skip to main content
research-article

Delayed Rejection Metropolis Light Transport

Published: 13 May 2020 Publication History

Abstract

Designing robust mutation strategies for primary sample space Metropolis light transport is a challenging problem: poorly tuned mutations both hinder state space exploration and introduce structured image artifacts. Scenes with complex materials, lighting, and geometry make hand-designing strategies that remain optimal over the entire state space infeasible. Moreover, these difficult regions are often sparse in state space, and so relying exclusively on intricate—and often expensive—proposal mechanisms can be wasteful, whereas simpler inexpensive mechanisms are more sample efficient. We generalize Metropolis–Hastings light transport to employ a flexible two-stage mutation strategy based on delayed rejection Markov chain Monte Carlo. Our approach generates multiple proposals based on the failure of previous ones, all while preserving Markov chain ergodicity. This allows us to reduce error while maintaining fast global exploration and low correlation across chains. Direct application of delayed rejection to light transport leads to low acceptance probabilities, and so we also propose a novel transition kernel to alleviate this issue. We benchmark our approach on several applications including bold-then-timid and cheap-then-expensive proposals across different light transport algorithms. Our method is applicable to any primary sample space algorithm with minimal implementation effort, producing consistently better results on a variety of challenging scenes.

References

[1]
Christophe Andrieu and Johannes Thoms. 2008. A tutorial on adaptive MCMC. Statistics and Computing 18, 4 (2008), 343--373.
[2]
ichael Ashikhmin, Simon Premože, Peter Shirley, and Brian Smits. 2001. A variance analysis of the Metropolis light transport algorithm. Computers & Graphics 25, 2 (2001), 287--294.
[3]
Benedikt Bitterli. 2016. Rendering Resources. Retrieved March 25, 2020 from https://benedikt-bitterli.me/resources.
[4]
Benedikt Bitterli, Wenzel Jakob, Jan Novák, and Wojciech Jarosz. 2018. Reversible jump Metropolis light transport using inverse mappings. ACM Transactions on Graphics 37, 1 (Jan. 2018), Article 1, 12 pages.
[5]
Benedikt Bitterli and Wojciech Jarosz. 2019. Selectively Metropolised Monte Carlo light transport simulation. ACM Transactions on Graphics 38, 6 (Nov. 2019), Article 153, 10 pages.
[6]
J. Andrés Christen and Colin Fox. 2005. Markov chain Monte Carlo using an approximation. Journal of Computational and Graphical Statistics 14, 4 (2005), 795--810.
[7]
David Cline, Justin Talbot, and Parris Egbert. 2005. Energy redistribution path tracing. ACM Transactions on Graphics 24, 3 (July 2005), 1186--1195.
[8]
Simon Duane, A. D. Kennedy, Brian J. Pendleton, and Duncan Roweth. 1987. Hybrid Monte Carlo. Physics Letters B 195, 2 (1987), 216--222.
[9]
Nicholas I. Fisher. 1995. Statistical Analysis of Circular Data. Cambridge University Press.
[10]
Alan E. Gelfand and Sujit K. Sahu. 1994. On Markov chain Monte Carlo acceleration. Journal of Computational and Graphical Statistics 3, 3 (1994), 261--276.
[11]
Mark Girolami, Ben Calderhead, and Siu A. Chin. 2011. Riemann manifold Langevin and Hamiltonian Monte Carlo methods. Journal of the Royal Statistical Society, Series B (Methodological) 73, 2 (2011), 123--214.
[12]
Peter J. Green. 1995. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 4 (Dec. 1995), 711--732.
[13]
Peter J. Green and Antonietta Mira. 2001. Delayed rejection in reversible jump Metropolis--Hastings. Biometrika 88, 4 (2001), 1035--1053.
[14]
