“Manifold exploration: a Markov Chain Monte Carlo technique for rendering scenes with difficult specular transport” by Jakob and Marschner

It is a long-standing problem in unbiased Monte Carlo methods for rendering that certain difficult types of light transport paths, particularly those involving viewing and illumination along paths containing specular or glossy surfaces, cause unusably slow convergence. In this paper we introduce Manifold Exploration, a new way of handling specular paths in rendering. It is based on the idea that sets of paths contributing to the image naturally form manifolds in path space, which can be explored locally by a simple equation-solving iteration. This paper shows how to formulate and solve the required equations using only geometric information that is already generally available in ray tracing systems, and how to use this method in in two different Markov Chain Monte Carlo frameworks to accurately compute illumination from general families of paths. The resulting rendering algorithms handle specular, near-specular, glossy, and diffuse surface interactions as well as isotropic or highly anisotropic volume scattering interactions, all using the same fundamental algorithm. An implementation is demonstrated on a range of challenging scenes and evaluated against previous methods.

1. Chen, M., and Arvo, J. 2000. Perturbation methods for interactive specular reflections. IEEE Trans. Vis. and Comp. Graph. 6, 3 (July/Sept.), 253–264. Google ScholarDigital Library
2. Chen, M., and Arvo, J. 2000. Theory and application of specular path perturbation. ACM Trans. Graph. 19, 4 (Oct.), 246–278. Google ScholarDigital Library
3. Chen, J., Wang, B., and Yong, J.-H. 2011. Improved stochastic progressive photon mapping with metropolis sampling. Computer Graphics Forum 30, 4, 1205–1213. Google ScholarDigital Library
4. Cline, D., Talbot, J., and Egbert, P. 2005. Energy redistribution path tracing. ACM Trans. Graph. 24, 3 (Aug.), 1186–1195. Google ScholarDigital Library
5. Cook, R. L., Porter, T., and Carpenter, L. 1984. Distributed ray tracing. In Computer Graphics (Proceedings of SIGGRAPH 84), 137–145. Google ScholarDigital Library
6. Goral, C. M., Torrance, K. E., Greenberg, D. P., and Battaile, B. 1984. Modeling the interaction of light between diffuse surfaces. In Computer Graphics (Proceedings of SIGGRAPH 84), 213–222. Google ScholarDigital Library
7. Hachisuka, T., and Jensen, H. W. 2009. Stochastic progressive photon mapping. ACM Trans. Graph. 28, 5 (Dec.). Google ScholarDigital Library
8. Hachisuka, T., and Jensen, H. W. 2011. Robust adaptive photon tracing using photon path visibility. ACM Trans. Graph. 30, 5 (Oct.), 114:1–114:11. Google ScholarDigital Library
9. Hastings, W. K. 1970. Monte carlo sampling methods using markov chains and their applications. Biometrika 57, 1, 97–109.Google ScholarCross Ref
10. Heckbert, P. S. 1990. Adaptive radiosity textures for bidirectional ray tracing. In Computer Graphics (Proceedings of SIGGRAPH 90), 145–154. Google ScholarDigital Library
11. Igehy, H. 1999. Tracing ray differentials. In Computer Graphics (Proceedings of SIGGRAPH 99), 179–186. Google ScholarDigital Library
12. Jakob, W., 2010. Mitsuba renderer. http://www.mitsubarenderer.org.Google Scholar
13. Jarosz, W., Zwicker, M., and Jensen, H. W. 2008. The beam radiance estimate for volumetric photon mapping. Computer Graphics Forum 27, 2 (Apr.), 557–566.Google ScholarCross Ref
14. Jensen, H. W., and Christensen, P. H. 1998. Efficient simulation of light transport in scenes with participating media using photon maps. In Computer Graphics (Proceedings of SIGGRAPH 98), 311–320. Google ScholarDigital Library
