Diffusion Based Photon Mapping

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 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 important illumination features, while eliminating noise. We demonstrate the applicability of our algorithm through a series of tests. In the tests, we evaluate the visual and computational performance of our algorithm comparing it to existing popular algorithms.

Realistically rendering polluted water

“…2D Simpson's kernel reduces the circular artifacts in Pharr's pictures. Schjøth et al [12] proposed diffusion based photon mapping. They used the 2D Epanechnikov kernel and reshaped it based on the distribution of photons to obtain surface caustics with higher quality.…”

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.…”

Progressive photon relaxation

“…Further research focuses on complementing intelligent bandwidth selection by dynamically adjusting the filter support of the kernel, thereby minimizing proximity and boundary bias. Schjøth et al [2005] proposed deriving a structure tensor from the local distribution in order to constrain smoothing perpendicular to the illumination gradient. Later, Schjøth et al [2007] adapted Igehy's [1999] ray differential framework to store additional information about photon footprints, thereby greatly increasing the fidelity of highly focused caustics.…”