Rao-Blackwellized Markov chain Monte Carlo Light Transport

TL;DR

This paper introduces a new Rao-Blackwellization technique for Metropolis-Hastings algorithms in light transport simulation, significantly reducing variance and accelerating convergence compared to traditional methods.

Contribution

A novel Rao-Blackwellization method for Metropolis-Hastings that improves variance reduction and convergence speed in light transport algorithms.

Findings

Our RB technique outperforms waste-recycling in variance reduction.

The method accelerates convergence in light transport simulations.

Extensive experiments confirm substantial improvements over traditional approaches.

Abstract

In light transport simulation, Markov chain Monte Carlo methods are particularly effective at exploring regions with complex lighting characteristics. However, estimator variance is a central concern across Monte Carlo methods in general. In light transport, high variance directly manifests as increased noise or, equivalently, longer rendering times at fixed image quality. Variance reduction techniques based on Rao-Blackwellization have proven particularly effective. In practice, however, the RB approach traditionally used in light transport, waste-recycling, can yield little to no measurable variance reduction, a fact we empirically confirm in this work. Motivated by this lack of effective variance reduction, we introduce a novel RB technique for the general-purpose Metropolis-Hastings algorithm that is computationally efficient and achieves substantial variance reduction. We show that this method consistently outperforms waste-recycling in terms of both variance reduction and convergence speed. Building on this result, we adapt the proposed RB approach to the recently introduced general-purpose Jump Restore algorithm, where it similarly achieves substantial variance reduction and accelerated convergence. Through extensive experiments in light transport simulation, we demonstrate that our \gls{rb} technique significantly outperforms the traditional approaches for both MH-based light transport algorithms and Jump Restore Light Transport, under both equal-time and equal-sample-count comparisons.