15. Jensen, H. W. 1996. Global illumination using photon maps. In Eurographics Rendering Workshop 1996, 21–30. Google ScholarDigital Library
16. Kajiya, J. T. 1986. The rendering equation. In Computer Graphics (Proceedings of SIGGRAPH 86), 143–150. Google ScholarDigital Library
17. Kelemen, C., Szirmay-Kalos, L., Antal, G., and Csonka, F. 2002. A simple and robust mutation strategy for the metropolis light transport algorithm. Computer Graphics Forum 21, 3, 531–540.Google ScholarCross Ref
18. Kitaoka, S., Kitamura, Y., and Kishino, F. 2009. Replica exchange light transport. Computer Graphics Forum 28, 8 (Dec.), 2330–2342.Google ScholarCross Ref
19. Lafortune, E. P., and Willems, Y. D. 1993. Bi-directional path tracing. In Proceedings of Compugraphics 93.Google Scholar
20. Lai, Y.-C., Fan, S. H., Chenney, S., and Dyer, C. 2007. Photorealistic image rendering with population monte carlo energy redistribution. In Rendering Techniques 2007: 18th Eurographics Workshop on Rendering, 287–296. Google ScholarDigital Library
21. Liu, J. S. 2001. Monte Carlo strategies in scientific computing. Springer. Google ScholarDigital Library
22. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. 1953. Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 6.Google ScholarCross Ref
23. Mitchell, D. P., and Hanrahan, P. 1992. Illumination from curved reflectors. In Computer Graphics (Proceedings of SIGGRAPH 92), 283–291. Google ScholarDigital Library
24. Pauly, M., Kollig, T., and Keller, A. 2000. Metropolis light transport for participating media. In Rendering Techniques 2000: 11th Eurographics Workshop on Rendering, 11–22. Google ScholarDigital Library
25. Premoze, S., Ashikhmin, M., and Shirley, P. 2003. Path integration for light transport in volumes. In Eurographics Symposium on Rendering: 14th Eurographics Workshop on Rendering. Google ScholarDigital Library
26. Segovia, B., Iehl, J., and Péroche, B. 2007. Metropolis instant radiosity. Computer Graphics Forum 26, 3 (Sept.), 425–434.Google ScholarCross Ref
27. Shirley, P. S., Wade, B., Hubbard, P., Zareski, D., Walter, B., and Greenberg, D. P. 1995. Global illumination via density estimation. In Eurographics Rendering Workshop 1995, 219–231.Google Scholar
28. Sillion, F. X., and Puech, C. 1989. A general two-pass method integrating specular and diffuse reflection. In Computer Graphics (Proceedings of SIGGRAPH 89), 335–344. Google ScholarDigital Library
29. Spivak, M. 1965. Calculus on Manifolds. Addison-Wesley.Google Scholar
30. Veach, E., and Guibas, L. 1994. Bidirectional estimators for light transport. In Fifth Eurographics Workshop on Rendering.Google Scholar
31. Veach, E., and Guibas, L. J. 1997. Metropolis light transport. In Computer Graphics (Proceedings of SIGGRAPH 97), 65–76. Google ScholarDigital Library
32. Veach, E. 1997. Robust Monte Carlo Methods for Light Transport Simulation. PhD thesis, Stanford University. Google ScholarDigital Library
33. Walter, B., Hubbard, P. M., Shirley, P. S., and Greenberg, D. F. 1997. Global illumination using local linear density estimation. ACM Trans. Graph. 16, 3 (July), 217–259. Google ScholarDigital Library
34. Walter, B., Marschner, S. R., Li, H., and Torrance, K. E. 2007. Microfacet models for refraction through rough surfaces. In Rendering Techniques 2007: 18th Eurographics Workshop on Rendering, 195–206. Google ScholarDigital Library
35. Walter, B., Zhao, S., Holzschuch, N., and Bala, K. 2009. Single scattering in refractive media with triangle mesh boundaries. ACM Trans. Graph. 28, 3 (July), 92:1–92:8. Google ScholarDigital Library
36. Whitted, T. 1980. An improved illumination model for shaded display. Communications of the ACM 23, 6 (June), 343–349. Google ScholarDigital Library