Quadric-Based Silhouette Sampling for Differentiable Rendering

Physically based differentiable rendering has established itself as key to inverse rendering, in which scenes are recovered from images through gradient-based optimization. Taking the derivative of the rendering equation is made difficult by the presence of discontinuities in the integrand at object silhouettes. To obtain correct derivatives w.r.t. changing geometry, accounting e.g. for changing penumbras or silhouettes in glossy reflections, differentiable renderers must compute an integral over these silhouettes. Prior work proposed importance sampling of silhouette edges for a given shading point. The main challenge is to efficiently reject parts of the mesh without silhouettes during sampling, which has been done using top-down traversal of a tree. Inaccuracies of this existing rejection procedure result in many samples with zero contribution. Thus, variance remains high and subsequent work has focused on alternatives such as area sampling or path space differentiable rendering. We propose an improved rejection test. It reduces variance substantially, which makes edge sampling in a unidirectional path tracer competitive again. Our rejection test relies on two approximations to the triangle planes of a mesh patch: A bounding box in dual space and dual quadrics. Additionally, we improve the heuristics used for stochastic traversal of the tree. We evaluate our method in a unidirectional path tracer and achieve drastic improvements over the original edge sampling and outperform methods based on area sampling.