Adrian Jarabo
Skip Abstract Section
Skip Supplemental Material SectionAbstract
We introduce a non-exponential radiative framework that takes into account the local spatial correlation of scattering particles in a medium. Most previous works in graphics have ignored this, assuming uncorrelated media with a uniform, random local distribution of particles. However, positive and negative correlation lead to slower- and faster-than-exponential attenuation respectively, which cannot be predicted by the Beer-Lambert law. As our results show, this has a major effect on extinction, and thus appearance. From recent advances in neutron transport, we first introduce our Extended Generalized Boltzmann Equation, and develop a general framework for light transport in correlated media. We lift the limitations of the original formulation, including an analysis of the boundary conditions, and present a model suitable for computer graphics, based on optical properties of the media and statistical distributions of scatterers. In addition, we present an analytic expression for transmittance in the case of positive correlation, and show how to incorporate it efficiently into a Monte Carlo renderer. We show results with a wide range of both positive and negative correlation, and demonstrate the differences compared to classic light transport.
Supplemental Material
- Carlos Aliaga, Carlos Castillo, Diego Gutierrez, Miguel A. Otaduy, Jorge Lopez-Moreno, and Adrian Jarabo. 2017. An Appearance Model for Textile Fibers. Computer Graphics Forum (Proc. EGSR 2017) 36, 4 (2017). Google Scholar
Digital Library
- John Amanatides and Andrew Woo. 1987. A fast voxel traversal algorithm for ray tracing. In Eurographics, Vol. 87. 3--10.Google Scholar
- Marco Ament, Christoph Bergmann, and Daniel Weiskopf. 2014. Refractive radiative transfer equation. ACM Trans. Graph. 33, 2 (2014). Google ScholarDigital Library
- James Arvo. 1993. Transfer equations in global illumination. SIGGRAPH '93 Course Notes 2 (1993).Google Scholar
- Howard W Barker, Bruce A Wiellicki, and Lindsay Parker. 1996. A parameterization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds. Part II: Validation using satellite data. Journal of the Atmospheric Sciences 53, 16 (1996).Google Scholar
- Fabien Bellet, Elie Chalopin, Florian Fichot, Estelle Iacona, and Jean Taine. 2009. RDFI determination of anisotropic and scattering dependent radiative conductivity tensors in porous media: Application to rod bundles. International Journal of Heat and Mass Transfer 52, 5 (2009), 1544--1551.Google ScholarCross Ref
- Thomas Camminady, Martin Frank, and Edward W. Larsen. 2017. Nonclassical Particle Transport in Heterogeneous Materials. In International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering.Google Scholar
- Subrahmanyan Chandrasekhar. 1960. Radiative Transfer. Dover.Google Scholar
- WA 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 (1968), 76--81.Google Scholar
- R Coquard and D Baillis. 2006. Radiative properties of dense fibrous medium containing fibers in the geometric limit. Journal of heat transfer 128, 10 (2006), 1022--1030.Google ScholarCross Ref
- Anthony B Davis and Alexander Marshak. 2004. Photon propagation in heterogeneous optical media with spatial correlations: enhanced mean-free-paths and wider-than-exponential free-path distributions. Journal of Quantitative Spectroscopy and Radiative Transfer 84, 1 (2004).Google ScholarCross Ref
- Anthony B Davis, Alexander Marshak, H Gerber, and Warren J Wiscombe. 1999. Horizontal structure of marine boundary layer clouds from centimeter to kilometer scales. Journal of Geophysical Research: Atmospheres 104, D6 (1999).Google ScholarCross Ref
