A forward scattering dipole model from a functional integral approximation

Abstract

In this paper, we present an analytical subsurface scattering model, derived with the explicit assumption of strong forward scattering. Our model is not based on di usion theory, but follows from a connection that we identi ed between the functional integral formulation of radiative transport and the partition function of a worm-like chain in polymer physics. Our resulting model does not need a separate Monte Carlo solution for unscattered or single-scattered contributions, nor does it require ad-hoc regularization procedures. It has a single singularity by design, corresponding to the initial unscattered propagation, which can be accounted for by the extensive analytical importance sampling scheme that we provide. Our model captures the full behaviour of forward scattering media, ranging from unscattered straight-line propagation to the fully di usive limit. Moreover, we derive a novel forward scattering BRDF as limiting case of our subsurface scattering model, which can be used in a level of detail hierarchy. We show how our model can be integrated in existing Monte Carlo rendering algorithms, and make comparisons to previous approaches. CCS Concepts: • Computing methodologies → Rendering; Ray tracing;

Monte Carlo Methods for Volumetric Light Transport Simulation

“…This is also analyzed in appendix L.1 in [FD17] and is even more true for multi‐lobe approximations of phase functions predicted by Lorenz‐Mie theory, which include more back‐scattering contribution. In that sense the most‐probable‐path theory is an approximation that neglects the back scattering effects present in scattering regimes governed by Mie theory.…”

“…These techniques were introduced to graphics by Premoze et al [PAS03, PAT*04] based on theory initially developed by Tessendorf in a string of publications [Tes87, Tes09]. Frederickx and Dutré [FD17] provide an excellent summary of the derivation of these methods in their supplemental material. Note that in this context, path integral refers to the Feynman integral [FH65], not to what we describe in Equation .…”

A guided Monte Carlo radiative transfer method using mixture importance sampling

“…Here,ω(r i ) is the single scattering albedo. This is actually a negative log-likelihood function, which is quite similar to the energy function in polymer statistical physics and has been used for solving radiative transfer problems (Frederickx & Dutré 2017). It is noted that similar path space integral techniques (Pauly et al 2000;Premože et al 2003;Jakob 2016) have been widely used in computer graphics for physically based rendering.…”

Interactive Subsurface Scattering for Materials With High Scattering Distances

“…Frederickx et al . [FD17] proposed a model for forward scattering materials. Due to the higher number of parameters it is rather hard to tabulate and thus not suitable for real‐time applications.…”