“A forward scattering dipole model from a functional integral approximation” by Kutz, Habel, Li and Novák
Conference:
Type(s):
Title:
- A forward scattering dipole model from a functional integral approximation
Session/Category Title: Rendering Volumes
Presenter(s)/Author(s):
Moderator(s):
Abstract:
Rendering translucent materials with physically based Monte Carlo methods tends to be computationally expensive due to the long chains of volumetric scattering interactions. In the case of strongly forward scattering materials, the problem gets compounded since each scattering interaction becomes highly anisotropic and near-specular. Various well-known approaches try to avoid the resulting sampling problem through analytical approximations based on diffusion theory. Although these methods are computationally efficient, their assumption of diffusive, isotropic scattering can lead to considerable errors when rendering forward scattering materials, even in the optically dense limit. In this paper, we present an analytical subsurface scattering model, derived with the explicit assumption of strong forward scattering. Our model is not based on diffusion theory, but follows from a connection that we identified between the functional integral formulation of radiative transport and the partition function of a worm-like chain in polymer physics. Our resulting model does not need a separate Monte Carlo solution for unscattered or single-scattered contributions, nor does it require ad-hoc regularization procedures. It has a single singularity by design, corresponding to the initial unscattered propagation, which can be accounted for by the extensive analytical importance sampling scheme that we provide. Our model captures the full behaviour of forward scattering media, ranging from unscattered straight-line propagation to the fully diffusive limit. Moreover, we derive a novel forward scattering BRDF as limiting case of our subsurface scattering model, which can be used in a level of detail hierarchy. We show how our model can be integrated in existing Monte Carlo rendering algorithms, and make comparisons to previous approaches.
References:
1. R. Aronson. 1995. Boundary conditions for diffusion of light. JOSA A 12, 11 (1995). Google ScholarCross Ref
2. M. Ashikhmin, S. Premože, R. Ramamoorthi, and S. K. Nayar. 2004. Blurring of Light Due to Multiple Scattering by the Medium: A Path Integral Approach. Technical Report CUCS-017–04. Columbia University.Google Scholar
3. G. I. Bell and S. Glasstone. 1970. Nuclear Reactor Theory. Van Nostrand Reinhold Co.Google Scholar
4. E. Cerezo, F. Pérez, X. Pueyo, F. J. Seron, and F. X. Sillion. 2005. A Survey on Participating Media Rendering Techniques. Vis. Comput. 21, 5 (2005). Google ScholarDigital Library
5. S. Chandrasekhar. 1943. Stochastic Problems in Physics and Astronomy. Reviews of modern physics 15, 1 (1943). Google ScholarCross Ref
6. E. d’Eon. 2014. A Dual-beam 3D Searchlight BSSRDF. In ACM SIGGRAPH 2014 Talks (SIGGRAPH ’14). ACM, Article 65.Google Scholar
7. E. d’Eon and G. Irving. 2011. A Quantized-diffusion Model for Rendering Translucent Materials. ACM Trans. Graph. 30, 4, Article 56 (2011). Google ScholarDigital Library
8. C. Donner and H. W. Jensen. 2005. Light Diffusion in Multi-layered Translucent Materials. ACM Trans. Graph. 24, 3 (2005). Google ScholarDigital Library
9. C. Donner and H. W. Jensen. 2006. A Spectral BSSRDF for Shading Human Skin. In Proceedings of the 17th Eurographics Conference on Rendering Techniques (EGSR ’06). Eurographics Association.Google Scholar
10. C. Donner, J. Lawrence, R. Ramamoorthi, T. Hachisuka, H. W. Jensen, and S. Nayar. 2009. An Empirical BSSRDF Model. ACM Trans. Graph. 28, 3, Article 30 (2009). Google ScholarDigital Library
11. O. Elek, T. Ritschel, and H.-P. Seidel. 2013. Real-Time Screen-Space Scattering in Homogeneous Environments. IEEE Computer Graphics and Applications 33, 3 (2013). Google ScholarDigital Library
12. K. F. Freed. 1972. Functional Integrals and Polymer Statistics. Advances in Chemical Physics 22 (1972). Google ScholarCross Ref
13. J. R. Frisvad, T. Hachisuka, and T. K. Kjeldsen. 2014. Directional Dipole Model for Subsurface Scattering. ACM Trans. Graph. 34, 1, Article 5 (2014). Google ScholarDigital Library
14. I. Georgiev, J. Křivánek, T Hachisuka, D. Nowrouzezahrai, and W. Jarosz. 2013. Joint Importance Sampling of Low-Order Volumetric Scattering. ACM Trans. Graph. (Proceedings of SIGGRAPH Asia) 32, 6 (2013). Google ScholarDigital Library
15. I. Gkioulekas, S. Zhao, K. Bala, T. Zickler, and A. Levin. 2013. Inverse Volume Rendering with Material Dictionaries. ACM Trans. Graph. 32, 6, Article 162 (2013). Google ScholarDigital Library
16. R. Habel, P. H. Christensen, and W. Jarosz. 2013. Photon Beam Diffusion: A Hybrid Monte Carlo Method for Subsurface Scattering. In Proceedings of the Eurographics Symposium on Rendering (EGSR ’13). Eurographics Association. Google ScholarDigital Library
17. L. G. Henyey and J. Leonard Greenstein. 1941. Diffuse radiation in the Galaxy. The Astrophysical Journal 93 (1941). Google ScholarCross Ref
18. W. Jakob and S. Marschner. 2012. Manifold Exploration: A Markov Chain Monte Carlo Technique for Rendering Scenes with Difficult Specular Transport. ACM Trans. Graph. 31, 4, Article 58 (2012). Google ScholarDigital Library
19. W. A. Jakob. 2013. Light Transport On Path-Space Manifolds. Ph.D. Dissertation.Google Scholar
20. H. W. Jensen, S. R. Marschner, M. Levoy, and P. Hanrahan. 2001. A Practical Model for Subsurface Light Transport. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’01). ACM. Google ScholarDigital Library
21. M. Kardar. 2007. Statistical Physics of Particles. Cambridge University Press. Google ScholarCross Ref
22. P. Kilgo and J. Tessendorf 2015. Accelerated Path Generation and Visualization for Numerical Integration of Feynman Path Integrals for Radiative Transfer. In Joint International Conference on Mathematics and Computation, Supercomputing in Nuclear Applications and the Monte Carlo Method.Google Scholar
23. J. Křivánek and E. d’Eon. 2014. A Zero-variance-based Sampling Scheme for Monte Carlo Subsurface Scattering. In ACM SIGGRAPH 2014 Talks (SIGGRAPH ’14). ACM, Article 66. Google ScholarDigital Library
24. J. Křivánek, I. Georgiev, T. Hachisuka, P. Vévoda, M. Šik, D. Nowrouzezahrai, and W. Jarosz. 2014. Unifying Points, Beams, and Paths in Volumetric Light Transport Simulation. ACM Trans. Graph. (Proceedings of SIGGRAPH) 33, 4 (2014). Google ScholarDigital Library
25. J. R. Lamarsh. 1975. Introduction to Nuclear Engineering. Addison-Wesley Pub. Co.Google Scholar
26. H. Li, F. Pellacini, and K. E. Torrance. 2005. A Hybrid Monte Carlo Method for Accurate and Efficient Subsurface Scattering. In Proceedings of the Sixteenth Eurographics Conference on Rendering Techniques (EGSR ’05). Eurographics Association.Google ScholarDigital Library
27. A. Liemert and A. Kienle. 2013. Exact and efficient solution of the radiative transport equation for the semi-infinite medium. Scientific Reports 3, 2018 (2013). Google ScholarCross Ref
28. M. Machida. 2016. How to Construct Three-Dimensional Transport Theory Using Rotated Reference Frames. Journal of Computational and Theoretical Transport 45, 7 (2016). Google ScholarCross Ref
29. V. A Markel. 2004. Modified spherical harmonics method for solving the radiative transport equation. Waves in Random Media 14, 1 (2004). Google ScholarCross Ref
30. F. Martelli, A. Sassaroli, A. Pifferi, A. Torricelli, L. Spinelli, and G. Zaccanti. 2007. Heuristic Green’s function of the time dependent radiative transfer equation for a semi-infinite medium. Optics Express 15, 26 (2007). Google ScholarCross Ref
31. J. Meng, J. Hanika, and C. Dachsbacher. 2016. Improving the Dwivedi Sampling Scheme. Computer Graphics Forum 35, 4 (2016). Google ScholarDigital Library
32. T. Mertens, J. Kautz, P. Bekaert, F. Van Reeth, and H.-P. Seidel. 2005. Efficient rendering of local subsurface scattering. In Computer Graphics Forum, Vol. 24. Wiley Online Library. Google ScholarCross Ref
