirmay-Kalos. 2016. Variance Analysis of Multi-sample and One-sample Multiple Importance Sampling. Computer Graphics Forum 35 (10 2016), 451–460. Google ScholarCross Ref
30. Mateu Sbert, Vlastimil Havran, and Laszlo Szirmay-Kalos. 2018. Multiple Importance Sampling Revisited: Breaking the Bounds. EURASIP Journal on Advances in Signal Processing 2018, 1 (Feb. 2018), 15. Google ScholarCross Ref
31. Benjamin Segovia, Jean Claude Iehl, Richard Mitanchey, and Bernard Péroche. 2006. Bidirectional Instant Radiosity. 389–397.Google Scholar
32. Eric Veach. 1997. Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. Thesis. Stanford University, United States – California.Google ScholarDigital Library
33. Eric Veach and Leonidas J. Guibas. 1995. Optimally Combining Sampling Techniques for Monte Carlo Rendering, Vol. 29. 419–428. https://doi.org/10/d7b6n4Google Scholar
34. Gregory J. Ward and Paul S. Heckbert. 1992. Irradiance Gradients. In CE_EGWR93, Alan Chalmers, Derek Paddon, and François X. Sillion (Eds.). Consolidation Express Bristol, 85–98.Google Scholar
35. Alexander Wilkie, Sehera Nawaz, Marc Droske, Andrea Weidlich, and Johannes Hanika. 2014. Hero Wavelength Spectral Sampling. 33, 4 (June 2014), 123–131. https://doi.org/10/f6fgb4Google Scholar