Heikki Haario, Marko Laine, Antonietta Mira, and Eero Saksman. 2006. DRAM: Efficient adaptive MCMC. Statistics and Computing 16, 4 (Dec. 2006), 339--354.
[15]
Heikki Haario, Eero Saksman, and Johanna Tamminen. 1998. An adaptive Metropolis algorithm. Bernoulli 7 (1998), 223--242.
[16]
Toshiya Hachisuka and Henrik Wann Jensen. 2011. Robust adaptive photon tracing using photon path visibility. ACM Transactions on Graphics 30, 5 (Oct. 2011), Article 114, 11 pages.
[17]
Toshiya Hachisuka, Anton S. Kaplanyan, and Carsten Dachsbacher. 2014. Multiplexed Metropolis light transport. ACM Transactions on Graphics 33, 4 (July 2014), Article 100, 10 pages.
[18]
Charles Han, Bo Sun, Ravi Ramamoorthi, and Eitan Grinspun. 2007. Frequency domain normal map filtering. ACM Transactions on Graphics 26, 3 (2007), 28.
[19]
Johannes Hanika, Anton Kaplanyan, and Carsten Dachsbacher. 2015. Improved half vector space light transport. Computer Graphics Forum 34, 4 (July 2015), 65--74.
[20]
Wilfred K. Hastings. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 1 (April 1970), 97--109.
[21]
Wenzel Jakob. 2013. Mitsuba Renderer. Retrieved March 25, 2020 from http://www.mitsuba-renderer.org
[22]
Wenzel Jakob and Steve Marschner. 2012. Manifold exploration: A Markov chain Monte Carlo technique for rendering scenes with difficult specular transport. ACM Transactions on Graphics 31, 4 (July 2012), Article 58, 13 pages.
[23]
James T. Kajiya. 1986. The rendering equation. Computer Graphics 20, 4 (Aug. 1986), 143--150.
[24]
Anton S. Kaplanyan and Carsten Dachsbacher. 2013. Path space regularization for holistic and robust light transport. Computer Graphics Forum 32, 2 (2013), 63--72.
[25]
Anton S. Kaplanyan, Johannes Hanika, and Carsten Dachsbacher. 2014. The natural-constraint representation of the path space for efficient light transport simulation. ACM Transactions on Graphics 33, 4 (July 2014), Article 102, 13 pages.
[26]
Csaba Kelemen, László Szirmay-Kalos, György Antal, and Ferenc Csonka. 2002. A simple and robust mutation strategy for the Metropolis light transport algorithm. Computer Graphics Forum 21, 3 (Sept. 2002), 531--540.
[27]
Eric P. Lafortune and Yves D. Willems. 1993. Bi-directional path tracing. In Proceedings of the International Conference on Computational Graphics and Visualization Techniques, Vol. 93. 145--153.
[28]
Yu-Chi Lai, Shao Hua Fan, Stephen Chenney, and Charcle Dyer. 2007. Photorealistic image rendering with Population Monte Carlo energy redistribution. In Proceedings of the 18th Eurographics Conference on Rendering Techniques (EGSR’07). 287--295.
[29]
Tzu-Mao Li, Miika Aittala, Frédo Durand, and Jaakko Lehtinen. 2018. Differentiable Monte Carlo ray tracing through edge sampling. ACM Transactions on Graphics 37, 6 (2018), Article 222.
[30]
Tzu-Mao Li, Jaakko Lehtinen, Ravi Ramamoorthi, Wenzel Jakob, and Frédo Durand. 2015. Anisotropic Gaussian mutations for Metropolis light transport through Hessian-Hamiltonian dynamics. ACM Transactions on Graphics 34, 6 (Oct. 2015), Article 209, 13 pages.
[31]
Jun S. Liu, Faming Liang, and Wing Hung Wong. 2000. The multiple-try method and local optimization in Metropolis sampling. Journal of the American Statistical Association 95, 449 (March 2000), 121--134.
[32]
Samuel Livingstone and Mark Girolami. 2014. Information-geometric Markov chain Monte Carlo methods using diffusions. Entropy 16, 6 (2014), 3074--3102.
[33]
Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller. 1953. Equation of state calculations by fast computing machines. Journal of Chemical Physics 21, 6 (June 1953), 1087--1092.
[34]
Antonietta Mira. 2001. On Metropolis--Hastings algorithms with delayed rejection. Metron 59, 3--4 (2001), 231--241.
[35]
