“Volume Path Guiding Based on Zero-Variance Random Walk Theory” by Herholz, Zhao, Elek, Nowrouzezahrai, Lensch, et al. …

  • ©

Conference:


Type(s):


Title:

    Volume Path Guiding Based on Zero-Variance Random Walk Theory

Session/Category Title:   Advanced Volume Rendering

Presenter(s)/Author(s):


Abstract:


    The efficiency of Monte Carlo methods, commonly used to render participating media, is directly linked to the manner in which random sampling decisions are made during path construction. Notably, path construction is influenced by scattering direction and distance sampling, Russian roulette, and splitting strategies. We present a consistent suite of volumetric path construction techniques where all these sampling decisions are guided by a cached estimate of the adjoint transport solution. The proposed strategy is based on the theory of zero-variance path sampling schemes, accounting for the spatial and directional variation in volumetric transport. Our key technical contribution, enabling the use of this approach in the context of volume light transport, is a novel guiding strategy for sampling the particle collision distance proportionally to the product of transmittance and the adjoint transport solution (e.g., in-scattered radiance). Furthermore, scattering directions are likewise sampled according to the product of the phase function and the incident radiance estimate. Combined with guided Russian roulette and splitting strategies tailored to volumes, we demonstrate about an order-of-magnitude error reduction compared to standard unidirectional methods. Consequently, our approach can render scenes otherwise intractable for such methods, while still retaining their simplicity (compared to, e.g., bidirectional methods).

References:


