Variance Analysis of Multi-sample and One-sample Multiple Importance Sampling

We reexamine in this paper the variance for the Multiple Importance Sampling (MIS) estimator for multi‐sample and one‐sample model. As a result of our analysis we can obtain the optimal estimator for the multi‐sample model for the case where the weights do not depend on the count of samples. We exte...

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Veröffentlicht in:Computer graphics forum Jg. 35; H. 7; S. 451 - 460
Hauptverfasser: Sbert, M., Havran, V., Szirmay-Kalos, L.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford Blackwell Publishing Ltd 01.10.2016
Schlagworte:
Analysis
Categories and Subject Descriptors (according to ACM CCS)
Computer graphics
Counting
Estimating techniques
Estimators
G.3 [Computer Graphics]: Mathematics of Computing / PROBABILITY AND STATISTICS-Probabilistic algorithms
global illumination
Heuristic
Importance sampling
Monte Carlo
multiple importance sampling
Optimization
rendering equation analysis
Sampling
Studies
Variance
Variance analysis
ISSN:0167-7055, 1467-8659
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Zusammenfassung:We reexamine in this paper the variance for the Multiple Importance Sampling (MIS) estimator for multi‐sample and one‐sample model. As a result of our analysis we can obtain the optimal estimator for the multi‐sample model for the case where the weights do not depend on the count of samples. We extend the analysis to include the cost of sampling. With these results in hand we find a better estimator than balance heuristic with equal count of samples. Further, we show that the variance for the one‐sample model is larger or equal than for the multi‐sample model, and that there are only two cases where the variance is the same. Finally, we study on four examples the difference of variances for equal count as used by Veach, our new estimator, and a recently introduced heuristic.
Bibliographie:Supporting InformationSupporting Information
ArticleID:CGF13042
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.13042