Two decades have passed since the introduction of Markov chain Monte Carlo (MCMC) into light transport simulation by Veach and Guibas, and numerous follow-up works have been published since then. However, up until now no survey has attempted to cover the majority of these methods. The aim of this paper is therefore to offer a first comprehensive survey of MCMC algorithms for light transport simulation. The methods presented in this paper are categorized by their objectives and properties, while we point out their strengths and weaknesses. We discuss how the methods handle the main issues of MCMC and how they could be combined or improved in the near future. To make the paper suitable for readers unacquainted with MCMC methods, we include an introduction to general MCMC and its demonstration on a simple example.

Multiple importance sampling (MIS) has become an indispensable tool in Monte Carlo rendering, widely accepted as a near-optimal solution for combining different sampling techniques. But an MIS combination, using the common balance or power heuristics, often results in an overly defensive estimator, leading to high variance. We show that by generalizing the MIS framework, variance can be substantially reduced. Specifically, we optimize one of the combined sampling techniques so as to decrease the overall variance of the resulting MIS estimator. We apply the approach to the computation of direct illumination due to an HDR environment map and to the computation of global illumination using a path guiding algorithm. The implementation can be as simple as subtracting a constant value from the tabulated sampling density done entirely in a preprocessing step. This produces a consistent noise reduction in all our tests with no negative influence on run time, no artifacts or bias, and no failure cases.

The human visual system is sensitive to relative differences in luminance, but light transport simulation algorithms based on Metropolis sampling often result in a highly nonuniform relative error distribution over the rendered image. Although this issue has previously been addressed in the context of the Metropolis light transport algorithm, our work focuses on Metropolis photon tracing. We present a new target function (TF) for Metropolis photon tracing that ensures good stratification of photons leading to pixel estimates with equalized relative error. We develop a hierarchical scheme for progressive construction of the TF from paths sampled during rendering. In addition to the approach taken in previous work, where the TF is defined in the image plane, ours can be associated with compact spatial regions. This allows us to take advantage of illumination coherence to more robustly estimate the TF while adapting to geometry discontinuities. To sample from this TF, we design a new replica exchange Metropolis scheme. We apply our algorithm in progressive photon mapping and show that it often outperforms alternative approaches in terms of image quality by a large margin.

Efficiently simulating light transport in various scenes with a single algorithm is a difficult and important problem in computer graphics. Two major issues have been shown to hinder the efficiency of the existing solutions: light transport due to multiple highly glossy or specular interactions, and scenes with complex visibility between the camera and light sources. While recent bidirectional path sampling methods such as vertex connection and merging/unified path sampling (VCM/UPS) efficiently deal with highly glossy or specular transport, they tend to perform poorly in scenes with complex visibility. On the other hand, Markov chain Monte Carlo (MCMC) methods have been able to show some excellent results in scenes with complex visibility, but they behave unpredictably in scenes with glossy or specular surfaces due to their fundamental issue of sample correlation. In this paper, we show how to fuse the underlying key ideas behind VCM/UPS and MCMC into a single, efficient light transport solution. Our algorithm is specifically designed to retain the advantages of both approaches, while alleviating their limitations. Our experiments show that the algorithm can efficiently render scenes with both highly glossy or specular materials and complex visibility, without compromising the performance in simpler cases.

Efficiently computing light transport in participating media in a manner that is robust to variations in media density, scattering albedo, and anisotropy is a difficult and important problem in realistic image synthesis. While many specialized rendering techniques can efficiently resolve subsets of transport in specific media, no single approach can robustly handle all types of effects. To address this problem we unify volumetric density estimation, using point and beam estimators, and Monte Carlo solutions to the path integral formulation of the rendering and radiative transport equations. We extend multiple importance sampling to correctly handle combinations of these fundamentally different classes of estimators. This, in turn, allows us to develop a single rendering algorithm that correctly combines the benefits and mediates the limitations of these powerful volume rendering techniques.

Monte Carlo techniques for light transport simulation rely on importance sampling when constructing light transport paths. Previous work has shown that suitable sampling distributions can be recovered from particles distributed in the scene prior to rendering. We propose to represent the distributions by a parametric mixture model trained in an on-line (i.e. progressive) manner from a potentially infinite stream of particles. This enables recovering good sampling distributions in scenes with complex lighting, where the necessary number of particles may exceed available memory. Using these distributions for sampling scattering directions and light emission significantly improves the performance of state-of-the-art light transport simulation algorithms when dealing with complex lighting.