Charted Metropolis Light Transport

Abstract: In this manuscript, inspired by a simpler reformulation of primary sample space Metropolis light transport, we derive a novel family of general Markov chain Monte Carlo algorithms called charted Metropolis-Hastings, that introduces the notion of sampling charts to extend a given sampling domain and making it easier to sample the desired target distribution and escape from local maxima through coordinate changes. We further apply the novel algorithms to light transport simulation, obtaining a new type of algorithm called charted Metropolis light transport, that can be seen as a bridge between primary sample space and path space Metropolis light transport. The new algorithms require to provide only right inverses of the sampling functions, a property that we believe crucial to make them practical in the context of light transport simulation. We further propose a method to integrate density estimation into this framework through a novel scheme that uses it as an independence sampler.