- Anthony B Davis and Mark B Mineev-Weinstein. 2011. Radiation propagation in random media: From positive to negative correlations in high-frequency fluctuations. Journal of Quantitative Spectroscopy and Radiative Transfer 112, 4 (2011).Google ScholarCross Ref
- Anthony B Davis and Feng Xu. 2014. A Generalized Linear Transport Model for Spatially Correlated Stochastic Media. Journal of Computational and Theoretical Transport 43, 1--7 (2014).Google ScholarCross Ref
- Eugene d'Eon. 2014a. Computer graphics and particle transport: our common heritage, recent cross-field parallels and the future of our rendering equation. In Digipro 2014.Google Scholar
- Eugene d'Eon. 2014b. Rigorous asymptotic and moment-preserving diffusion approximations for generalized linear Boltzmann transport in arbitrary dimension. Transport Theory and Statistical Physics 42, 6-7 (2014), 237--297.Google Scholar
- Eugene d'Eon. 2016a. Diffusion approximations for nonclassical Boltzmann transport in arbitrary dimension. Technical Report.Google Scholar
- Eugene d'Eon. 2016b. A Hitchhiker's Guide to Multiple Scattering.Google Scholar
- Martin Frank and Thierry Goudon. 2010. On a generalized Boltzmann equation for non-classical particle transport. Kinetic and Related Models 3 (2010).Google Scholar
- Jeppe Revall Frisvad, Niels Jørgen Christensen, and Henrik Wann Jensen. 2007. Computing the scattering properties of participating media using Lorenz-Mie theory. ACM Trans. Graph. 26, 3 (2007). Google ScholarDigital Library
- Giovanni Gallavotti. 1972. Rigorous Theory Of The Boltzmann Equation In The Lorentz Gas. Technical Report. Istituto di Fisica, Univ. di Roma.Google Scholar
- Diego Gutierrez, Adolfo Munoz, Oscar Anson, and Francisco Seron. 2006. Simulation of Atmospheric Phenomena. Computers & Graphics 20, 6 (2006), 994:1010. Google ScholarDigital Library
- Diego Gutierrez, Srinivasa G. Narasimhan, Henrik Wann Jensen, and Wojciech Jarosz. 2008. Scattering. In ACM SIGGRAPH ASIA 2008 Courses. Google ScholarDigital Library
- Eric Heitz, Jonathan Dupuy, Cyril Crassin, and Carsten Dachsbacher. 2015. The SGGX Microflake Distribution. ACM Trans. Graph. 34, 4, Article 48 (2015). Google ScholarDigital Library
- Wenzel Jakob. 2010. Mitsuba renderer. http://www.mitsuba-renderer.org.Google Scholar
- Wenzel Jakob, Adam Arbree, Jonathan T Moon, Kavita Bala, and Steve Marschner. 2010. A radiative transfer framework for rendering materials with anisotropic structure. ACM Trans. Graph. 29, 4 (2010). Google ScholarDigital Library
- Adrian Jarabo and Victor Arellano. 2018. Bidirectional Rendering of Vector Light Transport. Computer Graphics Forum To appear (2018). Google ScholarDigital Library
- Wojciech Jarosz, Derek Nowrouzezahrai, Iman Sadeghi, and Henrik Wann Jensen. 2011. A Comprehensive Theory of Volumetric Radiance Estimation Using Photon Points and Beams. ACM Trans. Graph. 30, 1 (2011). Google ScholarDigital Library
- Henrik Wann Jensen. 2001. Realistic Image Synthesis Using Photon Mapping. AK Peters. Google ScholarDigital Library
- Pramook Khungurn, Daniel Schroeder, Shuang Zhao, Kavita Bala, and Steve Marschner. 2015. Matching Real Fabrics with Micro-Appearance Models. ACM Trans. Graph. 35, 1 (2015). Google ScholarDigital Library
- Yuri Knyazikhin, JöRn Kranigk, Ranga B Myneni, Oleg Panfyorov, and Gode Gravenhorst. 1998. Influence of small-scale structure on radiative transfer and photosynthesis in vegetation canopies. Journal of Geophysical Research 103 (1998), 6133--6144.Google ScholarCross Ref
- Alexander B Kostinski. 2001. On the extinction of radiation by a homogeneous but spatially correlated random medium. JOSA A 18, 8 (2001).Google Scholar
