A Radiative Transfer Framework for Spatially-Correlated Materials

Abstract

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.

References in corpus (3)

• Non-classical transport with angular-dependent path-length distributions. 1: Theory
• A Generalized Linear Transport Model for Spatially-Correlated Stochastic Media
• Rigorous asymptotic and moment-preserving diffusion approximations for generalized linear Boltzmann transport in arbitrary dimension

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• A Reciprocal Formulation of Nonexponential Radiative Transfer. 2: Monte Carlo Estimation and Diffusion Approximation
• Deep Appearance Prefiltering
• Efficient Scene Appearance Aggregation for Level-of-Detail Rendering
• Solution of the Generalized Linear Boltzmann Equation for Transport in Multidimensional Stochastic Media
• Solving partial differential equations in participating media
• Asymptotic Derivation of the Simplified $P_N$ Equations for Nonclassical Transport with Anisotropic Scattering
• Rendering Discrete Participating Media with Geometrical Optics Approximation
• Green's functions for non-classical transport with general anisotropic scattering