Resampling-aware Weighting Functions for Bidirectional Path Tracing Using Multiple Light Sub-Paths

Abstract

Bidirectional path tracing (BPT) with multiple importance sampling (MIS) is a popular technique for rendering realistic images. Recently, it has been shown that BPT can be improved by preparing multiple light sub-paths and by resampling a small number of light sub-paths from them to generate full paths with large contribution. Traditionally, for MIS weights, the balance heuristic has widely been used to minimize the upper bound of variance, where each full path is weighted in proportion to the probability of the path. Although the probability of the path can change due to the resampling process, the weighting functions used in the previous methods remain unaffected by the change in probability, resulting in less efficiency. To address this problem, we propose new weighting functions for BPT with multiple light sub-paths. Our main contribution is a precise formulation of the variance and the derivation of the weighting functions that can appropriately treat the change in probability. We demonstrate that our weighting functions significantly improve the image quality. We will release a simple version of our implementation as open source to ensure reproducibility.

Two‐stage Resampling for Bidirectional Path Tracing with Multiple Light Sub‐paths

“…Nabata et al interpret the resampling of light sub-paths from the pre-sampled light sub-paths as RIS in the context of BPT [NID20]. We refer to this as RISBPT.…”

“…We also incorporate the resampling-aware weighting function using p ris [NID20] into our two-stage resampling BPT by substituting M = M 2 and q = q 2 in Eq. (9).…”

“…Comparison between RISBPT [NID20] and two‐stage resampling in equal number of iterations (16 iterations) and equal rendering time (2 min). After 16 iterations, (a) two‐stage resampling yields similar results as (b) RISBPT, though q 2 is not used for all proposals in two‐stage resampling.…”

“…We also propose a weighting function tailored to two‐stage resampling. By combining our weighting function with this two‐stage resampling method, our method can reduce the variance and achieve stable noise reduction compared with previous BPT methods using multiple light sub‐paths [PRDD15, NID20].…”

“…Recent developments in BPT [PRDD15, NID20] have demonstrated that the use of multiple light sub‐paths and the resampling of a small number of light sub‐paths from them taking into account the contribution of each connection can improve the rendering efficiency (i.e., the noise reduction). Since the pre‐sampled light subpaths are shared and reused by all the eye sub‐paths, preparing a small number of pre‐sampled light sub‐paths leads to correlation of the light sub‐paths, resulting in artifacts.…”