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. We introduce Multiresolution Deep Implicit Functions (MDIF), a hierarchical representation that can recover fine geometry detail, while being able to perform global operations such as shape completion. Our model represents a complex 3D shape with a hierarchy of latent grids, which can be decoded into different levels of detail and also achieve better accuracy. For shape completion, we propose latent grid dropout to simulate partial data in the latent space and therefore defer the completing functionality to the decoder side. This along with our multires design significantly improves the shape completion quality under decoder-only latent optimization. To the best of our knowledge, MDIF is the first deep implicit function model that can at the same time (1) represent different levels of detail and allow progressive decoding; (2) support both encoder-decoder inference and decoder-only latent optimization, and fulfill multiple applications; (3) perform detailed decoder-only shape completion. Experiments demonstrate its superior performance against prior art in various 3D reconstruction tasks.
