“A Spatial Target Function for Metropolis Photon Tracing”

  • ©Adrien Gruson, Mickaël Ribardière, Martin Šik, Jiří Vorba, Rémi Cozot, Kadi Bouatouch, and Jaroslav Křivánek



Session Title:

    Rendering in Path Space


    A Spatial Target Function for Metropolis Photon Tracing




    The human visual system is sensitive to relative differences in luminance, but light transport simulation algorithms based on Metropolis sampling often result in a highly nonuniform relative error distribution over the rendered image. Although this issue has previously been addressed in the context of the Metropolis light transport algorithm, our work focuses on Metropolis photon tracing. We present a new target function (TF) for Metropolis photon tracing that ensures good stratification of photons leading to pixel estimates with equalized relative error. We develop a hierarchical scheme for progressive construction of the TF from paths sampled during rendering. In addition to the approach taken in previous work, where the TF is defined in the image plane, ours can be associated with compact spatial regions. This allows us to take advantage of illumination coherence to more robustly estimate the TF while adapting to geometry discontinuities. To sample from this TF, we design a new replica exchange Metropolis scheme. We apply our algorithm in progressive photon mapping and show that it often outperforms alternative approaches in terms of image quality by a large margin.


    1. T. Bashford-Rogers, K. Debattista, and A. Chalmers. 2014. Importance driven environment map sampling. IEEE Transactions on Visualization and Computer Graphics 20, 6, 907–918. DOI:http://dx.doi.org/10.1109/TVCG.2013.258 Google ScholarDigital Library
    2. Jiating Chen, Bin Wang, and Jun-Hai Yong. 2011. Improved stochastic progressive photon mapping with Metropolis sampling. Computer Graphics Forum 30, 4, 1205–1213. DOI:http://dx.doi.org/10.1111/j.1467-8659.2011.01979.x Google ScholarDigital Library
    3. P. H. Christensen. 2003. Adjoints and importance in rendering: An overview. IEEE Transactions on Visualization and Computer Graphics 9, 3, 329–340. DOI:http://dx.doi.org/10.1109/TVCG.2003.1207441 Google ScholarDigital Library
    4. David Cline, Justin Talbot, and Parris Egbert. 2005. Energy redistribution path tracing. ACM Transactions on Graphics 24, 3, 1186–1195. DOI:http://dx.doi.org/10.1145/1073204.1073330 Google ScholarDigital Library
    5. Carsten Dachsbacher, Jaroslav Křivánek, Miloš Hašan, Adam Arbree, Bruce Walter, and Jan Novák. 2014. Scalable realistic rendering with many-light methods. Computer Graphics Forum 33, 1, 88–104. DOI:http://dx.doi.org/10.1111/cgf.12256 Google ScholarDigital Library
    6. Philip Dutré and Yves Willems. 1995. Potential-driven Monte Carlo particle tracing for diffuse environments with adaptive probability density functions. In Proceedings of the Eurographics Workshop on Rendering.Google Scholar
    7. Shaohua Fan, Stephen Chenney, and Yu-Chi Lai. 2005. Metropolis photon sampling with optional user guidance. In Proceedings of the Eurographics Symposium on Rendering. Google ScholarDigital Library
    8. Iliyan Georgiev, Jaroslav Křivánek, Tomáš Davidovič, and Philipp Slusallek. 2012. Light transport simulation with vertex connection and merging. ACM Transactions on Graphics 31, 6, Article No. 192. DOI:http://dx.doi.org/10.1145/2366145.2366211 Google ScholarDigital Library
    9. Adrien Gruson, Mickael Ribardière, Remy Cozot, and Kadi Bouatouch. 2014. Rendu progressif base Metropolis-Hasting dans des scenes a contextes topologiques multiples. Revue Electronique Francophone d’Informatique Graphique 8, 1.Google Scholar
    10. Toshiya Hachisuka and Henrik Wann Jensen. 2009. Stochastic progressive photon mapping. ACM Transactions on Graphics 28, 5, Article No. 141. DOI:http://dx.doi.org/10.1145/1618452.1618487 Google ScholarDigital Library
    11. Toshiya Hachisuka and Henrik Wann Jensen. 2011. Robust adaptive photon tracing using photon path visibility. ACM Transactions on Graphics 30, 5, Article No. 114. DOI:http://dx.doi.org/10.1145/2019627.2019633 Google ScholarDigital Library
    12. Toshiya Hachisuka, Anton S. Kaplanyan, and Carsten Dachsbacher. 2014. Multiplexed Metropolis light transport. ACM Transactions on Graphics 33, 4, 100:1–100:10. Google ScholarDigital Library
    13. Toshiya Hachisuka, Jacopo Pantaleoni, and Henrik Wann Jensen. 2012. A path space extension for robust light transport simulation. ACM Transactions on Graphics 31, 6, Article No. 191. DOI:http://dx.doi.org/10.1145/2366145.2366210 Google ScholarDigital Library
    14. Johannes Hanika, Anton Kaplanyan, and Carsten Dachsbacher. 2015. Improved half vector space light transport. Computer Graphics Forum 34, 4, 65–74. Google ScholarDigital Library