33. M. F. Modest. 2013. Radiative Heat Transfer. Academic press.Google Scholar
34. S. G. Narasimhan, M. Gupta, C. Donner, R. Ramamoorthi, S. K. Nayar, and H. W. Jensen. 2006. Acquiring Scattering Properties of Participating Media by Dilution. ACM Trans. Graph. 25, 3 (2006). Google ScholarDigital Library
35. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis. 1977. Geometrical Considerations and Nomenclature for Reflectance. U.S. Government Printing Office. Google ScholarCross Ref
36. J. C. J. Paasschens. 1997. Solution of the time-dependent Boltzmann equation. Physical Review E 56, 1 (1997). Google ScholarCross Ref
37. M. S. Patterson, B. Chance, and B. C. Wilson. 1989. Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties. Applied Optics 28, 12 (1989). Google ScholarCross Ref
38. S. Premože, M. Ashikhmin, and P. Shirley. 2003. Path Integration for Light Transport in Volumes. In Proceedings of the 14th Eurographics Workshop on Rendering (EGRW ’03). Eurographics Association.Google Scholar
39. S. Premože, M. Ashikhmin, J. Tessendorf, R. Ramamoorthi, and S. Nayar. 2004. Practical Rendering of Multiple Scattering Effects in Participating Media. In Proceedings of the Fifteenth Eurographics Conference on Rendering Techniques (EGSR’04). Eurographics Association.Google Scholar
40. A. J. Spakowitz and Z.-G. Wang. 2005. End-to-end distance vector distribution with fixed end orientations for the wormlike chain model. Physical Review E 72 (2005). Issue 4.Google Scholar
41. J. Tessendorf. 1987. Radiative transfer as a sum over paths. Physical Review A 35 (1987). Issue 2.Google Scholar
42. J. Tessendorf. 1989. Time-dependent radiative transfer and pulse evolution. JOSA A 6, 2 (1989). Google ScholarCross Ref
43. J. Tessendorf. 1990. Radiative transfer on curved surfaces. J. Math. Phys. 31, 4 (1990). Google ScholarCross Ref
44. J. Tessendorf. 1991. Underwater solar light field: analytical model from a WKB evaluation, In Underwater Imaging, Photography, and Visibility. Proc. SPIE 1537 (1991).Google Scholar
45. J. Tessendorf. 2003. Concepts for Volume Rendering. Technical Report. Rhythm & Hues Studios.Google Scholar
46. J. Tessendorf. 2009. Numerical integration of the Feynman Path Integral for radiative transport (International Conference on Advances in Mathematics, Computational Methods, and Reactor Physics). American Nuclear Society.Google Scholar
47. J. Tessendorf and D. Wasson. 1994. 3D Cloud Scene Simulator V2 Algorithm for Scattering. Technical Report. Clemson University.Google Scholar
48. E. Veach. 1998. Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. Dissertation.Google Scholar
49. T. Vo-Dinh. 2003. Biomedical photonics handbook. CRC Press. Google ScholarCross Ref
50. J. Vorba and J. Křivánek. 2016. Adjoint-driven Russian Roulette and Splitting in Light Transport Simulation. ACM Trans. Graph. 35, 4, Article 42 (2016). Google ScholarDigital Library
51. P. Weber, J. Hanika, and C. Dachsbacher. 2017. Multiple Vertex Next Event Estimation for Lighting in dense, forward-scattering Media. In Proceedings of the EUROGRAPHICS 2017 Conference. Google ScholarDigital Library
52. J. Wenzel. 2010. Mitsuba Physically Based Renderer. (2010). http://www.mitsuba-renderer.org/.Google Scholar
53. R. R. Wilcox. 2005. Introduction to Robust Estimation and Hypothesis Testing (2nd ed ed.). Academic Press.Google Scholar
54. R. G. Winkler, P. Reineker, and L. Harnau. 1994. Models and equilibrium properties of stiff molecular chains. The Journal of Chemical Physics 101, 9 (1994). Google ScholarCross Ref
55. D. R. Wyman, M. S. Patterson, and B. C. Wilson. 1989. Similarity Relations for Anisotropic Scattering in Monte Carlo Simulations of Deeply Penetrating Neutral Particles. J. Comput. Phys. 81, 1 (1989). Google ScholarDigital Library
56. A. Zee. 2003. Quantum Field Theory in a Nutshell. Princeton University Press.Google Scholar
57. S. Zhao, R. Ramamoorthi, and K. Bala. 2014. High-order Similarity Relations in Radiative Transfer. ACM Trans. Graph. 33, 4, Article 104 (2014). Google ScholarDigital Library
