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 [2012] extended path space formulation 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.