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Deterministic Consistent Density Estimation for Light Transport Simulation

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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

Quasi-Monte Carlo methods often are more efficient than Monte Carlo methods, mainly, because deterministic low discrepancy sequences are more uniformly distributed than independent random numbers ever can be. So far, tensor product quasi-Monte Carlo techniques have been the only deterministic approach to consistent density estimation. By avoiding the repeated computation of identical information, which is intrinsic to the tensor product approach, a more efficient quasi-Monte Carlo method is derived. Its analysis relies on the properties of (0, 1)-sequences, provides new insights, and generalizes previous approaches to light transport simulation.

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Acknowledgements

The authors would like to thank Leonhard Grünschloß for the profound discussions.

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Authors and Affiliations

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

    Alexander Keller & Nikolaus Binder

Authors
  1. Alexander Keller
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  2. Nikolaus Binder
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Corresponding author

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., Binder, N. (2013). Deterministic Consistent Density Estimation for Light Transport Simulation. 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_23

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