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.
Jarabo, A., Aliaga, C., & Gutierrez, D. (2018). A radiative transfer framework for spatially-correlated materials. ACM Transactions on Graphics, 37(4). https://doi.org/10.1145/3197517.3201282