    1. John Amanatides and Andrew Woo. 1987. A fast voxel traversal algorithm for ray tracing. In Eurographics ’87. 3–10.
    2. Parthasarathy Bagchi and Irwin Guttman. 1988. Theoretical considerations of the multivariate von Mises-Fisher distribution. J. Appl. Stat. 15, 2 (Jan. 1988), 149–169.
    3. Arindam Banerjee, Inderjit S. Dhillon, Joydeep Ghosh, and Suvrit Sra. 2005. Clustering on the unit hypersphere using von Mises-Fisher distributions. J. Mach. Learn. Res. 6 (2005), 1345–1382.
    4. Mark Bangert, Philipp Hennig, and Uwe Oelfke. 2010. Using an infinite von Mises-Fisher mixture model to cluster treatment beam directions in external radiation therapy. In Conference on Machine Learning and Applications.
    5. Thomas Bashford-Rogers, Kurt Debattista, and Alan Chalmers. 2012. A significance cache for accelerating global illumination. Comput. Graph. Forum 31, 6 (2012), 1837–1851.
    6. Laurent Belcour, Kavita Bala, and Cyril Soler. 2014. A local frequency analysis of light scattering and absorption. ACM Trans. Graph. 33 (2014), 5.
    7. Benedikt Bitterli and Wojciech Jarosz. 2017. Beyond points and beams: Higher-dimensional photon samples for volumetric light transport. ACM Trans. Graph. 36, 4 (2017), 112:1–112:12.
    8. Norbert Bus and Tamy Boubekeur. 2017. Double hierarchies for directional importance sampling in Monte Carlo rendering. J. Comput. Graphics Techn. 6, 3 (2017), 25–37.
    9. Florent Chatelain and Nicolas Le Bihan. 2013. Von Mises-Fisher approximation of multiple scattering process on the hypersphere. In International Conference on Acoustics, Speech, and Signal Processing.
    10. Per H. Christensen. 2003. Adjoints and importance in rendering: An overview. IEEE Trans. Visual. Comput. Graphics 9, 3 (2003), 329–340.
    11. Per H. Christensen and Wojciech Jarosz. 2016. The path to path-traced movies. Found. Trends Comput. Graphics Vision 10, 2 (2016), 103–175.
    12. Ken Dahm and Alexander Keller. 2017. Learning light transport the reinforced way. In ACM SIGGRAPH 2017 Talks. 73:1–73:2.
    13. Michael Donikian, Bruce Walter, Kavita Bala, Sebastian Fernandez, and Donald P. Greenberg. 2006. Accurate direct illumination using iterative adaptive sampling. IEEE Trans. Visual. Comput. Graphics 12, 3 (2006), 353–364.
    14. Craig Donner and Henrik Wann Jensen. 2006. A spectral BSSRDF for shading human skin. In Proceedings of the 17th Eurographics Conference on Rendering Techniques. 409–417.
    15. S. R. Dwivedi. 1982. A new importance biasing scheme for deep-penetration Monte Carlo. Ann. Nucl. Energy 9, 7 (1982).
    16. Thomas Engelhardt and Carsten Dachsbacher. 2010. Epipolar sampling for shadows and crepuscular rays in participating media with single scattering. In Proc. I3D.
    17. Thomas Engelhardt, Jan Novák, Thorsten-W. Schmidt, and Carsten Dachsbacher. 2012. Approximate bias compensation for rendering scenes with heterogeneous participating media. Comp. Graph. Forum 31 (2012), 2145–2154.
    18. Luca Fascione, Johannes Hanika, Marcos Fajardo, Per Christensen, Brent Burley, and Brian Green. 2017. Path tracing in production. In ACM SIGGRAPH 2017 Courses.
    19. Julian Fong, Magnus Wrenninge, Christopher Kulla, and Ralf Habel. 2017. Production volume rendering. In ACM SIGGRAPH 2017 Courses. 2:1–2:79.
    20. Jeppe Revall Frisvad. 2011. Importance sampling the Rayleigh phase function. J. Opt. Soc. Am. A 28 (2011), 2436–2441.
    21. M. Galtier, S. Blanco, C. Caliot, C. Coustet, J. Dauchet, M. El Hafi, V. Eymet, R. Fournier, J. Gautrais, A. Khuong, B. Piaud, and G. Terrée. 2013. Integral formulation of null-collision Monte Carlo algorithms. J. Quant. Spectrosc. Radiat. Transfer 125, C (2013), 57–68.
    22. Iliyan Georgiev, Jaroslav Křivánek, Toshiya Hachisuka, Derek Nowrouzezahrai, and Wojciech Jarosz. 2013. Joint importance sampling of low-order volumetric scattering. ACM Trans. Graph. 32, 6 (2013), 164:1–164:14.
    23. Peter Grassberger. 2002. Go with the winners: A general Monte Carlo strategy. Comput. Phys. Commun. 147, 1 (2002), 64–70.
    24. Jerry Guo, Pablo Bauszat, Jacco Bikker, and Elmar Eisemann. 2018. Primary sample space path guiding. In Eurographics Symposium on Rendering—EI 8 I. 73–82.
