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Path Space MCMC Methods in Computer Graphics

Wenzel Jakob
Book chapter Monte Carlo and Quasi-Monte Carlo Methods (Springer Proceedings in Mathematics & Statistics)

Illustration of the local energy balance equation which describes light transport on surfaces. In the above example, it is used to compute the pixel color of the surface location highlighted in white.

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Abstract

The objective of a rendering algorithm is to compute a photograph of a simulated reality, which entails finding all the paths along which light can flow from a set of light sources to the camera. The purpose of this article is to present a high-level overview of the underlying physics and analyze how this leads to a high-dimensional integration problem that is typically handled using Monte Carlo methods. Following this, we survey recent work on path space Markov Chain Monte Carlo (MCMC) methods that compute the resulting integrals using proposal distributions defined on sets of light paths.

Text citation

Wenzel Jakob. 2016. Path Space MCMC Methods in Computer Graphics. In Monte Carlo and Quasi-Monte Carlo Methods (Springer Proceedings in Mathematics & Statistics).

BibTeX
@incollection{Jakob2016Path,
    author = {Wenzel Jakob},
    title = {Path Space MCMC Methods in Computer Graphics},
    booktitle = {Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014 (Springer Proceedings in Mathematics & Statistics)},
    editor = {Ronald Cools and Dirk Nuyens},
    publisher = {Springer International Publishing},
    year = {2016},
    month = jul,
    doi = {10.1007/978-3-319-33507-0}
}