A comprehensive theory of volumetric radiance estimation using photon points and beams

We present two contributions to the area of volumetric rendering. We develop a novel, comprehensive theory of volumetric radiance estimation that leads to several new insights and includes all previously published estimates as special cases. This theory allows for estimating in-scattered radiance at a point, or accumulated radiance along a camera ray, with the standard photon particle representation used in previous work. Furthermore, we generalize these operations to include a more compact, and more expressive intermediate representation of lighting in participating media, which we call “photon beams.” The combination of these representations and their respective query operations results in a collection of nine distinct volumetric radiance estimates. Our second contribution is a more efficient rendering method for participating media based on photon beams. Even when shooting and storing less photons and using less computation time, our method significantly reduces both bias (blur) and variance in volumetric radiance estimation. This enables us to render sharp lighting details (e.g., volume caustics) using just tens of thousands of photon beams, instead of the millions to billions of photon points required with previous methods.