  Shape priors learned from data are commonly used to reconstruct 3D objects
from partial or noisy data. Yet no such shape priors are available for indoor
scenes, since typical 3D autoencoders cannot handle their scale, complexity, or
diversity. In this paper, we introduce Local Implicit Grid Representations, a
new 3D shape representation designed for scalability and generality. The
motivating idea is that most 3D surfaces share geometric details at some scale
-- i.e., at a scale smaller than an entire object and larger than a small
patch. We train an autoencoder to learn an embedding of local crops of 3D
shapes at that size. Then, we use the decoder as a component in a shape
optimization that solves for a set of latent codes on a regular grid of
overlapping crops such that an interpolation of the decoded local shapes
matches a partial or noisy observation. We demonstrate the value of this
proposed approach for 3D surface reconstruction from sparse point observations,
showing significantly better results than alternative approaches.
