Error analysis of estimators that use combinations of stochastic sampling strategies for direct illumination

We present a theoretical analysis of error of combinations of Monte Carlo estimators used in image synthesis. Importance sampling and multiple importance sampling are popular variance‐reduction strategies. Unfortunately, neither strategy improves the rate of convergence of Monte Carlo integration. J...

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Bibliographic Details
Published in:Computer graphics forum Vol. 33; no. 4; pp. 93 - 102
Main Authors: Subr, Kartic, Nowrouzezahrai, Derek, Jarosz, Wojciech, Kautz, Jan, Mitchell, Kenny
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.07.2014
Subjects:
Analysis
Categories and Subject Descriptors (according to ACM CCS)
Computer graphics
Computer simulation
Convergence
Estimating techniques
Estimators
I.3.3 [Computer Graphics]: Picture/Image Generation-Line and curve generation
Illumination
Importance sampling
Monte Carlo methods
Monte Carlo simulation
Multimedia computer applications
Sampling
Strategy
Studies
Telematics
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:We present a theoretical analysis of error of combinations of Monte Carlo estimators used in image synthesis. Importance sampling and multiple importance sampling are popular variance‐reduction strategies. Unfortunately, neither strategy improves the rate of convergence of Monte Carlo integration. Jittered sampling (a type of stratified sampling), on the other hand is known to improve the convergence rate. Most rendering software optimistically combine importance sampling with jittered sampling, hoping to achieve both. We derive the exact error of the combination of multiple importance sampling with jittered sampling. In addition, we demonstrate a further benefit of introducing negative correlations (antithetic sampling) between estimates to the convergence rate. As with importance sampling, antithetic sampling is known to reduce error for certain classes of integrands without affecting the convergence rate. In this paper, our analysis and experiments reveal that importance and antithetic sampling, if used judiciously and in conjunction with jittered sampling, may improve convergence rates. We show the impact of such combinations of strategies on the convergence rate of estimators for direct illumination.
Bibliography:ark:/67375/WNG-9GB6TNC2-P
ArticleID:CGF12416
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12416