- Published 2012

We first summarize the path integral formulation by Veach [Veach 1998]. Using the path integral formulation, light transport simulation can be expressed as: Ij = Ω fj (¯ x)dµ(¯ x), (1) where j is an index to the pixel (or measurement), fj is the measurement contribution function, µ is a measure of paths, and Ω is the set of transport paths of all lengths. We evaluate this integral using Monte Carlo integration with a random path ¯ X with the probability density p(¯ X) by: E fj (¯ X) p(¯ X) = Ω fj (¯ x) p(¯ x) p(¯ x)dµ(¯ x) = Ij. Each term is defined as follows.

@inproceedings{Hachisuka2012SupplementalDO,
title={Supplemental Document of `A Path Space Extension for Robust Light Transport Simulation''},
author={Toshiya Hachisuka and Jacopo Pantaleoni and Henrik Wann Jensen},
year={2012}
}