PRIF: Primary Ray-based Implicit Function

We introduce a new implicit shape representation called Primary Ray-based Implicit Function (PRIF). In contrast to most existing approaches based on the signed distance function (SDF) which handles spatial locations, our representation operates on oriented rays. Specifically, PRIF is formulated to directly produce the surface hit point of a given input ray, without the expensive sphere-tracing operations, hence enabling efficient shape extraction and differentiable rendering. We demonstrate that neural networks trained to encode PRIF achieve successes in various tasks including single shape representation, category-wise shape generation, shape completion from sparse or noisy observations, inverse rendering for camera pose estimation, and neural rendering with color.