Extended Path Integral Formulation for Volumetric Transport

EGSR 2017 (EI&I)

Abstract

We propose an extension of the path integral formulation amenable to the expression of volumetric light transport with photon beam estimates. Our main contribution is a generalization of Hachisuka et al.'s extended path space formulation [Hachisuka et al. 2012] to light transport in participating media. Our formulation supports various point- and beam-based volumetric density estimators, unifying them with path integration in the spirit of the work by Křivánek et al. [2014]. One unique and useful property of our formulation is that it recasts beam-based density estimation as Monte Carlo path vertex sampling in a higher-dimensional space, rather than beam merging in a lower-dimensional space, which enables a practical algorithm for beam estimators with 3D-blur kernels. We thus establish a complementary theoretical foundation for the development of rendering algorithms using points, beams, and paths in participating media.

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BibTeX reference

@article{Hachisuka:2017:ExtendedIntegralVolumes,
    author = {Toshiya Hachisuka and Iliyan Georgiev and Wojciech Jarosz and Jaroslav K\v{r}iv{\'a}nek and Derek Nowrouzezahrai},
    title = {Extended Path Integral Formulation for Volumetric Transport},
    booktitle = {Proceedings of EGSR (Experimental Ideas & Implementations)},
    year = {2017},
    month = jun,
    publisher = {The Eurographics Association}
}