A Variance Analysis of the Metropolis Light Transport Algorithm
Computers & Graphics, Elsevier Science
Authors
Abstract
The Metropolis Light Transport algorithm is a variant of the
classic Metropolis method used in statistical physics.
A variance analysis of the Metropolis Light Transport algorithm is
presented that bounds its variance in terms of the number of paths
used and the intrinsic correlation between samples.
It is shown that the variance of a pixel is Theta(1/N) where
N is the number of samples for the entire image. The analysis uses
basic probability, Bayes' law, and the principle of stationary
distributions. This result implies that the presence of
correlation in the algorithm does not make its asymptotic
time complexity worse than uncorrelated Monte Carlo methods
such as path tracing.