Progressive expectation-maximization for hierarchical volumetric photon mapping

Abstract

State-of-the-art density estimation methods for rendering participating media rely on a dense photon representation of the radiance distribution within a scene. A parametric density estimation technique is used to represent radiance using a hierarchical Gaussian mixture. Coefficients of this mixture are efficiently obtained for use in a progressive and accelerated form of the Expectation-Maximization algorithm. Noise-free renderings of high-frequency illumination are created using only a few thousand Gaussian terms, where millions of photons are traditionally required. Temporal coherence is trivially supported within this framework, and the compact footprint is also useful in the context of real-time visualization. A hierarchical ray tracing-based implementation is demonstrated, as well as a fast splatting approach that can interactively render animated volume caustics.