- Alexander B Kostinski. 2002. On the extinction of radiation by a homogeneous but spatially correlated random medium: reply to comment. JOSA A 19, 12 (2002), 2521--2525.Google ScholarCross Ref
- Jaroslav Křivánek, Iliyan Georgiev, Toshiya Hachisuka, Petr Vévoda, Martin Šik, Derek Nowrouzezahrai, and Wojciech Jarosz. 2014. Unifying points, beams, and paths in volumetric light transport simulation. ACM Trans. Graph. 33, 4 (2014). Google ScholarDigital Library
- Peter Kutz, Ralf Habel, Yining Karl Li, and Jan Novák. 2017. Spectral and Decomposition Tracking for Rendering Heterogeneous Volumes. ACM Trans. Graph. 36, 4 (2017). Google ScholarDigital Library
- Eric P Lafortune and Yves D Willems. 1996. Rendering participating media with bidirectional path tracing. In Rendering TechniquesâĂŹ 96. Google ScholarDigital Library
- Edward W Larsen. 2007. A generalized Boltzmann equation for non-classical particle transport. In Proceedings of the International Conference on Mathematics and Computations and Supercomputing in Nuclear Applications.Google Scholar
- Edward W Larsen and Richard Vasques. 2011. A generalized linear Boltzmann equation for non-classical particle transport. Journal of Quantitative Spectroscopy and Radiative Transfer 112, 4 (2011).Google ScholarCross Ref
- C D Levermore, G C Pomraning, D L Sanzo, and J Wong. 1986. Linear transport theory in a random medium. Journal of mathematical physics 27, 10 (1986).Google ScholarCross Ref
- Jorge Lopez-Moreno, David Miraut, Gabriel Cirio, and Miguel A. Otaduy. 2015. Sparse GPU Voxelization of Yarn-Level Cloth. Computer Graphics Forum 36, 1 (2015). Google ScholarDigital Library
- Guillaume Loubet and Fabrice Neyret. 2017. Hybrid mesh-volume LoDs for all-scale pre-filtering of complex 3D assets. Computer Graphics Forum 36 (2017). Google ScholarDigital Library
- S Lovejoy, G Brosamlen, and B Watson. 1995. Scattering in multifractal media. In Particle Transport in Stochastic Media.Google Scholar
- Alexander Marshak, Anthony Davis, Warren Wiscombe, and Robert Cahalan. 1998. Radiative effects of sub-mean free path liquid water variability observed in stratiform clouds. Journal of Geophysical Research: Atmospheres 103, D16 (1998), 19557--19567.Google ScholarCross Ref
- Johannes Meng, Marios Papas, Ralf Habel, Carsten Dachsbacher, Steve Marschner, Markus Gross, and Wojciech Jarosz. 2015. Multi-Scale Modeling and Rendering of Granular Materials. ACM Trans. Graph. 34, 4 (2015). Google ScholarDigital Library
- Jonathan T Moon, Bruce Walter, and Stephen R Marschner. 2007. Rendering discrete random media using precomputed scattering solutions. In Proceedings of EGSR. Google ScholarDigital Library
- Thomas Müller, Marios Papas, Markus Gross, Wojciech Jarosz, and Jan Novák. 2016. Efficient Rendering of Heterogeneous Polydisperse Granular Media. ACM Trans. Graph. 35, 6 (2016). Google ScholarDigital Library
- William I Newman, Jeffrey K Lew, George L Siscoe, and Robert G Fovell. 1995. Systematic effects of randomness in radiative transfer. Journal of the atmospheric sciences 52, 4 (1995).Google ScholarCross Ref
- Fabrice Neyret. 1998. Modeling, animating, and rendering complex scenes using volumetric textures. IEEE Transactions on Visualization and Computer Graphics 4, 1 (1998), 55--70. Google ScholarDigital Library
- Jan Novák, Andrew Selle, and Wojciech Jarosz. 2014. Residual Ratio Tracking for Estimating Attenuation in Participating Media. ACM Trans. Graph. 33, 6 (2014). Google ScholarDigital Library
- Jouni I Peltoniemi and Kari Lumme. 1992. Light scattering by closely packed particulate media. JOSA A 9, 8 (1992).Google Scholar
- Iman Sadeghi, Adolfo Munoz, Philip Laven, Wojciech Jarosz, Francisco Seron, Diego Gutierrez, and Henrik Wann Jensen. 2012. Physically-based simulation of rainbows. ACM Trans. Graph. 31, 1 (2012). Google ScholarDigital Library