Iain Murray, Ryan Adams, and David MacKay. 2010. Elliptical slice sampling. In Proceedings of the 13th International Conference on Artificial Intelligence and Statistics, Vol. 9. 541--548.
[36]
Merlin Nimier-David, Delio Vicini, Tizian Zeltner, and Wenzel Jakob. 2019. Mitsuba 2: A retargetable forward and inverse renderer. ACM Transactions on Graphics 38, 6 (2019), Article 203.
[37]
Hisanari Otsu, Johannes Hanika, Toshiya Hachisuka, and Carsten Dachsbacher. 2018. Geometry-aware Metropolis light transport. ACM Transactions on Graphics 37, 6 (2018), Article 278, 11 pages.
[38]
Hisanari Otsu, Anton S. Kaplanyan, Johannes Hanika, Carsten Dachsbacher, and Toshiya Hachisuka. 2017. Fusing state spaces for Markov chain Monte Carlo rendering. ACM Transactions on Graphics 36, 4 (July 2017), Article 74, 10 pages.
[39]
Hisanari Otsu, Yonghao Yue, Qiming Hou, Kei Iwasaki, Yoshinori Dobashi, and Tomoyuki Nishita. 2013. Replica exchange light transport on relaxed distributions. In ACM SIGGRAPH 2013 Posters (SIGGRAPH’13). ACM, New York, NY, Article 106, 1 page.
[40]
Jacopo Pantaleoni. 2017. Charted metropolis light transport. ACM Transactions on Graphics 36, 4 (2017), Article 75, 14 pages.
[41]
Christian Robert and George Casella. 2005. Monte Carlo Statistical Methods. Springer Texts in Statistics. Springer-Verlag.
[42]
Gareth O. Roberts and Jeffrey S. Rosenthal. 2009. Examples of adaptive MCMC. Journal of Computational and Graphical Statistics 18, 2 (2009), 349--367.
[43]
Benjamin Segovia, Jean-Claude Iehl, and Bernard Peroche. 2007. Coherent Metropolis Light Transport with Multiple-Try Mutations. Technical Report RR-LIRIS-2007-015. Universite Lyon, Lyon, France.
[44]
Chris Sherlock, Andrew Golightly, and Daniel A. Henderson. 2017. Adaptive, delayed-acceptance MCMC for targets with expensive likelihoods. Journal of Computational and Graphical Statistics 26, 2 (2017), 434--444.
[45]
Martin Šik and Jaroslav Křivánek. 2016. Improving global exploration of MCMC light transport simulation. In ACM SIGGRAPH 2016 Posters (SIGGRAPH’16). Article 50, 2 pages.
[46]
Martin Šik and Jaroslav Křivánek. 2018. Survey of Markov chain Monte Carlo methods in light transport simulation. IEEE Transactions on Visualization and Computer Graphics 26, 4 (2018), 1821--1840.
[47]
László Szirmay-Kalos and László Szécsi. 2017. Improved stratification for metropolis light transport. Computers 8 Graphics 68 (2017), 11--20.
[48]
Luke Tierney and Antonietta Mira. 1999. Some adaptive Monte Carlo methods for Bayesian inference. Statistics in Medicine 18, 17--18 (1999), 2507--2515.
[49]
Miquel Trias, Alberto Vecchio, and John Veitch. 2009. Delayed rejection schemes for efficient Markov-chain Monte-Carlo sampling of multimodal distributions. arXiv:0904.2207.
[50]
Eric Veach. 1997. Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. Dissertation. Stanford University, Stanford, CA.
[51]
Eric Veach and Leonidas J. Guibas. 1995. Bidirectional estimators for light transport. In Photorealistic Rendering Techniques. Focus on Computer Graphics. Springer-Verlag, 145--167.
[52]
Eric Veach and Leonidas J. Guibas. 1997. Metropolis light transport. In Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’97), Vol. 31. ACM, New York, NY, 65--76.
[53]
Jiří Vorba, Johannes Hanika, Sebastian Herholz, Thomas Müller, Jaroslav Křivánek, and Alexander Keller. 2019. Path guiding in production. In ACM SIGGRAPH Course Notes. ACM, New York, NY, Article 18, 77 pages.
[54]
Károly Zsolnai and László Szirmay-Kalos. 2013. Automatic parameter control for Metropolis light transport. In Proceedings of Eurographics Short Papers, M.-A. Otaduy and O. Sorkine (Eds.). Eurographics Association, Girona, Spain, 53--56.

