Regional Adaptive Metropolis Light Transport (2402.08273v1)

Abstract: The design of the proposal distributions, and most notably the kernel parameters, are crucial for the performance of Markov chain Monte Carlo (MCMC) rendering. A poor selection of parameters can increase the correlation of the Markov chain and result in bad rendering performance. We approach this problem by a novel path perturbation strategy for online-learning of state-dependent kernel parameters. We base our approach on the theoretical framework of regional adaptive MCMC which enables the adaptation of parameters depending on the region of the state space which contains the current sample, and on information collected from previous samples. For this, we define a partitioning of the path space on a low-dimensional canonical space to capture the characteristics of paths, with a focus on path segments closer to the sensor. Fast convergence is achieved by adaptive refinement of the partitions. Exemplarily, we present two novel regional adaptive path perturbation techniques akin to lens and multi-chain perturbations. Our approach can easily be used on top of existing path space MLT methods to improve rendering efficiency, while being agnostic to the initial choice of kernel parameters.