Diffusion Based Photon Mapping

Abstract

Abstract. Density estimation employed in multi-pass global illumination algorithms give cause to a trade-off problem between bias and noise. The problem is seen most evident as blurring of strong illumination features. In particular this blurring erodes fine structures and sharp lines prominent in caustics. To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features, while eliminating noise. We call our method diffusion based photon mapping.

Photon Parameterisation for Robust Relaxation Constraints

“…We compare our algorithm against the classic photon mapping algorithm introduced by Jensen, the original photon relaxation method [SJ09], diffusion‐based photon mapping [SOS08] and, for reference, progressive photon mapping [HOJ08]. All tests were performed using an Intel Core i7 with 8GB of RAM running Windows 7.…”

“…When rendering with diffusion‐based photon mapping, we used 500‐nearest neighbours to achieve comparable levels of noise removal. Schjøth et al [SOS08] specify a diffusivity function [PM90] which controls the anisotropy of the kernel filter. To yield visually comparable levels of blurring due to kernel bias we set the control parameter, q , to 0.02.…”

“…In Figure 6, a glass prism generates intricate shards of caustic illumination when lit from behind. In frame c we use the anisotropic, shape‐adapting kernel introduced by Schjøth et al [SOS08]. The visible contouring effect is due to noise being misidentified as structure.…”

“…Schjøth et al [SOS05] demonstrated the limitations of isotropic, variable bandwidth kernels and proposed that filtering the estimate anisotropically could dramatically improve results. Later, Schjøth et al [SFES07] adapted the ray differential framework [Ige99] to shape the filter based on photon ray footprints.…”

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

“…The shape of this kernel does not influence the algorithm's correctness, only the behavior of bias and variance. In fact, this fact has been exploited previously by aligning kernels with structures in the lighting to minimize bias [Schjøth et al 2006;Schjøth et al 2007;Schjøth et al 2008]. Consequently, we could choose a 3D region other than a sphere to perform our blur (e.g.…”