- Kai Schröder, Reinhard Klein, and Arno Zinke. 2011. A Volumetric Approach to Predictive Rendering of Fabrics. Computer Graphics Forum 30, 4 (2011).Google Scholar
- László Szirmay-Kalos, Iliyan Georgiev, Milán Magdics, Balázs Molnár, and Dávid Légrády. 2017. Unbiased Estimators to Render Procedurally Generated Inhomogeneous Participating Media. Computer Graphics Forum 36, 2 (2017). EUROGRAPHICS 2017. Google ScholarDigital Library
- Jean Taine, Fabien Bellet, Vincent Leroy, and Estelle Iacona. 2010. Generalized radiative transfer equation for porous medium upscaling: Application to the radiative Fourier law. International Journal of Heat and Mass Transfer 53, 19 (2010), 4071--4081.Google ScholarCross Ref
- Richard Vasques and Edward W Larsen. 2014. Non-classical particle transport with angular-dependent path-length distributions. I: Theory. Annals of Nuclear Energy 70 (2014), 292--300.Google ScholarCross Ref
- Eric Veach. 1997. Robust Monte Carlo methods for light transport simulation. Ph.D. Dissertation. Stanford. Google ScholarDigital Library
- E. Woodcock, T. Murphi, P. Hemmings, and S. Longworth. 1965. Techniques used in the GEM code for Monte Carlo neutronics calculations in reactors and other systems of complex geometry.. In Proc. Conf. Applications of Computing Methods to Reactors, ANL-7050.Google Scholar
- Magnus Wrenninge, Ryusuke Villemin, and Christophe Hery. 2017. Path Traced Sub-surface Scattering using Anisotropic Phase Functions and Non-Exponential Free Flights. Technical Report Pixar Technical Memo 17-07. Pixar Inc.Google Scholar
- Douglas R Wyman, Michael S Patterson, and Brian C Wilson. 1989. Similarity relations for the interaction parameters in radiation transport. Applied optics 28, 24 (1989), 5243--5249.Google Scholar
- Shuang Zhao, Wenzel Jakob, Steve Marschner, and Kavita Bala. 2011. Building volumetric appearance models of fabric using micro CT imaging. ACM Trans. Graph. 30, 4 (2011). Google ScholarDigital Library
- Shuang Zhao, Wenzel Jakob, Steve Marschner, and Kavita Bala. 2012. Structure-aware synthesis for predictive woven fabric appearance. ACM Trans. Graph. 31, 4 (2012). Google ScholarDigital Library
- Shuang Zhao, Ravi Ramamoorthi, and Kavita Bala. 2014. High-order similarity relations in radiative transfer. ACM Transactions on Graphics (TOG) 33, 4 (2014). Google ScholarDigital Library
- Shaung Zhao, Lifan Wu, Frédo Durand, and Ravi Ramamoorthi. 2016. Downsampling Scattering Parameters for Rendering Anisotropic Media. ACM Trans. Graph. 35, 6 (2016). Google ScholarDigital Library
Index Terms
- A radiative transfer framework for spatially-correlated materials
Recommendations
A radiative transfer framework for non-exponential media
We develop a new theory of volumetric light transport for media with non-exponential free-flight distributions. Recent insights from atmospheric sciences and neutron transport demonstrate that such distributions arise in the presence of correlated ...
Fractional gaussian fields for modeling and rendering of spatially-correlated media
Transmission of radiation through spatially-correlated media has demonstrated deviations from the classical exponential law of the corresponding uncorrelated media. In this paper, we propose a general, physically-based method for modeling such ...
Refractive radiative transfer equation
We introduce a refractive radiative transfer equation to the graphics community for the physically based rendering of participating media that have a spatially varying index of refraction. We review principles of geometric nonlinear optics that are ...
Comments