A variance analysis of the Metropolis Light Transport algorithm

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...

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Published in:Computers & graphics Vol. 25; no. 2; pp. 287 - 294
Main Authors: Ashikhmin, Michael, Premože, Simon, Shirley, Peter, Smits, Brian
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.04.2001
Subjects:
Analysis of algorithms and problem complexity
Monte Carlo
numerical algorithms and problems
Probability and statistics
raytracing
Simulation and modeling
Three-dimensional graphics and realism
Analysis of algorithms and problem complexity
Three-dimensional graphics and realism
Monte Carlo
raytracing
Probability and statistics
numerical algorithms and problems
Simulation and modeling
ISSN:0097-8493, 1873-7684
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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 Θ(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.
AbstractList 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. copyright 2001 Elsevier Science Ltd.
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 Θ(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.
Author Ashikhmin, Michael
Smits, Brian
Shirley, Peter
Premože, Simon
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Cites_doi 10.1145/258734.258775
10.1145/192161.192179
10.1146/annurev.pc.27.100176.001535
10.1145/258734.258818
10.1063/1.1699114
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Issue 2
Keywords Analysis of algorithms and problem complexity
Three-dimensional graphics and realism
Monte Carlo
raytracing
Probability and statistics
numerical algorithms and problems
Simulation and modeling
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Snippet The Metropolis Light Transport algorithm is a variant of the classic Metropolis method used in statistical physics. A variance analysis of the Metropolis Light...
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SubjectTerms Analysis of algorithms and problem complexity
Monte Carlo
numerical algorithms and problems
Probability and statistics
raytracing
Simulation and modeling
Three-dimensional graphics and realism
Title A variance analysis of the Metropolis Light Transport algorithm
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