“The natural-constraint representation of the path space for efficient light transport simulation” by Kaplanyan, Hanika and Dachsbacher

  • ©Anton S. Kaplanyan, Johannes Hanika, and Carsten Dachsbacher

Conference:


Type:


Title:

    The natural-constraint representation of the path space for efficient light transport simulation

Session/Category Title: Light Transport


Presenter(s)/Author(s):


Moderator(s):



Abstract:


    The path integral formulation of light transport is the basis for (Markov chain) Monte Carlo global illumination methods. In this paper we present half vector space light transport (HSLT), a novel approach to sampling and integrating light transport paths on surfaces. The key is a partitioning of the path space into subspaces in which a path is represented by its start and end point constraints and a sequence of generalized half vectors. We show that this representation has several benefits. It enables importance sampling of all interactions along paths in between two endpoints. Based on this, we propose a new mutation strategy, to be used with Markov chain Monte Carlo methods such as Metropolis light transport (MLT), which is well-suited for all types of surface transport paths (diffuse/glossy/specular interaction). One important characteristic of our approach is that the Fourier-domain properties of the path integral can be easily estimated. These can be used to achieve optimal correlation of the samples due to well-chosen mutation step sizes, leading to more efficient exploration of light transport features. We also propose a novel approach to control stratification in MLT with our mutation strategy.

References:


    1. Arvo, J. 1986. Backward ray tracing. In SIGGRAPH Course Notes, 259–263.Google Scholar
    2. Ashikhmin, M., and Shirley, P. 2000. An anisotropic Phong BRDF model. Journal of Graphics Tools 5, 2, 25–32. Google ScholarDigital Library
    3. Bremaud, P. 1999. Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues. Springer. ISBN 0-387-98509-3.Google ScholarCross Ref
    4. Cappé, O., Guillin, A., Marin, J.-M., and Robert, C. P. 2004. Population Monte Carlo. Journal of Computational and Graphical Statistics 13, 4.Google ScholarCross Ref
    5. 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
    6. Cline, D., Talbot, J., and Egbert, P. K. 2005. Energy redistribution path tracing. ACM Trans. on Graphics (Proc. SIGGRAPH) 24, 3, 1186–1195. Google ScholarDigital Library
    7. Dachsbacher, C., Krivánek, J., Hasan, M., Arbree, A., Walter, B., and Novák, J. 2013. Scalable realistic rendering with many-light methods. Computer Graphics Forum DOI: 10.1111/cgf.12256. Google ScholarDigital Library
    8. Fan, S., Chenney, S., and chi Lai, Y. 2005. Metropolis photon sampling with optional user guidance. In Proc. Eurographics Symposium on Rendering, 127–138. Google ScholarDigital Library
    9. Georgiev, I., Krivanek, J., Davidovic, T., and Slusallek, P. 2012. Light transport simulation with vertex connection and merging. ACM Trans. on Graphics (Proc. SIGGRAPH Asia) 31, 6, 192:1–192:10. Google ScholarDigital Library
    10. Hachisuka, T., and Jensen, H. W. 2011. Robust adaptive photon tracing using photon path visibility. ACM Trans. on Graphics 30, 5, 114:1–114:11. Google ScholarDigital Library
    11. Hachisuka, T., Ogaki, S., and Jensen, H. W. 2008. Progressive photon mapping. ACM Trans. on Graphics (Proc. SIGGRAPH Asia) 27, 5, 130:1–130:8. Google ScholarDigital Library
    12. Hachisuka, T., Pantaleoni, J., and Jensen, H. W. 2012. A path space extension for robust light transport simulation. ACM Trans. on Graphics (Proc. SIGGRAPH Asia) 31, 6, 191:1–191:10. Google ScholarDigital Library
    13. Hanika, J. 2011. Spectral light transport simulation using a precision-based ray tracing architecture. PhD thesis, Ulm University. VTS-ID/7539.Google Scholar
    14. Hastings, W. K. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 1, 97–109.Google ScholarCross Ref
    15. Igehy, H. 1999. Tracing ray differentials. Proc. SIGGRAPH, 179–186. Google ScholarDigital Library
    16. Jakob, W., and Marschner, S. 2012. Manifold exploration: a Markov chain Monte Carlo technique for rendering scenes with difficult specular transport. ACM Trans. on Graphics (Proc. SIGGRAPH) 31, 4, 58:1–58:13. Google ScholarDigital Library
    17. Jakob, W., 2010. Mitsuba renderer. http://www.mitsuba-renderer.org.Google Scholar
    18. Jakob, W. 2013. Light transport on path-space manifolds. PhD thesis, Cornell University.Google Scholar
    19. Jensen, H. W. 1996. Global illumination using photon maps. In Proc. Eurographics Workshop on Rendering, 21–30. Google ScholarDigital Library
    20. Kajiya, J. T. 1986. The rendering equation. Computer Graphics (Proc. SIGGRAPH), 143–150. Google ScholarDigital Library
    21. Kaplanyan, A. S., and Dachsbacher, C. 2013. Adaptive progressive photon mapping. ACM Trans. on Graphics 32, 2, 16:1–16:13. Google ScholarDigital Library
    22. Kaplanyan, A. S., and Dachsbacher, C. 2013. Path space regularization for holistic and robust light transport. Computer Graphics Forum (Proc. of Eurographics) 32, 2, 63–72.Google ScholarCross Ref
    23. 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
    24. Keller, A. 1997. Instant radiosity. Proc. SIGGRAPH, 49–56. Google ScholarDigital Library
    25. Knaus, C., and Zwicker, M. 2011. Progressive photon mapping: A probabilistic approach. ACM Trans. on Graphics 30, 3, 25:1–25:13. Google ScholarDigital Library
    26. Krivánek, J., Georgiev, I., Kaplanyan, A., and Canada, J. 2013. Recent advances in light transport simulation: Theory and practice. In ACM SIGGRAPH Courses. Google ScholarDigital Library
    27. Lafortune, E. P., and Willems, Y. D. 1993. Bi-directional path tracing. In Proc. of COMPUGRAPHICS, 145–153.Google Scholar
    28. Lehtinen, J., Karras, T., Laine, S., Aittala, M., Durand, F., and Aila, T. 2013. Gradient-domain Metropolis light transport. ACM Trans. on Graphics (Proc. SIGGRAPH) 32, 4, 95:1–95:12. Google ScholarDigital Library
    29. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. 1953. Equation of state calculations by fast computing machines. The Journal of Chemical Physics 21, 6, 1087–1092.Google ScholarCross Ref
    30. Rusinkiewicz, S. 1998. A new change of variables for efficient BRDF representation. In Proc. Eurographics Workshop on Rendering, 11–22.Google ScholarCross Ref
    31. Shinya, M., Takahashi, T., and Naito, S. 1987. Principles and applications of pencil tracing. Computer Graphics (Proc. SIGGRAPH), 45–54. Google ScholarDigital Library
    32. Shirley, P., Wade, B., Hubbard, P. M., Zareski, D., Walter, B., and Greenberg, D. P. 1995. Global illumination via density-estimation. In Proc. Eurographics Workshop on Rendering, 219–230.Google Scholar
    33. Sommerfeld, A., and Runge, J. 1911. Anwendung der Vektorrechnung auf die Grundlagen der geometrischen Optik. Annalen der Physik 340, 277–298.Google ScholarCross Ref
    34. Spivak, M. 1965. Calculus on manifolds. Addison-Wesley. ISBN 978-0-81-334612-0.Google Scholar
    35. Subr, K., and Kautz, J. 2013. Fourier analysis of stochastic sampling strategies for assessing bias and variance in integration. ACM Trans. on Graphics (Proc. SIGGRAPH) 32, 4, 128:1–128:12. Google ScholarDigital Library
    36. Veach, E., and Guibas, L. 1994. Bidirectional estimators for light transport. In Proc. Eurographics Workshop on Rendering, 147–162.Google Scholar
    37. Veach, E., and Guibas, L. J. 1997. Metropolis light transport. Proc. SIGGRAPH, 65–76. Google ScholarDigital Library
    38. Veach, E. 1998. Robust Monte Carlo methods for light transport simulation. PhD thesis, Stanford University. AAI9837162. Google ScholarDigital Library
    39. Walter, B., Fernandez, S., Arbree, A., Bala, K., Donikian, M., and Greenberg, D. P. 2005. Lightcuts: a scalable approach to illumination. ACM Trans. on Graphics (Proc. SIGGRAPH) 24, 3, 1098–1107. Google ScholarDigital Library
    40. Walter, B., Marschner, S., Li, H., and Torrance, K. 2007. Microfacet models for refraction through rough surfaces. In Proc. Eurographics Symposium on Rendering, 195–206. Google ScholarDigital Library
    41. Walter, B., Khungurn, P., and Bala, K. 2012. Bidirectional lightcuts. ACM Trans. on Graphics (Proc. SIGGRAPH) 31, 4, 59:1–59:11. Google ScholarDigital Library


ACM Digital Library Publication: