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Quasi-Monte Carlo Image Synthesis in a Nutshell

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Monte Carlo and Quasi-Monte Carlo Methods 2012

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 65))

Abstract

This self-contained tutorial surveys the state of the art in quasi-Monte Carlo rendering algorithms as used for image synthesis in the product design and movie industry. Based on the number theoretic constructions of low discrepancy sequences, it explains techniques to generate light transport paths to connect cameras and light sources. Summing up their contributions on the image plane results in a consistent numerical algorithm, which due to the superior uniformity of low discrepancy sequences often converges faster than its (pseudo-) random counterparts. In addition, its deterministic nature allows for simple and efficient parallelization while guaranteeing exact reproducibility. The underlying techniques of parallel quasi-Monte Carlo integro-approximation, the high speed generation of quasi-Monte Carlo points, treating weak singularities in a robust way, and high performance ray tracing have many applications outside computer graphics, too.

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Acknowledgements

The author likes to thank Ian Sloan, Frances Kuo, Josef Dick, and Gareth Peters for the extraordinary opportunity to present this tutorial at the MCQMC 2012 conference and Pierre L’Ecuyer for the invitation to present an initial tutorial on “Monte Carlo and Quasi-Monte Carlo Methods in Computer Graphics” at MCQMC 2008. In addition, the author is grateful to the anonymous reviewers, Nikolaus Binder, and Ken Dahm.

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  1. NVIDIA, Fasanenstraße 81, 10623, Berlin, Germany

    Alexander Keller

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  1. Alexander Keller
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Correspondence to Alexander Keller .

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Editors and Affiliations

  1. The University of New South Wales School of Mathematics and Statistics, Sydney, New South Wales, Australia

    Josef Dick

  2. The University of New South Wales School of Mathematics and Statistics, Sydney, New South Wales, Australia

    Frances Y. Kuo

  3. The University of New South Wales School of Mathematics and Statistics, Sydney, New South Wales, Australia

    Gareth W. Peters

  4. The University of New South Wales School of Mathematics and Statistics, Sydney, New South Wales, Australia

    Ian H. Sloan

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Keller, A. (2013). Quasi-Monte Carlo Image Synthesis in a Nutshell. In: Dick, J., Kuo, F., Peters, G., Sloan, I. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2012. Springer Proceedings in Mathematics & Statistics, vol 65. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41095-6_8

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