“Variance-aware path guiding” by Rath, Grittmann, Herholz, Vévoda, Slusallek, et al. …

  • ©Alexander Rath, Pascal Grittmann, Sebastian Herholz, Petr Vévoda, Philipp Slusallek, and Jaroslav Křivánek



Session Title:

    Smart Sampling


    Variance-aware path guiding



    Path guiding is a promising tool to improve the performance of path tracing algorithms. However, not much research has investigated what target densities a guiding method should strive to learn for optimal performance. Instead, most previous work pursues the zero-variance goal: The local decisions are guided under the assumption that all other decisions along the random walk will be sampled perfectly. In practice, however, many decisions are poorly guided, or not guided at all. Furthermore, learned distributions are often marginalized, e.g., by neglecting the BSDF. We present a generic procedure to derive theoretically optimal target densities for local path guiding. These densities account for variance in nested estimators, and marginalize provably well over, e.g., the BSDF. We apply our theory in two state-of-the-art rendering applications: a path guiding solution for unidirectional path tracing [Müller et al. 2017] and a guiding method for light source selection for the many lights problem [Vévoda et al. 2018]. In both cases, we observe significant improvements, especially on glossy surfaces. The implementations for both applications consist of trivial modifications to the original code base, without introducing any additional overhead.


    1. Steve Bako, Mark Meyer, Tony DeRose, and Pradeep Sen. 2019. Offline Deep Importance Sampling for Monte Carlo Path Tracing. Comput. Graph. Forum (Proceedings of Pacific Graphics 2019) 38, 7 (2019), 527–542.Google Scholar
    2. Thomas Bashford-Rogers, Kurt Debattista, and Alan Chalmers. 2012. A significance cache for accelerating global illumination. In Comput. Graph. Forum, Vol. 31. Wiley Online Library, 1837–1851.Google Scholar
    3. Benedikt Bitterli. 2016. Rendering resources. https://benedikt-bitterli.me/resources/Google Scholar
    4. Brent Burley, David Adler, Matt Jen-Yuan Chiang, Hank Driskill, Ralf Habel, Patrick Kelly, Peter Kutz, Yining Karl Li, and Daniel Teece. 2018. The design and evolution of disney’s hyperion renderer. ACM Trans. Graph. (TOG) 37, 3 (2018), 33.Google ScholarDigital Library
    5. Norbert Bus and Tamy Boubekeur. 2017. Double Hierarchies for Directional Importance Sampling in Monte Carlo Rendering. Journal of Computer Graphics Techniques (JCGT) 6, 3 (28 August 2017), 25–37. http://jcgt.org/published/0006/03/02Google Scholar
    6. Luca Fascione, Johannes Hanika, Mark Leone, Marc Droske, Jorge Schwarzhaupt, Tomáš Davidovič, Andrea Weidlich, and Johannes Meng. 2018. Manuka: A batch-shading architecture for spectral path tracing in movie production. ACM Trans. Graph. (TOG) 37, 3 (2018), 31.Google ScholarDigital Library
    7. Iliyan Georgiev, Thiago Ize, Mike Farnsworth, Ramón Montoya-Vozmediano, Alan King, Brecht Van Lommel, Angel Jimenez, Oscar Anson, Shinji Ogaki, Eric Johnston, et al. 2018. Arnold: A brute-force production path tracer. ACM Trans. Graph. (TOG) 37, 3 (2018), 32.Google ScholarDigital Library
    8. Iliyan Georgiev, Jaroslav Křivánek, Tomáš Davidovič, and Philipp Slusallek. 2012a. Light transport simulation with vertex connection and merging. ACM Trans. Graph. 31, 6 (2012), 192–1.Google ScholarDigital Library
    9. Iliyan Georgiev, Jaroslav Křivánek, Stefan Popov, and Philipp Slusallek. 2012b. Importance caching for complex illumination. In Comput. Graph. Forum, Vol. 31. Wiley Online Library, 701–710.Google Scholar
    10. Pascal Grittmann, Arsène Pérard-Gayot, Philipp Slusallek, and Jaroslav Křivánek. 2018. Efficient Caustic Rendering with Lightweight Photon Mapping. In Comput. Graph. Forum (EGSR ’18), Vol. 37. Wiley Online Library, 133–142.Google Scholar
