Beyond points and beams: higher-dimensional photon samples for volumetric light transport

In ACM Transactions on Graphics (Proceedings of SIGGRAPH), 2017

We generalize 0D photon points (a) and 1D beams (b) to produce progressively higher-dimensional nD samples such as 2D “photon planes” (c) and 3D “photon volumes” (d). We form these estimators by computing the limit process of “marching” or sweeping photons along preceding light path segments, which allows us to progressively reduce variance and bias. The motivational experiment in the bottom row uses these successive estimators (each shown vertically split at two sample counts) on a searchlight problem setup (left), confirming that higher-order nD samples have the potential to dramatically improve quality in volumetric light transport.

Abstract

We develop a theory of volumetric density estimation which generalizes prior photon point (0D) and beam (1D) approaches to a broader class of estimators using “nD” samples along photon and/or camera subpaths. Volumetric photon mapping performs density estimation by point sampling propagation distances within the medium and performing density estimation over the generated points (0D). Beam-based (1D) approaches consider the expected value of this distance sampling process along the last camera and/or light subpath segments. Our theory shows how to replace propagation distance sampling steps across multiple bounces to form higher-dimensional samples such as photon planes (2D), photon volumes (3D), their camera path equivalents, and beyond. We perform a theoretical error analysis which reveals that in scenarios where beams already outperform points, each additional dimension of nD samples compounds these benefits further. Moreover, each additional sample dimension reduces the required dimensionality of the blurring needed for density estimation, allowing us to formulate, for the first time, fully unbiased forms of volumetric photon mapping. We demonstrate practical implementations of several of the new estimators our theory predicts, including both biased and unbiased variants, and show that they outperform state-of-the-art beam-based volumetric photon mapping by a factor of 2.4–40×.

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• Data

  • Image comparison (12MB web page, may load slowly) - an interactive JavaScript comparison of the results
  • Supplemental archive, ZIP (125MB) - additional results and comparisons

• Code

  • WebGL demo of our method
  • Full reference implementation (paper-relevant portions here)

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Cite

@article{bitterli17beyond,
    author   = {Bitterli, Benedikt and Jarosz, Wojciech},
    title    = {Beyond Points and Beams: Higher-Dimensional Photon Samples for Volumetric Light Transport},
    journal  = {ACM Transactions on Graphics (Proceedings of SIGGRAPH)},
    volume   = {36},
    number   = {4},
    year     = {2017},
    month    = jul,
    doi      = {10/gfznbr},
    keywords = {track-length estimator, expected value estimator, photon beams, photon mapping, participating media}
}

Related Projects

• 2019 Paper: Photon surfaces for robust, unbiased volumetric density estimation
• 2017 Paper: Extended path integral formulation for volumetric transport
• 2014 Paper: Unifying points, beams, and paths in volumetric light transport simulation
• 2011 Paper: Progressive photon beams
• 2011 Paper: A comprehensive theory of volumetric radiance estimation using photon points and beams
• 2008 Paper: The beam radiance estimate for volumetric photon mapping

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