Analysis of sample correlations for Monte Carlo rendering

1Max-Planck Institute for Informatics, Saarbrücken 2Disney Research, Zurich 3KAUST, Saudi Arabia 4Université de Lyon, CNRS, France 5University of Edinburgh, UK 6University of Konstanz, Germany 7University of California, San Diego, USA 8Dartmouth College, USA

In Computer Graphics Forum (Proceedings of Eurographics - State of the Art Reports), 2019

Teaser
Various 2D stratification techniques (top) along with their 1D projections onto the x-axis, and (bottom) their corresponding expected power spectra.

Abstract

Modern physically based rendering techniques critically depend on approximating integrals of high dimensional functions representing radiant light energy. Monte Carlo based integrators are the choice for complex scenes and effects. These integrators work by sampling the integrand at sample point locations. The distribution of these sample points determines convergence rates and noise in the final renderings. The characteristics of such distributions can be uniquely represented in terms of correlations of sampling point locations. Hence, it is essential to study these correlations to understand and adapt sample distributions for low error in integral approximation. In this work, we aim at providing a comprehensive and accessible overview of the techniques developed over the last decades to analyze such correlations, relate them to error in integrators, and understand when and how to use existing sampling algorithms for effective rendering workflows.

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Acknowledgements

We are grateful to all the anonymous reviewers for their constructive remarks. This work was partially supported by the Fraunhofer and Max Planck cooperation program within the German pact for research and innovation (PFI). Kartic Subr was supported by a Royal Society University Research Fellowship, Ravi Ramamoorthi was supported by NSF grant 1451830 and Wojciech Jarosz was partially supported by NSF grant IIS-1812796.

Cite

Gurprit Singh, Cengiz Öztireli, Abdalla G.M. Ahmed, David Coeurjolly, Kartic Subr, Oliver Deussen, Victor Ostromoukhov, Ravi Ramamoorthi, Wojciech Jarosz. Analysis of sample correlations for Monte Carlo rendering. Computer Graphics Forum (Proceedings of Eurographics - State of the Art Reports), 38(2):473-491, May 2019.
@article{singh19analysis,
    author = "Singh, Gurprit and Öztireli, Cengiz and Ahmed, Abdalla G.M. and Coeurjolly, David and Subr, Kartic and Deussen, Oliver and Ostromoukhov, Victor and Ramamoorthi, Ravi and Jarosz, Wojciech",
    title = "Analysis of sample correlations for {{Monte}} {{Carlo}} rendering",
    journal = "Computer Graphics Forum (Proceedings of Eurographics - State of the Art Reports)",
    month = may,
    number = "2",
    volume = "38",
    year = "2019",
    issn = "1467-8659",
    doi = "10/gf6rzc",
    pages = "473-491",
    abstract = "Modern physically based rendering techniques critically depend on approximating integrals of high dimensional functions representing radiant light energy. Monte Carlo based integrators are the choice for complex scenes and effects. These integrators work by sampling the integrand at sample point locations. The distribution of these sample points determines convergence rates and noise in the final renderings. The characteristics of such distributions can be uniquely represented in terms of correlations of sampling point locations. Hence, it is essential to study these correlations to understand and adapt sample distributions for low error in integral approximation. In this work, we aim at providing a comprehensive and accessible overview of the techniques developed over the last decades to analyze such correlations, relate them to error in integrators, and understand when and how to use existing sampling algorithms for effective rendering workflows."
}
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