    25. Sebastian Herholz, Oskar Elek, Jiří Vorba, Hendrik Lensch, and Jaroslav Křivánek. 2016. Product importance sampling for light transport path guiding. Comput. Graphics Forum 35, 4 (2016), 67–77.
    26. Heinrich Hey and Werner Purgathofer. 2002. Importance sampling with hemispherical particle footprints. In Proc. of SCCG. 107–114.
    27. J. Eduard Hoogenboom. 2008. Zero-variance Monte Carlo schemes revisited. Nucl. Sci. Eng. 160, 1 (2008), 1–22.
    28. Wenzel Jakob. 2010. Mitsuba renderer. Retrieved from http://www.mitsuba-renderer.org.
    29. Wenzel Jakob. 2012. Numerically Stable Sampling of the von Mises-Fisher Distribution on (and Other Tricks). Technical Report. Cornell University.
    30. Wojciech Jarosz. 2013. The perils of evolutionary rendering research: Beyond the point sample. (2013). Eurographics Symposium on Rendering, Invited Talk.
    31. Wojciech Jarosz, Craig Donner, Matthias Zwicker, and Henrik Wann Jensen. 2008. Radiance caching for participating media. ACM Trans. Graph. 27, 1 (2008), 7:1–7:11.
    32. Wojciech Jarosz, Derek Nowrouzezahrai, Iman Sadeghi, and Henrik Wann Jensen. 2011. A comprehensive theory of volumetric radiance estimation using photon points and beams. ACM Trans. Graphics 30, 1 (2011), 5:1–5:19.
    33. Henrik Wann Jensen. 1995. Importance driven path tracing using the photon map. In Rendering Techniques (Proc. of EGWR).
    34. Henrik Wann Jensen and Per H. Christensen. 1998. Efficient simulation of light transport in scenes with participating media using photon maps. In Proc. of SIGGRAPH. 311–320.
    35. Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH). 511–518.
    36. James T. Kajiya. 1986. The rendering equation. SIGGRAPH Comput. Graph. 20 (1986).
    37. Malvin H. Kalos and Paula A. Whitlock. 2008. Monte Carlo Methods. Wiley-VCH.
    38. David Koerner, Jan Novák, Peter Kutz, Ralf Habel, and Wojciech Jarosz. 2016. Subdivision next-event estimation for path-traced subsurface scattering. In Eurographics Symposium on Rendering—Experimental Ideas 8 Implementations. 91–96.
    39. Christopher Kulla and Marcos Fajardo. 2012. Importance sampling techniques for path tracing in participating media. Comput. Graphics Forum 31, 4 (2012), 1519–1528.
    40. Peter Kutz, Ralf Habel, Yining Karl Li, and Jan Novák. 2017. Spectral and decomposition tracking for rendering heterogeneous volumes. ACM Trans. Graphics (Proceedings of SIGGRAPH) 36, 4 (2017), 111:1–111:16.
    41. Jaroslav Křivánek and Eugene d’Eon. 2014. A zero-variance-based sampling scheme for Monte Carlo subsurface scattering. In ACM SIGGRAPH 2014 Talks. 66:1–66:1.
    42. 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. ACM Trans. Graphics (Proceedings of SIGGRAPH) 33, 4 (2014).
    43. Eric P. Lafortune and Yves D. Willems. 1995. A 5D tree to reduce the variance of Monte Carlo ray tracing. In Rendering Techniques. 11–20.
    44. NJ McCormick and I. Kuscer. 1973. Singular eigenfunction expansions in neutron transport theory. Advan. Nucl. Sci. Technol. 7 (1973), 181–282.
    45. Johannes Meng, Johannes Hanika, and Carsten Dachsbacher. 2016. Improving the Dwivedi sampling scheme. Comput. Graphics Forum 35, 4 (2016), 037–044.
    46. L.W.G. Morgan and D. Kotlyar. 2015. Weighted-delta-tracking for Monte Carlo particle transport. Ann. Nucl. Energy 85, C (2015), 1184–1188.
    47. Thomas Müller, Markus Gross, and Jan Novák. 2017. Practical path guiding for efficient light-transport simulation. Computer Graphics Forum 36, 4 (2017), 91–100.
    48. Thomas Müller, Brian McWilliams, Fabrice Rousselle, Markus Gross, and Jan Novák. 2018. Neural importance sampling. CoRR abs/1808.03856 (2018). arxiv:1808.03856 http://arxiv.org/abs/1808.03856.
    49. R. F. Murray and Y. Morgenstern. 2010. Cue combination on the circle and the sphere. J. Vision 10, 11 (2010), 15–15.
    50. Jan Novák, Iliyan Georgiev, Johannes Hanika, and Wojciech Jarosz. 2018. Monte Carlo methods for volumetric light transport simulation. Comput. Graphics Forum (Proceedings of Eurographics – State of the Art Reports) 37, 2 (2018).
    51. Jan Novák, Derek Nowrouzezahrai, Carsten Dachsbacher, and Wojciech Jarosz. 2012b. Progressive virtual beam lights. Comput. Graphics Forum (Proceedings of EGSR) 31, 4 (2012), 1407–1413.