    11. Adrien Gruson, Mickaël Ribardière, Martin Šik, Jiří Vorba, Rémi Cozot, Kadi Bouatouch, and Jaroslav Křivánek. 2017. A spatial target function for metropolis photon tracing. ACM Trans. Graph. (TOG) 36, 1 (2017), 4.Google ScholarDigital Library
    12. Jerry Guo, Pablo Bauszat, Jacco Bikker, and Elmar Eisemann. 2018. Primary sample space path guiding. In Eurographics Symposium on Rendering, Vol. 2018. The Eurographics Association, 73–82.Google Scholar
    13. Toshiya Hachisuka and Henrik Wann Jensen. 2011. Robust adaptive photon tracing using photon path visibility. ACM Trans. Graph. (TOG) 30, 5 (2011), 114.Google ScholarDigital Library
    14. Toshiya Hachisuka, Shinji Ogaki, and Henrik Wann Jensen. 2008. Progressive photon mapping. In ACM Trans. Graph. (TOG), Vol. 27. ACM, 130.Google ScholarDigital Library
    15. Toshiya Hachisuka, Jacopo Pantaleoni, and Henrik Wann Jensen. 2012. A path space extension for robust light transport simulation. ACM Trans. Graph. (TOG) 31, 6 (2012), 191.Google ScholarDigital Library
    16. Vlastimil Havran and Mateu Sbert. 2014. Optimal Combination of Techniques in Multiple Importance Sampling. ACM, New York, NY, 141–150.Google Scholar
    17. Sebastian Herholz, Oskar Elek, Jens Schindel, Jaroslav Křivánek, and Hendrik Lensch. 2018. A Unified Manifold Framework for Efficient BRDF Sampling based on Parametric Mixture Model. In EGSR ’18 EI&I (EGSR ’18). Eurographics Association.Google Scholar
    18. Sebastian Herholz, Oskar Elek, Jiří Vorba, Hendrik P. A. Lensch, and Jaroslav Křivánek. 2016. Product Importance Sampling for Light Transport Path Guiding. Comput. Graph. Forum 35 (2016), 67–77.Google ScholarDigital Library
    19. Sebastian Herholz, Yangyang Zhao, Oskar Elek, Derek Nowrouzezahrai, Hendrik P. A. Lensch, and Jaroslav Křivánek. 2019. Volume Path Guiding Based on Zero-Variance Random Walk Theory. ACM Trans. Graph. 38, 3, Article 25 (June 2019), 19 pages.Google ScholarDigital Library
    20. Heinrich Hey and Werner Purgathofer. 2002. Importance Sampling with Hemispherical Particle Footprints (SCCG ’02). ACM, 107–114.Google Scholar
    21. Wenzel Jakob. 2010. Mitsuba renderer. http://www.mitsuba-renderer.org.Google Scholar
    22. Henrik Wann Jensen. 1995. Importance Driven Path Tracing using the Photon Map. In Rendering Techniques.Google Scholar
    23. Henrik Wann Jensen. 1996. Global illumination using photon maps. In Rendering Techniques’ 96. Springer, 21–30.Google Scholar
    24. James T. Kajiya. 1986. The Rendering Equation. SIGGRAPH Comput. Graph. 20, 4 (Aug. 1986), 143–150.Google ScholarDigital Library
    25. Anton S Kaplanyan and Carsten Dachsbacher. 2013. Path space regularization for holistic and robust light transport. In Comput. Graph. Forum, Vol. 32. Wiley Online Library, 63–72.Google Scholar
    26. 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 ’19) 38, 6 (2019), 12.Google ScholarDigital Library
    27. Alexander Keller, Luca Fascione, Marcos Fajardo, Iliyan Georgiev, Per H Christensen, Johannes Hanika, Christian Eisenacher, and Gregory Nichols. 2015. The path tracing revolution in the movie industry.. In SIGGRAPH Courses. 24–1.Google Scholar
    28. Ivo Kondapaneni, Petr Vévoda, Pascal Grittmann, Tomáš Skřivan, Philipp Slusallek, and Jaroslav Křivánek. 2019. Optimal Multiple Importance Sampling. ACM Trans. Graph. (SIGGRAPH 2019) 38, 4 (July 2019), 37:1–37:14.Google Scholar
    29. Eric P. Lafortune and Yves D. Willems. 1993. Bi-Directional Path Tracing. 93 (Dec. 1993), 145–153.Google Scholar
    30. Eric P. Lafortune and Yves D. Willems. 1995. A 5D Tree to Reduce the Variance of Monte Carlo Ray Tracing. In Rendering Techniques.Google Scholar
    31. Thomas Müller, Markus H. Gross, and Jan Novák. 2017. Practical Path Guiding for Efficient Light-Transport Simulation. Comput. Graph. Forum 36 (2017), 91–100.Google ScholarDigital Library
