A radiative transfer framework for spatially-correlated materials

Abstract

Fig. 1. Spatial correlation in media leads to non-exponential light transport, which significantly affects appearance. The image shows volumetric renderings of translucent dragons made of materials with the same density per unit differential volume µ = 10 (isotropic, albedo Λ = .8), but different correlations. Left: using classic light transport, where material particles are assumed to be uncorrelated. Middle and right: positive and negative correlation, respectively, using our novel framework for spatially-correlated materials. The insets show illustrative views of scatterer correlation for each dragon.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.

A spectral approach for solving the nonclassical transport equation

“…[2]). The theory has been extended over the last few years [3][4][5][6][7] and has found applications in other areas, including neutron transport in certain types of nuclear reactors [8][9][10], computer graphics [11][12][13], and problems involving anomalous diffusion (cf. [14]).…”

A practical path guiding method for participating media

“…In future, we will consider introducing our method to heterogeneous participating media and we also wish to combine the volume path guiding representation and the surface path guiding representation. As for non-exponentially correlated media [32], changing exponential distance sampling to non-exponential sampling will require further consideration of the volumetric path guiding domain.…”

A Monte Carlo framework for rendering speckle statistics in scattering media

“…is macroscopic treatment of sca ering underlies all current Monte Carlo volume rendering algorithms, and has also been used to accelerate rendering of so-called discrete random media, where the sca erers can be arbitrarily large or dense (Meng et al 2015;Moon et al 2007;Müller et al 2016). More recently, a number of works have used this approach to derive generalized versions of the RTE and Monte Carlo rendering algorithms, for media where the distribution of sca erer locations has spatial correlations, so-called non-exponential media (Bi erli et al 2018;d'Eon 2018a,b;Jarabo et al 2018). Even though we focus exclusively on exponential media, our work provides the foundations for future investigations of Monte Carlo rendering of speckles in non-exponential media.…”