Sample Space Partitioning and Spatiotemporal Resampling for Specular Manifold Sampling

Abstract

Caustics rendering remains a long-standing challenge in Monte Carlo rendering because high-energy specular paths occupy only a small region of path space, making them difficult to sample effectively. Recent work such as Specular Manifold Sampling (SMS) [Zeltner et al. 2020] can stochastically sample these specular paths and estimate their unbiased weights using Bernoulli trials. However, applying SMS in interactive rendering is non-trivial because it is slow and delivers noisy images given a very limited time budget.

In this work, we extend SMS for high-quality caustic rendering in interactive settings using sample space partitioning. Our insight is that Newton iterations, the main performance bottleneck of SMS, can be restricted to the vicinity of the seed path, which can dramatically improve the performance. We achieve this with tile-based sample space partitioning, which bounds the manifold walk region and allows building a per-frame prior distribution that concentrates initial guesses around solutions. This reduces the cost of SMS and improves its sampling quality. Applying spatiotemporal reuse (ReSTIR) further amortizes the sample generation cost, greatly increasing the effective sample count. As a result, we achieve significant variance reduction compared to SMS in interactive rendering scenarios.