Rao-Blackwellized Markov Chain Monte Carlo Light Transport

In light transport simulation, Markov chain Monte Carlo (MCMC) methods are particularly effective at exploring regions with complex lighting characteristics. However, estimator variance is a central concern across Monte Carlo (MC) 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 (RB) 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 (MH) 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 light transport experiments, we show that our RB technique significantly outperforms traditional estimators for both MH-based algorithms and Jump Restore Light Transport (JRLT) under equal-time and equal-sample-count budgets.