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

Abstract

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.

Gradient-domain volumetric photon density estimation

“…Jarosz et al's beam radiance estimate (BRE) [2008] performs density estimation directly along an entire camera ray, leading to significant performance improvements. A recent extension of photon point primitives to beam primitives, including a theory of density estimation using these photon beams, has led to improvements when rendering scenes in certain scenarios [Jarosz et al 2011a]: Krivanek et al 's [2014] variance analysis of various point-and beam-based estimators concludes that point-based estimators are best-suited to optically thick media, whereas beam primitive-based estimators are beneficial in optically thin media. More recently, Bitterli and Jarosz [2017] proposed to use higher order primitives (like plane or volume) to get smoother results of multiple-scattering inside the participating media.…”

“…A pathx can be constructed by connecting a camera subpathz and light subpathȳ with a blurring kernel. We follow the comprehensive theory of radiance estimation in volumes using photons points and beams [Jarosz et al 2011a] and a recent extension to photon planes [Bitterli and Jarosz 2017] and consider four typical estimators (in camera ray query × photon data order): point-point, beam-point, beam-beam, and beam-plane estimators. In general, the major difference among these estimators are how the last vertices of both subpaths are sampled, resulting in different strategies to generate the last two vertices on the camera and light subpath .…”

“…While Monte Carlo methods robustly render a range of surface-only scenes, density estimation techniques tend towards more desirable convergence behavior in scenes with volumetric media. Recent advances in volumetric density estimation, such as the beam radiance estimate [Jarosz et al 2008], photon point and beam estimators [Jarosz et al 2011a], virtual ray and beam lights [Novák et al 2012a,b], and other higher-dimensional representation such as photon planes and volumes [Bitterli and Jarosz 2017], further improve this behavior.…”

Basics of physically-based rendering

“…Here a set of points has the right density (like the energy on a surface for "baking" where results are stored over the model for later lookup) and density estimation estimates the underlying density that generated those points. Recent work on photon beams [5] has added legs to this approach and emphasizes that being comfortable with math on paths is a good thing. Key here is we have some function f (x) = kp(x) where p is a pdf (so non-negative with integral one).…”

Light Beam Tracing for Multi-Bounce Specular and Glossy Transport Paths

“…In 2011, Jarosz et al [44] discussed a very interesting photon beams rendering algorithm which improved upon the efficiency of the beam radiance estimate of Jarosz et al [34] and others. Using photon beams one does not need to generate and store as many photon scatter incidents because the radiance estimate is done on the whole photon path directly.…”