Hierarchical russian roulette for vertex connections

Abstract

While bidirectional path tracing is a well-established light transport algorithm, many samples are required to obtain high-quality results for specular-diffuse-glossy or glossy-diffuse-glossy reflections especially when they are highly glossy. To improve the efficiency for such light path configurations, we propose a hierarchical Russian roulette technique for vertex connections. Our technique accelerates a huge number of Russian roulette operations according to an approximate scattering lobe at an eye-subpath vertex for many cached light-subpath vertices. Our method dramatically reduces the number of random number generations needed for Russian roulette by introducing a hierarchical rejection algorithm which assigns random numbers in a top-down fashion. To efficiently reject light vertices in each hierarchy, we also introduce an efficient approximation of anisotropic scattering lobes used for the probability of Russian roulette. Our technique is easy to integrate into some existing bidirectional path tracing-based algorithms which cache light-subpath vertices (e.g., probabilistic connections, and vertex connection and merging). In addition, unlike existing many-light methods, our method does not restrict multiple importance sampling strategies thanks to the simplicity of Russian roulette. Although the proposed technique does not support perfectly specular surfaces, it significantly improves the efficiency for caustics reflected on extremely glossy surfaces in an unbiased fashion.

References

1. J. Arvo and D. Kirk. 1990. Particle Transport and Image Synthesis. SIGGRAPH Comput. Graph. 24, 4 (1990), 63--66.
2. R. L. Cook and K. E. Torrance. 1982. A Reflectance Model for Computer Graphics. ACM Trans. Graph. 1, 1 (1982), 7--24.
3. C. Dachsbacher, J. Křivánek, M. Hašan, A. Arbree, B. Walter, and J. Novák. 2014. Scalable Realistic Rendering with Many-Light Methods. Comput. Graph. Forum 33, 1 (2014), 88--104.
4. C. Dachsbacher and M. Stamminger. 2006. Splatting Indirect Illumination. In I3D '06. 93--100.
5. T. Davidovič, J. Křivánek, M. Hašan, and P. Slusallek. 2014. Progressive Light Transport Simulation on the GPU: Survey and Improvements. ACM Trans. Graph. 33, 3 (2014), 29:1--29:19.
6. A. C. Estevez and C. Kulla. 2018. Importance Sampling of Many Lights with Adaptive Tree Splitting. Proc. ACM Comput. Graph. Interact. Tech. 1, 2 (2018), 25:1--25:17.
7. A. C. Estevez and P. Lecocq. 2018. Fast Product Importance Sampling of Environment Maps. In SIGGRAPH '18 Talks. 69:1--69:2.
8. I. Georgiev. 2013. Combining Photon Mapping and Bidirectional Path Tracing. In SIGGRAPH Asia '13 Course: State of the Art in Photon Density Estimation. 15:475--15:515.
9. I. Georgiev, J. Křivánek, T. Davidovič, and P. Slusallek. 2012a. Light Transport Simulation with Vertex Connection and Merging. ACM Trans. Graph. 31, 6 (2012), 192:1--192:10.
10. I. Georgiev, J. Křivánek, S. Popov, and P. Slusallek. 2012b. Importance Caching for Complex Illumination. Comput. Graph. Forum 31, 2pt3 (2012), 701--710.
11. T. Hachisuka, S. Ogaki, and H. W. Jensen. 2008. Progressive Photon Mapping. ACM Trans. Graph. 27, 5 (2008), 130:1--130:8.
12. T. Hachisuka, J. Pantaleoni, and H. W. Jensen. 2012. A Path Space Extension for Robust Light Transport Simulation. ACM Trans. Graph. 31, 6 (2012), 191:1--191:10.
13. S. Herholz, O. Elek, J. Schindel, J. Křivánek, and H. P. A. Lensch. 2018. A Unified Manifold Framework for Efficient BRDF Sampling Based on Parametric Mixture Models. In EGSR '18 EI&I. 41--52.
