A zero-variance-based sampling scheme for Monte Carlo subsurface scattering

Abstract

We simulate subsurface scattering using a Monte Carlo random walk in the volumetric medium under the surface. The simulation involves two steps: transition distance sampling and direction sampling. Traditionally, the pdfs used for this purpose emulate the underlying physical processes (exponential law for distance sampling pd(s) = σt e−sσt , phase function pph(ωo|ωi) for direction sampling). However, this sampling is purely local as it has no information about where the important parts of the entire domain are. In subsurface scattering simulation it is not useful to explore the medium far from the boundary, given that we are interested in paths that make it back out of the medium. This idea can be formalized using the notion of the importance function: A zero-variance estimator can be constructed by sampling paths proportionately to the product of the importance function and the classical pdfs [Hoogenboom 2008], and an approximation of this zerovariance ideal yields estimators with low variance. Dwivedi [1982] exploited this idea in deep-penetration transport problems such as reactor shielding. We show how this work can be adapted to reduce variance of subsurface scattering simulation.