Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for image rendering. One of the methods includes receiving data describing a scene, wherein the scene comprises one or more light sources and one or more objects having different surface optical properties; receiving a request to render an image of the scene using a multiple importance sampling method that combines a plurality of sampling techniques, wherein each sampling technique uses a different probability distribution to sample a respective fraction of total number of samples; modifying a particular one of the probability distributions to reduce a variance of the multiple importance sampling while holding the respective fractions and the other probability distributions fixed; rendering the scene using the multiple importance sampling using the modified particular probability distribution and the other probability distributions; and outputting the rendered scene in response to the request.

Abstract: Methods and systems of joint path importance sampling are provided to construct light paths in participating media. The product of anisotropic phase functions and geometric terms across a sequence of path vertices are considered. A connection subpath is determined to join a light source subpath with a light receiver subpath with multiple intermediate vertices while considering the product of phase functions and geometry terms. A joint probability density function (“PDF”) may be factorized unidirectional or bidirectional. The joint PDF may be factorized into a product of multiple conditional PDFs, each of which corresponds to a sampling routine. Analytic importance sampling may be performed for isotropic scattering, whereas tabulated importance sampling may be performed for anisotropic scattering.

Abstract: Methods and systems of joint path importance sampling are provided to construct light paths in participating media. The product of anisotropic phase functions and geometric terms across a sequence of path vertices are considered. A connection subpath is determined to join a light source subpath with a light receiver subpath with multiple intermediate vertices while considering the product of phase functions and geometry terms. A joint probability density function (“PDF”) may be factorized unidirectional or bidirectional. The joint PDF may be factorized into a product of multiple conditional PDFs, each of which corresponds to a sampling routine. Analytic importance sampling may be performed for isotropic scattering, whereas tabulated importance sampling may be performed for anisotropic scattering.