Rex West
Iliyan Georgiev
ABSTRACT
Multiple importance sampling (MIS) is a powerful tool to combine different sampling techniques in a provably good manner. MIS requires that the techniques’ probability density functions (PDFs) are readily evaluable point-wise. However, this requirement may not be satisfied when (some of) those PDFs are marginals, i.e., integrals of other PDFs. We generalize MIS to combine samples from such marginal PDFs. The key idea is to consider each marginalization domain as a continuous space of sampling techniques with readily evaluable (conditional) PDFs. We stochastically select techniques from these spaces and combine the samples drawn from them into an unbiased estimator. Prior work has dealt with the special cases of multiple classical techniques or a single marginal one. Our formulation can handle mixtures of those.
We apply our marginal MIS formulation to light-transport simulation to demonstrate its utility. We devise a marginal path sampling framework that makes previously intractable sampling techniques practical and significantly broadens the path-sampling choices beyond what is presently possible. We highlight results from two algorithms based on marginal MIS: a novel formulation of path-space filtering at multiple vertices along a camera path and a similar filtering method for photon-density estimation.
Supplemental Material
Available for Download
- Pablo Bauszat, Victor Petitjean, and Elmar Eisemann. 2017. Gradient-Domain Path Reusing. ACM Trans. Graph. 36, 6, Article Article 229 (Nov. 2017), 9 pages. https://doi.org/10.1145/3130800.3130886Google Scholar
Digital Library
- 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
- Xi Deng, Miloš Hašan, Nathan Carr, Zexiang Xu, and Steve Marschner. 2021. Path Graphs: Iterative Path Space Filtering. ACM Trans. Graph. 40, 6, Article 276 (dec 2021), 15 pages. https://doi.org/10.1145/3478513.3480547Google ScholarDigital Library
- Iliyan Georgiev, Jaroslav Křivánek, Tomáš Davidovič, and Philipp Slusallek. 2012. Light Transport Simulation with Vertex Connection and Merging. 31, 6 (Nov. 2012), 192:1–192:10. https://doi.org/10/gbb6q7Google Scholar
- Toshiya Hachisuka, Shinji Ogaki, and Henrik Wann Jensen. 2008. Progressive Photon Mapping. 27, 5 (Dec. 2008), 130:1–130:8. https://doi.org/10/cn8h39Google Scholar
- Toshiya Hachisuka, Jacopo Pantaleoni, and Henrik Wann Jensen. 2012. A Path Space Extension for Robust Light Transport Simulation. 31, 6 (Jan. 2012), 191:1–191:10. https://doi.org/10/gbb6n3Google Scholar
- Henrik Wann Jensen. 1996. The Photon Map in Global Illumination. Ph.D. Thesis. Technical University of Denmark.Google Scholar
- James T. Kajiya. 1986. The Rendering Equation. 20, 4 (Aug. 1986), 143–150. https://doi.org/10/cvf53jGoogle Scholar
- Alexander Keller, Ken Dahm, and Nikolaus Binder. 2014. Path Space Filtering(SIGGRAPH ’14). ACM, 68:1–68:1. https://doi.org/10/gfz6mrGoogle Scholar
- Zackary Misso, Benedikt Bitterli, Iliyan Georgiev, and Wojciech Jarosz. 2022. Unbiased and consistent rendering using biased estimators. ACM Transactions on Graphics (Proceedings of SIGGRAPH) 41, 4 (2022). https://doi.org/10.1145/3528223.3530160Google ScholarDigital Library
- Hao Qin, Xin Sun, Qiming Hou, Baining Guo, and Kun Zhou. 2015. Unbiased Photon Gathering for Light Transport Simulation. ACM Trans. Graph. 34, 6, Article 208 (Oct. 2015), 14 pages. https://doi.org/10.1145/2816795.2818119Google ScholarDigital Library
- Eric Veach. 1997. Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. Thesis. Stanford University, United States – California.Google ScholarDigital Library
- 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
- Rex West, Iliyan Georgiev, Adrien Gruson, and Toshiya Hachisuka. 2020. Continuous Multiple Importance Sampling. ACM Transactions on Graphics (Proceedings of SIGGRAPH) 39, 4 (July 2020). https://doi.org/10.1145/3386569.3392436Google ScholarDigital Library
Index Terms
- Marginal Multiple Importance Sampling
Recommendations
Adaptive multiple importance sampling for general functions
We propose a mathematical expression for the optimal distribution of the number of samples in multiple importance sampling (MIS) and also give heuristics that work well in practice. The MIS balance heuristic is based on weighting several sampling ...
Importance sampling techniques for policy optimization
How can we effectively exploit the collected samples when solving a continuous control task with Reinforcement Learning? Recent results have empirically demonstrated that multiple policy optimization steps can be performed with the same batch by using off-...
Screen Space Ambient Occlusion Based Multiple Importance Sampling for Real-Time Rendering
We propose a new approximation technique for accelerating the Global Illumination algorithm for real-time rendering. The proposed approach is based on the Screen-Space Ambient Occlusion (SSAO) method, which approximates the global illumination for large,...
Comments