    52. Jan Novák, Derek Nowrouzezahrai, Carsten Dachsbacher, and Wojciech Jarosz. 2012a. Virtual ray lights for rendering scenes with participating media. ACM Trans. Graphics (Proceedings of SIGGRAPH) 31, 4 (2012), 60:1–60:11.
    53. Jan Novák, Andrew Selle, and Wojciech Jarosz. 2014. Residual ratio tracking for estimating attenuation in participating media. ACM Trans. Graphics (Proceedings of SIGGRAPH Asia) 33, 6 (2014), 179:1–179:11.
    54. Vincent Pegoraro, Ingo Wald, and Steven G. Parker. 2008. Sequential Monte Carlo integration in low-anisotropy participating media. In Proceedings of the Eurographics Conference on Rendering. 1097–1104.
    55. Matt Pharr, Wenzel Jakob, and Greg Humphreys. 2016. Physically Based Rendering: From Theory to Implementation (3rd ed.). Morgan Kaufmann.
    56. Mathias Raab, Daniel Seibert, and Alexander Keller. 2006. Unbiased global illumination with participating media. In Proc. Monte Carlo and Quasi-Monte Carlo Methods. 591–606.
    57. Zhong Ren, Kun Zhou, Stephen Lin, and Baining Guo. 2008. Gradient-based Interpolation and Sampling for Real-time Rendering of Inhomogeneous, Single-scattering Media. Technical Report MSR-TR-2008-51. Microsoft Research.
    58. Fabrice Rousselle, Claude Knaus, and Matthias Zwicker. 2011. Adaptive sampling and reconstruction using greedy error minimization. In Proceedings of the 2011 SIGGRAPH Asia Conference. 159:1–159:12.
    59. M. Šik and J. Jaroslav Křivánek. 2018. Survey of Markov chain Monte Carlo methods in light transport simulation. IEEE Trans. Visual. Comput. Graphics 1–1.
    60. Florian Simon, Johannes Hanika, Tobias Zirr, and Carsten Dachsbacher. 2017. Line integration for rendering heterogeneous emissive volumes. Comput. Graphics Forum (Proc. of EGSR) 36, 4 (2017), 101–110.
    61. Florian Simon, Alisa Jung, Johannes Hanika, and Carsten Dachsbacher. 2018. Selective guided sampling with complete light transport paths. ACM Trans. Graphics (Proceedings of SIGGRAPH Asia) 37, 6 (2018), 223:1–223:14.
    62. Jerome Spanier and Ely Meyer Gelbard. 1969. Monte Carlo Principles and Neutron Transport Problems. Addison-Wesley.
    63. László Szirmay-Kalos. 2005. Go with the winners strategy in path tracing. J. WSCG 13, 1–3 (2005), 49–56.
    64. László Szirmay-Kalos, Iliyan Georgiev, Milán Magdics, Balázs Molnár, and Dávid Légrády. 2017. Unbiased light transport estimators for inhomogeneous participating media. Comput. Graphics Forum 36, 2 (2017), 9–19.
    65. László Szirmay-Kalos, Balázs Tóth, and Milan Magdics. 2011. Free path sampling in high resolution inhomogeneous participating media. Comput. Graphics Forum 30 (2011), 85–97.
    66. Eric Veach. 1997. Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. Dissertation. Stanford University.
    67. Petr Vévoda, Ivo Kondapaneni, and Jaroslav Křivánek. 2018. Bayesian online regression for adaptive direct illumination sampling. ACM Trans. Graphics (Proc. of SIGGRAPH 2018) 37, 4 (2018), 125:1–125:12.
    68. P. von Radziewsky, T. Kroes, M. Eisemann, and E. Eisemann. 2017. Efficient stochastic rendering of static and animated volumes using visibility sweeps. IEEE Trans. Visual. Comput. Graphics 23, 9 (2017), 2069–2081.
    69. 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. Graphics 33, 4 (2014), 101:1–101:11.
    70. Jiří Vorba and Jaroslav Křivánek. 2016. Adjoint-driven Russian roulette and splitting in light transport simulation. ACM Trans. Graphics 35, 4 (2016).
    71. Adolf N. Witt. 1977. Multiple scattering in reflection nebulae. Astrophys. J. Suppl. Ser. 35 (1977).
    72. E. Woodcock, T. Murphy, P. Hemmings, and S. Longworth. 1965. Techniques used in the GEM code for Monte Carlo neutronics calculations in reactors and other systems of complex geometry. In Proc. Conf. Applications of Computing Methods to Reactor Problems, Vol. 557.
    73. Yonghao Yue, Kei Iwasaki, Bing-Yu Chen, Yoshinori Dobashi, and Tomoyuki Nishita. 2010. Unbiased, adaptive stochastic sampling for rendering inhomogeneous participating media. ACM Trans. Graphics (Proc. SIGGRAPH) 29 (2010), 177:1–177:8.
    74. Quan Zheng and Matthias Zwicker. 2018. Learning to importance sample in primary sample space. CoRR abs/1808.07840 (2018). arxiv:1808.07840 http://arxiv.org/abs/1808.07840.

ACM Digital Library Publication:


Overview Page: