Importance Sampling Techniques for Path Tracing in Participating Media

Abstract

We introduce a set of robust importance sampling techniques which allow efficient calculation of direct and indirect lighting from arbitrary light sources in both homogeneous and heterogeneous media. We show how to distribute samples along a ray proportionally to the incoming radiance for point and area lights. In heterogeneous media, we decouple ray marching from light calculations by computing a representation of the transmittance function that can be quickly evaluated during sampling, at the cost of a small amount of bias. This representation also allows the calculation of another probability density function which can direct samples to regions most likely to scatter light. These techniques are orthogonal and can be combined via multiple importance sampling to further reduce variance. Our method has very modest per‐ray memory requirements and does not require any preprocessing, making it simple to integrate into production ray tracing based renderers.

Joint importance sampling of low-order volumetric scattering

“…Inspired by this line of work, Novák et al [2012] analyzed many-light rendering in anisotropically-scattering media and showed that such line-based path construction can provably reduce singularities in many-light rendering (see Křivánek et al [2012] for a comprehensive survey of many-light techniques). We show that the methods of Kulla and Fajardo [2012] and Novák et al [2012] can be interpreted as general path sampling techniques and employed for path construction in bidirectional path sampling algorithms using both segments (lines) and vertices. We unify and formalize these approaches with joint importance sampling, and propose new joint path sampling techniques for more substantial variance reduction.…”

“…Incremental, vertex-by-vertex path construction in participating media traditionally proceeds by sampling the direction of the next path segment proportionally to the phase function, and choosing the propagation distance along the segment proportionally to transmittance [Woodcock et al 1965;Raab et al 2008]. Kulla and Fajardo [2012] observed that the geometry term is often responsible for more variance than the transmittance term and proposed equiangular sampling to choose the propagation distance proportionally to the geometry term when computing single scattering in isotropic media. Recent extensions to density estimation [Jensen 1996;Jensen and Christensen 1998] have proposed using lines, instead of vertices, as the eye [Jarosz et al 2008] and light [Sun et al 2010;Jarosz et al 2011] path building block, leading to significant improvements.…”

Gradient-domain volumetric photon density estimation

“…Monte Carlo integration can be used to solve the radiative transfer equation (RTE) [Chandrasekhar 2013], and its application to rendering leads to the uni-and bi-directional volumetric path tracing algorithms [Lafortune and Willems 1996] that generate paths to connect sensors to lights. Kulla and Fajardo [2012] improve light sampling techniques for single-scattering, and Georgiev et al [2013] extended this idea to lower-order multiple scattering. Monte Carlo integration is very general but its convergence can be slow, even in geometrically (and visually) simple scenes, e.g., a Cornell Box with homogeneous media.…”

Separable subsurface scattering

“…A more recent technique improves upon the inherent inaccuracies of the diffusion theory by using a more refined diffusion model to separate single and multiple scattering terms, alongside with the quantization of the Green's function of the diffusion equation to obtain realistic all-frequency results [DI11]. Further improvements revolve around better importance sampling [KF12], while a recent class of techniques rely on solving the searchlight problem by means of Monte Carlo integration imbued by multiple importance sampling [HCJ13].…”