A Local Frequency Analysis of Light Scattering and Absorption

Abstract

(presented at SIGGRAPH 2014)International audienceRendering participating media requires significant computation, but the effect of volumetric scattering is often eventually smooth. This article proposes an innovative analysis of absorption and scattering of local light fields in the Fourier domain and derives the corresponding set of operators on the covariance matrix of the power spectrum of the light field. This analysis brings an efficient prediction tool for the behavior of light along a light path in participating media. We leverage this analysis to derive proper frequency prediction metrics in 3D by combining per-light path information in the volume.We demonstrate the use of these metrics to significantly improve the convergence of a variety of existing methods for the simulation of multiple scattering in participating media. First, we propose an efficient computation of second derivatives of the fluence, to be used in methods like irradiance caching. Second, we derive proper filters and adaptive sample densities for image-space adaptive sampling and reconstruction. Third, we propose an adaptive sampling for the integration of scattered illumination to the camera. Finally, we improve the convergence of progressive photon beams by predicting where the radius of light gathering can stop decreasing. Light paths in participating media can be very complex. Our key contribution is to show that analyzing local light fields in the Fourier domain reveals the consistency of illumination in such media and provides a set of simple and useful rules to be used to accelerate existing global illumination methods.Une nouvelle analyse locale de la diffusion et de l'absorption de la lumière dans l'espace de Fourier est combinée avec le tracé de covariance et permet une estimation rapide du contenu fréquentiel local; cette approche permet l'amélioration de nombreux algorithmes de rendu de milieux participants tels que Progressive Photon Beams et l'integration d'effets de diffusion simple et l'échantillonnage et la reconstruction d'effets de simple diffusion simple en espace image

Gradient-domain path tracing

“…Interestingly, there is a close connection between second order derivatives and Gaussian approximations of local frequency spectra [Belcour et al 2014].…”

Efficient rendering of layered materials using an atomic decomposition with statistical operators

“…As for rough interfaces, the incident variance increases by the width of the phase function in the forward direction Belcour et al [2014]. We empirically found a t of the equivalent GGX roughness for the Henyey-Greenstein phase function (HG) in the forward direction (see Fig.…”

Second-Order Occlusion-Aware Volumetric Radiance Caching

“…Each cache in both our method and Jarosz et al is computed using 16k stratified angular samples, and rendered using 16 samples per pixel. The progressive photon beams solution was obtained using the publicly available Tungsten rendering engine [Bitterli 2016a]. Note how the occlusion unaware method creates visible artifacts in the patterns created by the shadows crossing from different windows, while our method correctly captures those details in equal time.…”

“…Closely related to our work, Belcour et al [2014] performed a frequency analysis of light fields within participating media. They summarize the local light field using covariance matrices, which provides Hessians of fluence (up to sign) due to scattering and absorption.…”