A forward scattering dipole model from a functional integral approximation

Rendering translucent materials with physically based Monte Carlo methods tends to be computationally expensive due to the long chains of volumetric scattering interactions. In the case of strongly forward scattering materials, the problem gets compounded since each scattering interaction becomes highly anisotropic and near-specular. Various well-known approaches try to avoid the resulting sampling problem through analytical approximations based on diffusion theory. Although these methods are computationally efficient, their assumption of diffusive, isotropic scattering can lead to considerable errors when rendering forward scattering materials, even in the optically dense limit. 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 diffusion theory, but follows from a connection that we identified 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 diffusive 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.