14. S. Herholz, O. Elek, J. Vorba, H. Lensch, and J. Křivánek. 2016. Product Importance Sampling for Light Transport Path Guiding. Comput. Graph. Forum 35, 4 (2016), 67--77.
15. H. Igehy. 1999. Tracing Ray Differentials. In SIGGRAPH '99. 179--186.
16. J. Jendersie. 2019. Variance Reduction via Footprint Estimation in the Presence of Path Reuse. In Ray Tracing Gems: High-Quality and Real-Time Rendering with DXR and Other APIs. Apress, 557--569.
17. A. Keller. 1997. Instant Radiosity. In SIGGRAPH '97. 49--56.
18. C. Knaus and M. Zwicker. 2011. Progressive Photon Mapping: A Probabilistic Approach. ACM Trans. Graph. 30, 3 (2011), 25:1--25:13.
19. T. Kollig and A. Keller. 2006. Illumination in the Presence of Weak Singularities. In MCQMC '04. 245--257.
20. E. P. Lafortune and Y. D. Willems. 1993. Bi-Directional Path Tracing. In Compugraphics '93. 145--153.
21. O. Olsson, M. Billeter, and E. Persson. 2014. Efficient Real-Time Shading with Many Lights. In SIGGRAPH Asia '14 Courses. 11:1--11:310.
22. B. T. Phong. 1975. Illumination for Computer Generated Pictures. Commun. ACM 18, 6 (1975), 311--317.
23. S. Popov, R. Ramamoorthi, F. Durand, and G. Drettakis. 2015. Probabilistic Connections for Bidirectional Path Tracing. Comput. Graph. Forum 34, 4 (2015), 75--86.
24. J. Stewart. 2015. Compute-Based Tiled Culling. In GPU Pro 6: Advanced Rendering Techniques. A K Peters/CRC Press, 435--458.
25. Y. Tokuyoshi and T. Harada. 2016. Stochastic Light Culling. J. Comput. Graph. Tech. 5, 1 (2016), 35--60.
26. Y. Tokuyoshi and T. Harada. 2017. Stochastic Light Culling for VPLs on GGX Microsurfaces. Comput. Graph. Forum 36, 4 (2017), 55--63.
27. Y. Tokuyoshi and T. Harada. 2018. Bidirectional Path Tracing Using Backward Stochastic Light Culling. In SIGGRAPH '18 Talks. 70:1--70:2.
28. T. S. Trowbridge and K. P. Reitz. 1975. Average Irregularity Representation of a Rough Surface for Ray Reflection. J. Opt. Soc. Am. 65, 5 (1975), 531--536.
29. E. Veach. 1998. Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. Dissertation.
30. E. Veach and L. Guibas. 1994. Bidirectional Estimators for Light Transport. In EGWR '94. 147--162.
31. E. Veach and L. J. Guibas. 1995. Optimally Combining Sampling Techniques for Monte Carlo Rendering. In SIGGRAPH '95. 419--428.
32. J. Vorba, O. Karlik, M. Šik, T. Ritschel, and J. Křivánek. 2014. On-line Learning of Parametric Mixture Models for Light Transport Simulation. ACM Trans. Graph. 33, 4 (2014), 101:1--101:11.
33. B. Walter, A. Arbree, K. Bala, and D. P. Greenberg. 2006. Multidimensional Lightcuts. ACM Trans. Graph. 25, 3 (2006), 1081--1088.
34. B. Walter, S. Fernandez, A. Arbree, K. Bala, M. Donikian, and D. P. Greenberg. 2005. Lightcuts: A Scalable Approach to Illumination. ACM Trans. Graph. 24, 3 (2005), 1098--1107.
35. B. Walter, P. Khungurn, and K. Bala. 2012. Bidirectional Lightcuts. ACM Trans. Graph. 31, 4 (2012), 59:1--59:11.
36. B. Walter, S. R. Marschner, H. Li, and K. E. Torrance. 2007. Microfacet Models for Refraction Through Rough Surfaces. In EGSR '07. 195--206.
37. J. Wang, P. Ren, M. Gong, J. Snyder, and B. Guo. 2009. All-Frequency Rendering of Dynamic, Spatially-Varying Reflectance. ACM Trans. Graph. 28, 5 (2009), 133:1--133:10.
38. K. Xu, W.-L. Sun, Z. Dong, D.-Y. Zhao, R.-D. Wu, and S.-M. Hu. 2013. Anisotropic Spherical Gaussians. ACM Trans. Graph. 32, 6 (2013), 209:1--209:11.
39. T. Zirr, J. Hanika, and C. Dachsbacher. 2018. Reweighting Firefly Samples for Improved Finite-Sample Monte Carlo Estimates. Comput. Graph. Forum 37, 6 (2018), 410--421.

Index Terms

• Computing methodologies

  • Computer graphics

    • Rendering

      • Ray tracing