    15. W. K. Hastings. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 1, 97–109. Google ScholarCross Ref
    16. Jared Hoberock and John C. Hart. 2010. Arbitrary importance functions for Metropolis light transport. Computer Graphics Forum 29, 6, 1993–2003. DOI:http://dx.doi.org/10.1111/j.1467-8659.2010.01713.x Google ScholarCross Ref
    17. Wenzel Jakob. 2010. Mitsuba Renderer. Retrieved September 23, 2016, from http://www.mitsuba-renderer.org.Google Scholar
    18. 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, Article No. 58. DOI:http://dx.doi.org/10.1145/2185520.2185554 Google ScholarDigital Library
    19. Wenzel Jakob, Christian Regg, and Wojciech Jarosz. 2011. Progressive expectation-maximization for hierarchical volumetric photon mapping. Computer Graphics Forum 30, 4, 1287–1297. DOI:http://dx.doi.org/10.1111/j.1467-8659.2011.01988.x Google ScholarDigital Library
    20. Henrik Wann Jensen. 1995. Importance driven path tracing using the photon map. In Rendering Techniques’95. Eurographics. Springer, 326–335. Google ScholarCross Ref
    21. Anton S. Kaplanyan and Carsten Dachsbacher. 2013a. Adaptive progressive photon mapping. ACM Transactions on Graphics 32, 2, Article No. 16. DOI:http://dx.doi.org/10.1145/2451236.2451242 Google ScholarDigital Library
    22. Anton S. Kaplanyan and Carsten Dachsbacher. 2013b. Path space regularization for holistic and robust light transport. Computer Graphics Forum 32, 2, 63–72. Google ScholarCross Ref
    23. Csaba Kelemen, László Szirmay-Kalos, Gyorgy Antal, and Ferenc Csonka. 2002. A simple and robust mutation strategy for the Metropolis light transport. Computer Graphics Forum 21, 3531–540. Google ScholarCross Ref
    24. Shinya Kitaoka, Yoshifumi Kitamura, and Fumio Kishino. 2009. Replica exchange light transport. Computer Graphics Forum 28, 8, 2330–2342. DOI:http://dx.doi.org/10.1111/j.1467-8659.2009.01540.x Google ScholarCross Ref
    25. Eric P. Lafortune and Yves D. Willems. 1993. Bi-directional path tracing. In Proceedings of the Compugraphics Conference (Compugraphics’93). 145–153.Google Scholar
    26. Jaakko Lehtinen, Tero Karras, Samuli Laine, Miika Aittala, Frédo Durand, and Timo Aila. 2013. Gradient-domain Metropolis light transport. ACM Transactions on Graphics 32, 4, 95:1–95:12. Google ScholarDigital Library
    27. Radford M. Neal. 1996. Sampling from multimodal distributions using tempered transitions. Statistics and Computing 6, 4, 353–366. DOI:http://dx.doi.org/10.1007/BF00143556 Google ScholarCross Ref
    28. Ingmar Peter and Georg Pietrek. 1998. Importance driven construction of photon maps. In Rendering Techniques’98. Eurographics. Springer, 269–80. Google ScholarCross Ref
    29. Jeffrey S. Rosenthal. 2011. Optimal proposal distributions and adaptive MCMC. In Handbook of Markov Chain Monte Carlo, S. Brooks, A. Gelman, G. L. Jones, and X.-Li Meng (Eds.). Chapman 8 Hall/CRC. Google ScholarCross Ref
    30. Fabrice Rousselle, Claude Knaus, and Matthias Zwicker. 2012. Adaptive rendering with non-local means filtering. ACM Transactions on Graphics 31, 6, Article No. 195. DOI:http://dx.doi.org/10.1145/2366145.2366214 Google ScholarDigital Library
    31. Benjamin Segovia, Jean Claude Iehl, and Bernard Péroche. 2007. Metropolis instant radiosity. Computer Graphics Forum 26, 3, 425–434. Google ScholarCross Ref
    32. Eric Veach. 1997. Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. Dissertation. Stanford University, Stanford, CA. Google ScholarDigital Library
    33. 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). 65–76. Google ScholarDigital Library
    34. Edgar Velázquez-Armendáriz, Zhao Dong, Bruce Walter, and Donald P. Greenberg. 2015. Complex luminaires: Illumination and appearance rendering. ACM Transactions on Graphics 34, 3, Article No. 26. DOI:http://dx.doi.org/10.1145/2714571 Google ScholarDigital Library
    35. Jiří Vorba, Ondřej Karlík, Martin Šik, Tobias Ritschel, and Jaroslav Křivánek. 2014. On-line learning of parametric mixture models for light transport simulation. ACM Transactions on Graphics 33, 4, Article No. 101. Google ScholarDigital Library
    36. Quan Zheng and Chang-Wen Zheng. 2015. Visual importance-based adaptive photon tracing. Visual Computer 31, 6–8, 1001–1010. DOI:http://dx.doi.org/10.1007/s00371-015-1104-0 Google ScholarDigital Library
    37. Matthias Zwicker, Wojciech Jarosz, Jaakko Lehtinen, Bochang Moon, Ravi Ramamoorthi, Fabrice Rousselle, Pradeep Sen, Cyril Soler, and Sung-Eui Yoon. 2015. Recent advances in adaptive sampling and reconstruction for Monte Carlo rendering. Computer Graphics Forum 34, 2, 667–681. DOI:http://dx.doi.org/10.1111/cgf.12592 Google ScholarDigital Library

ACM Digital Library Publication: