Practical Product Importance Sampling for Direct Illumination

Abstract

We present a practical algorithm for sampling the product of environment map lighting and surface reflectance. Our method builds on wavelet-based importance sampling, but has a number of important advantages over previous methods. Most importantly, we avoid using precomputed reflectance functions by sampling the BRDF onthe-fly. Hence, all types of materials can be handled, including anisotropic and spatially varying BRDFs, as well as procedural shaders. This also opens up for using very high resolution, uncompressed, environment maps. Our results show that this gives a significant reduction of variance compared to using lower resolution approximations. In addition, we study the wavelet product, and present a faster algorithm geared for sampling purposes. For our application, the computations are reduced to a simple quadtree-based multiplication. We build the BRDF approximation and evaluate the product in a single tree traversal, which makes the algorithm both faster and more flexible than previous methods.

Second‐Order Approximation for Variance Reduction in Multiple Importance Sampling

“…For this purpose, Cline et al [CETC06] split the environment map according to BRDF peaks computed from BRDF‐based importance sampling. To be more conservative, Clarberg et al [CAM08b] use a wavelet representation of the environment map, a wavelet approximation of the BRDF, and a fast computation of their product. These techniques require dedicated representations to support a per‐pixel dynamic computation of the importance sampling structure.…”

Importance Caching for Complex Illumination

“…However, obtaining such a PDF in practice is unfeasible, particularly because the visibility function V is not given in a closed form, and/or the incoming radiance may not be known. The state-of-the-art importance sampling methods build distributions that include some of the terms in f , usually the product BL, for sampling environment [CJAMJ05,CETC06,CAM08b] Importance-driven VPL generation has recently received attention [WBS03,SIMP06,SIP07,GS10]. These methods sample VPLs based on their total image contribution, but do not adapt to individual locations.…”

Representativity for Robust and Adaptive Multiple Importance Sampling

“…Bidirectional importance sampling methods [16], [17], [18] have been mainly developed for direct lighting, where lighting is represented by environment maps. Recently, a similar method has been developed for indirect lighting represented by virtual point light sources [19].…”