A null-scattering path integral formulation of light transport

Unbiased rendering of general, heterogeneous participating media currently requires using null-collision approaches for estimating transmittance and generating free-flight distances. A long-standing limitation of these approaches, however, is that the corresponding path pdfs cannot be computed due to the black-box nature of the null-collision rejection sampling process. These techniques therefore cannot be combined with other sampling techniques via multiple importance sampling (MIS), which significantly limits their robustness and generality. Recently, Galtier et al. [2013] showed how to derive these algorithms directly from the radiative transfer equation (RTE). We build off this generalized RTE to derive a path integral formulation of null scattering, which reveals the sampling pdfs and allows us to devise new, express existing, and combine complementary unbiased techniques via MIS. We demonstrate the practicality of our theory by combining, for the first time, several path sampling techniques in spatially and spectrally varying media, generalizing and outperforming the prior state of the art.