Cited By

View all
  • (2023)Langevin dynamics in stochastic ray tracing: computing the preconditioning matrix according to restrictions and choice of time stepKeldysh Institute Preprints10.20948/prepr-2023-63(1-26)Online publication date: 2023
  • (2023)Federative rendering modelOptoelectronic Imaging and Multimedia Technology X10.1117/12.2686883(26)Online publication date: 27-Nov-2023
  • (2021)Light Transport Simulation and Realistic Rendering: State of the Art ReportProceedings of the 31th International Conference on Computer Graphics and Vision. Volume 210.20948/graphicon-2021-3027-1-12(1-12)Online publication date: 2021
  • Show More Cited By

Index Terms

  1. Delayed Rejection Metropolis Light Transport

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Transactions on Graphics
    ACM Transactions on Graphics  Volume 39, Issue 3
    June 2020
    179 pages
    ISSN:0730-0301
    EISSN:1557-7368
    DOI:10.1145/3388953
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 13 May 2020
    Online AM: 07 May 2020
    Accepted: 01 February 2020
    Revised: 01 February 2020
    Received: 01 October 2019
    Published in TOG Volume 39, Issue 3

    Permissions

    Request permissions for this article.

    Check for updates

    Author Tags

    1. Markov chain Monte Carlo light transport
    2. photorealistic rendering

    Qualifiers

    • Research-article
    • Research
    • Refereed

    Funding Sources

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)30
    • Downloads (Last 6 weeks)6
    Reflects downloads up to 18 Jan 2025

    Other Metrics

    Citations

    Cited By

    View all
    • (2023)Langevin dynamics in stochastic ray tracing: computing the preconditioning matrix according to restrictions and choice of time stepKeldysh Institute Preprints10.20948/prepr-2023-63(1-26)Online publication date: 2023
    • (2023)Federative rendering modelOptoelectronic Imaging and Multimedia Technology X10.1117/12.2686883(26)Online publication date: 27-Nov-2023
    • (2021)Light Transport Simulation and Realistic Rendering: State of the Art ReportProceedings of the 31th International Conference on Computer Graphics and Vision. Volume 210.20948/graphicon-2021-3027-1-12(1-12)Online publication date: 2021
    • (2021)Ensemble Metropolis Light TransportACM Transactions on Graphics10.1145/347229441:1(1-15)Online publication date: 20-Dec-2021
    • (2021)Light Transport in Realistic Rendering: State-of-the-Art Simulation MethodsProgramming and Computing Software10.1134/S036176882104003447:4(298-326)Online publication date: 1-Jul-2021
    • (2020)Unbiased warped-area sampling for differentiable renderingACM Transactions on Graphics10.1145/3414685.341783339:6(1-18)Online publication date: 27-Nov-2020

    View Options

    Login options

    Full Access

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    HTML Format

    View this article in HTML Format.

    HTML Format

    Media

    Figures

    Other

    Tables

    Share

    Share

    Share this Publication link

    Share on social media