Path-space Differentiable Rendering of Implicit Surfaces

Physics-based differentiable rendering is a key ingredient for integrating forward rendering into probabilistic inference and machine learning pipelines. As a state-of-the-art formulation for differentiable rendering, differential path integrals have enabled the development of efficient Monte Carlo estimators for both interior and boundary integrals. Unfortunately, this formulation has been designed mostly for explicit geometries like polygonal meshes. In this paper, we generalize the theory of differential path integrals to support implicit geometries like level sets and signeddistance functions (SDFs). In addition, we introduce new Monte Carlo estimators for efficiently sampling discontinuity boundaries that are also implicitly specified. We demonstrate the effectiveness of our theory and algorithms using several differentiable-rendering and inverse-rendering examples.