Joint importance sampling of low-order volumetric scattering

Abstract

Central to all Monte Carlo-based rendering algorithms is the construction of light transport paths from the light sources to the eye. Existing rendering approaches sample path vertices incrementally when constructing these light transport paths. The resulting probability density is thus a product of the conditional densities of each local sampling step, constructed without explicit control over the form of the final joint distribution of the complete path. We analyze why current incremental construction schemes often lead to high variance in the presence of participating media, and reveal that such approaches are an unnecessary legacy inherited from traditional surface-based rendering algorithms. We devise joint importance sampling of path vertices in participating media to construct paths that explicitly account for the product of all scattering and geometry terms along a sequence of vertices instead of just locally at a single vertex. This leads to a number of practical importance sampling routines to explicitly construct single-and double-scattering subpaths in anisotropically-scattering media. We demonstrate the benefit of our new sampling techniques, integrating them into several path-based rendering algorithms such as path tracing, bidirectional path tracing, and many-light methods. We also use our sampling routines to generalize deterministic shadow connections to connection subpaths consisting of two or three random decisions, to efficiently simulate higher-order multiple scattering. Our algorithms significantly reduce noise and increase performance in renderings with both isotropic and highly anisotropic, low-order scattering.

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.…”

Residual ratio tracking for estimating attenuation in participating media

“…All of these rely on generating random paths between the light(s) and the sensor, and there has been extensive research on importance sampling such paths to obtain low-noise images [Raab et al 2008;Kulla and Fajardo 2012;Georgiev et al 2013]. …”

Gaussian Product Sampling for Rendering Layered Materials

“…Our pair‐product and multiple‐product strategies are able to generate samples according to the product of two or more BSDFs. This idea of joint sampling scattering events also appears in a somewhat different setting in [HEV*16, GKH*13]. Gaussian mixtures are used to represent the illumination and the reflectance factors and perform product importance sampling in [HEV*16].…”

“…Georgiev et al . [GKH*13] proposed a joint path importance sampling method to efficiently render participating media. Their method constructs paths that account for the product of anisotropic phase functions and geometric terms across sequences of path vertices.…”