    32. Thomas Müller, Brian McWilliams, Fabrice Rousselle, Markus Gross, and Jan Novák. 2018. Neural importance sampling. arXiv preprint arXiv:1808.03856 (2018).Google Scholar
    33. Art Owen and Yi Zhou. 2000. Safe and Effective Importance Sampling. J. Amer. Statist. Assoc. 95, 449 (2000), 135–143.Google ScholarCross Ref
    34. Jacopo Pantaleoni. 2019. Importance Sampling of Many Lights with Reinforcement Lightcuts Learning. arXiv preprint arXiv:1911.10217 (2019).Google Scholar
    35. Jacopo Pantaleoni and Eric Heitz. 2017. Notes on optimal approximations for importance sampling. arXiv preprint arXiv:1707.08358 (2017).Google Scholar
    36. Vincent Pegoraro, Carson Brownlee, Peter S Shirley, and Steven G Parker. 2008. Towards interactive global illumination effects via sequential Monte Carlo adaptation. In 2008 IEEE Symposium on Interactive Ray Tracing. IEEE, 107–114.Google ScholarCross Ref
    37. Matt Pharr, Wenzel Jakob, and Greg Humphreys. 2016. Physically based rendering: From theory to implementation. Morgan Kaufmann.Google Scholar
    38. Florian Reibold, Johannes Hanika, Alisa Jung, and Carsten Dachsbacher. 2018. Selective guided sampling with complete light transport paths. In SIGGRAPH Asia 2018 Technical Papers. ACM, 223.Google Scholar
    39. Mateu Sbert, Vlastimil Havran, and Laszlo. Szirmay-Kalos. 2016. Variance Analysis of Multi-sample and One-sample Multiple Importance Sampling. Comput. Graph. Forum 35, 7 (2016), 451–460.Google ScholarDigital Library
    40. Martin Šik and Jaroslav Křivánek. 2018. Survey of Markov Chain Monte Carlo Methods in Light Transport Simulation. IEEE Transactions on Visualization and Computer Graphics (2018), 1–1.Google Scholar
    41. Martin Šik and Jaroslav Křivánek. 2019. Implementing One-Click Caustics in Corona Renderer. (2019).Google Scholar
    42. Martin Šik, Hisanari Otsu, Toshiya Hachisuka, and Jaroslav Křivánek. 2016. Robust light transport simulation via metropolised bidirectional estimators. ACM Trans. Graph. (TOG) 35, 6 (2016), 245.Google ScholarDigital Library
    43. Eric Veach. 1997. Robust Monte Carlo methods for light transport simulation. Stanford University PhD thesis.Google ScholarDigital Library
    44. Eric Veach and Leonidas Guibas. 1995a. Bidirectional estimators for light transport. In Photorealistic Rendering Techniques. Springer, 145–167.Google Scholar
    45. Eric Veach and Leonidas J Guibas. 1995b. Optimally Combining Sampling Techniques for Monte Carlo Rendering. In SIGGRAPH ’95. ACM, 419–428.Google Scholar
    46. Eric Veach and Leonidas J Guibas. 1997. Metropolis light transport. In Proceedings of the 24th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., 65–76.Google ScholarDigital Library
    47. Petr Vévoda, Ivo Kondapaneni, and Jaroslav Křivánek. 2018. Bayesian online regression for adaptive direct illumination sampling. ACM Trans. Graph. (TOG) 37, 4 (2018), 125.Google ScholarDigital Library
    48. Jiří Vorba, Johannes Hanika, Sebastian Herholz, Thomas Müller, Jaroslav Křivánek, and Alexander Keller. 2019. Path Guiding in Production (SIGGRAPH ’19). ACM, New York, NY, USA, Article 18, 18:1–18:77 pages. Google ScholarDigital Library
    49. Jiří Vorba, Ondřej Karlík, Martin Šik, Tobias Ritschel, and Jaroslav Křivánek. 2014. On-line Learning of Parametric Mixture Models for Light Transport Simulation. ACM Trans. Graph. (Proceedings of SIGGRAPH 2014) 33, 4 (2014).Google Scholar
    50. Jiří Vorba and Jaroslav Křivánek. 2016. Adjoint-driven Russian Roulette and Splitting in Light Transport Simulation. ACM Trans. Graph. 35, 4, Article 42 (July 2016), 11 pages.Google ScholarDigital Library
    51. Quan Zheng and Matthias Zwicker. 2019. Learning to importance sample in primary sample space. In Comput. Graph. Forum, Vol. 38. Wiley Online Library, 169–179.Google Scholar

ACM Digital Library Publication: