“Spectral and decomposition tracking for rendering heterogeneous volumes” by Kutz, Habel, Li and Novák
Conference:
Type:
Title:
- Spectral and decomposition tracking for rendering heterogeneous volumes
Session/Category Title: Rendering Volumes
Presenter(s)/Author(s):
Moderator(s):
Abstract:
We present two novel unbiased techniques for sampling free paths in heterogeneous participating media. Our decomposition tracking accelerates free-path construction by splitting the medium into a control component and a residual component and sampling each of them separately. To minimize expensive evaluations of spatially varying collision coefficients, we define the control component to allow constructing free paths in closed form. The residual heterogeneous component is then homogenized by adding a fictitious medium and handled using weighted delta tracking, which removes the need for computing strict bounds of the extinction function. Our second contribution, spectral tracking, enables efficient light transport simulation in chromatic media. We modify free-path distributions to minimize the fluctuation of path throughputs and thereby reduce the estimation variance. To demonstrate the correctness of our algorithms, we derive them directly from the radiative transfer equation by extending the integral formulation of null-collision algorithms recently developed in reactor physics. This mathematical framework, which we thoroughly review, encompasses existing trackers and postulates an entire family of new estimators for solving transport problems; our algorithms are examples of such. We analyze the proposed methods in canonical settings and on production scenes, and compare to the current state of the art in simulating light transport in heterogeneous participating media.
References:
1. J. Amanatides and A. Woo. 1987. A fast voxel traversal algorithm for ray tracing. In Eurographics ’87. 3–10.Google Scholar
2. H. W. Bertini. 1963. Monte Carlo simulations on intranuclear cascades. Technical Report ORNL-3383. Oak Ridge National Laboratory, Oak Ridge, TN, USA. Google ScholarCross Ref
3. F. B. Brown and W. R. Martin. 2003. Direct sampling of Monte Carlo flight paths in media with continuously varying cross-sections. In Proc. of ANS Mathematics & Computation Topical Meeting. 6–11.Google Scholar
4. L. L. Carter, E. D. Cashwell, and W. M. Taylor. 1972. Monte Carlo sampling with continuously varying cross sections along flight paths. Nuclear Science and Engineering 48, 4 (1972), 403–411. Google ScholarCross Ref
5. S. Chandrasekhar. 1960. Radiative transfer. Dover Publications.Google Scholar
6. M. J. Chiang, P. Kutz, and B. Burley. 2016. Practical and controllable subsurface scattering for production path tracing. In ACM SIGGRAPH 2016 Talks (SIGGRAPH ’16). ACM, New York, NY, USA, Article 49, 2 pages. Google ScholarDigital Library
7. W. A. Coleman. 1968. Mathematical verification of a certain Monte Carlo sampling technique and applications of the technique to radiation transport problems. Nuclear Science and Engineering 32, 1 (April 1968), 76–81. Google ScholarCross Ref
8. S. N. Cramer. 1978. Application of the fictitious scattering radiation transport model for deep-penetration Monte Carlo calculations. Nuclear Science and Engineering 65, 2 (1978), 237–253.Google ScholarCross Ref
9. S. R. Dwivedi. 1982. Zero variance biasing schemes for Monte Carlo calculations of neutron and radiation transport problems. Nuclear Science and Engineering 80, 1 (1982), 172–178.Google ScholarCross Ref
10. R. Eckhardt. 1987. Stan Ulam, John von Neumann, and the Monte Carlo Method. Los Alamos Science, Special Issue (1987), 131–137.Google Scholar
11. V. Eymet, D. Poitou, M. Galtier, M. El Hafi, G. Terrée, and R. Fournier. 2013. Null-collision meshless Monte-Carlo—Application to the validation of fast radiative transfer solvers embedded in combustion simulators. Journal of Quantitative Spectroscopy and Radiative Transfer 129 (April 2013), 145–157. Google ScholarCross Ref
12. 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. Journal of Quantitative Spectroscopy and Radiative Transfer 125 (April 2013), 57–68. Google ScholarCross Ref
13. M. Galtier, S. Blanco, J. Dauchet, M. El Hafi, V. Eymet, R. Fournier, M. Roger, C. Spiesser, and G. Terrée. 2016. Radiative transfer and spectroscopic databases: A line-sampling Monte Carlo approach. Journal of Quantitative Spectroscopy and Radiative Transfer 172 (March 2016), 83–97. Google ScholarCross Ref
14. I. Georgiev, J. Křivánek, T. Hachisuka, D. Nowrouzezahrai, and W. Jarosz. 2013. Joint importance sampling of low-order volumetric scattering. ACM TOG (Proc. of SIGGRAPH Asia) 32, 6 (Nov. 2013), 164:1–164:14. Google ScholarDigital Library
15. L. G. Henyey and J. L. Greenstein. 1941. Diffuse radiation in the galaxy. Astrophysical Journal 93 (Jan. 1941), 70–83. Google ScholarCross Ref
16. V. Hubert-Tremblay, L. Archambault, D. Tubic, R. Roy, and L. Beaulieu. 2006. Octree indexing of DICOM images for voxel number reduction and improvement of Monte Carlo simulation computing efficiency. Medical Physics 33, 8 (2006), 2819–2831. Google ScholarCross Ref
17. J. L. W. V. Jensen. 1906. Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Math. 30 (1906), 175–193. Google ScholarCross Ref
18. H. J. Kalli and E. D. Cashwell. 1977. Evaluation of three Monte Carlo estimation schemes for flux at a point. Technical Report LA-6865-MS. Los Alamos Scientific Lab.Google Scholar
19. C. Kulla and M. Fajardo. 2012. Importance sampling techniques for path tracing in participating media. CGF (Proc. of Eurographics Symposium on Rendering) 31, 4 (June 2012), 1519–1528. Google ScholarDigital Library
20. J. Lepp. 2010. Performance of Woodcock delta-tracking in lattice physics applications using the Serpent Monte Carlo reactor physics burnup calculation code. Annals of Nuclear Energy 37, 5 (2010), 715 — 722. Google ScholarCross Ref
21. L. B. Miller. 1967. Monte Carlo analysis of reactivity coefficients in fast reactors; general theory and applications. Technical Report ANL-7307. Argonne National Laboratory, Argonne, IL, USA. Google ScholarCross Ref
22. L. W. G. Morgan and D. Kotlyar. 2015. Weighted-delta-tracking for Monte Carlo particle transport. Annals of Nuclear Energy 85 (2015), 1184–1188. Google ScholarCross Ref
23. K. Museth. 2013. VDB: High-resolution sparse volumes with dynamic topology. ACM TOG 32, 3 (July 2013), 27:1–27:22. Google ScholarDigital Library
24. J. Novák, A. Selle, and W. Jarosz. 2014. Residual ratio tracking for estimating attenuation in participating media. ACM TOG (Proc. of SIGGRAPH Asia) 33, 6 (Nov. 2014), 179:1–179:11. Google ScholarDigital Library
25. K. H. Perlin and E. M. Hoffert. 1989. Hypertexture. Computer Graphics (Proc. of SIGGRAPH) 23, 3 (July 1989), 253–262. Google ScholarDigital Library
26. M. Raab, D. Seibert, and A. Keller. 2008. Unbiased global illumination with participating media. In Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer, 591–606. Google ScholarCross Ref
27. N. Shamsundar, E. M. Sparrow, and R. P. Heinisch. 1973. Monte Carlo radiation solutions—effect of energy partitioning and number of rays. International Journal of Heat and Mass Transfer 16, 3 (1973), 690–694. Google ScholarCross Ref
28. H. R. Skullerud. 1968. The stochastic computer simulation of ion motion in a gas subjected to a constant electric field. Journal of Physics D: Applied Physics 1, 11 (1968), 1567–1568. Google ScholarCross Ref
29. J. Spanier and E. M. Gelbard. 1969. Monte carlo principles and neutron transport problems. Addison-Wesley Pub. Co.Google Scholar
30. N. M. Steen. 1966. A simple method to improve the efficiency of the Σa/Σt estimator in certain Monte Carlo programs. Technical Report WAPD-TM-609. Bettis Atomic Power Lab., Pittsburgh, PA, USA.Google Scholar
31. T. M. Sutton, F. B. Brown, F. G. Bischoff, D. B. MacMillan, C. L. Ellis, J. T. Ward, C. T. Ballinger, D. J. Kelly, and L. Schindler. 1999. The physical models and statistical procedures used in the RACER Monte Carlo Code. Technical Report KAPL-4840. Knolls Atomic Power Laboratory, Niskayuna, NY, USA. Google ScholarCross Ref
32. L. Szirmay-Kalos, B. Tóth, and M. Magdics. 2011. Free path sampling in high resolution inhomogeneous participating media. Computer Graphics Forum 30, 1 (2011), 85–97. Google ScholarCross Ref
33. E. Veach. 1997. Robust Monte Carlo methods for light transport simulation. Ph.D. Dissertation. Stanford University, Stanford, CA, USA.Google Scholar
34. J. von Neumann. 1951. Various techniques used in connection with random digits. Journal of Research of the National Bureau of Standards, Appl. Math. Series 12 (1951), 36–38.Google Scholar
35. A. Wilkie, S. Nawaz, M. Droske, A. Weidlich, and J. Hanika. 2014. Hero wavelength spectral sampling. CGF (Proc. of Eurographics Symposium on Rendering) 33, 4 (June 2014), 123–131. Google ScholarDigital Library
36. E. R. Woodcock, T. Murphy, P. J. Hemmings, and T. C. Longworth. 1965. Techniques used in the GEM code for Monte Carlo neutronics calculations in reactors and other systems of complex geometry. In Applications of Computing Methods to Reactor Problems. Argonne National Laboratory.Google Scholar
37. Y. Yue, K. Iwasaki, B. Chen, Y. Dobashi, and T. Nishita. 2010. Unbiased, adaptive stochastic sampling for rendering inhomogeneous participating media. ACM TOG (Proc. of SIGGRAPH Asia) 29, 6 (Dec. 2010), 177:1–177:8. Google ScholarDigital Library
38. Y. Yue, K. Iwasaki, B. Chen, Y. Dobashi, and T. Nishita. 2011. Toward optimal space partitioning for unbiased, adaptive free path sampling of inhomogeneous participating media. CGF (Proc. of Pacific Graphics) 30, 7 (2011), 1911–1919. Google ScholarCross Ref
39. C. D. Zerby, R. B. Curtis, and H. W. Bertini. 1961. The relativistic doppler problem. Technical Report ORNL-61-7-20. Oak Ridge National Laboratory, Oak Ridge, TN, USA. Google ScholarCross Ref
