  We propose a novel method for 3D shape completion from a partial observation
of a point cloud. Existing methods either operate on a global latent code,
which limits the expressiveness of their model, or autoregressively estimate
the local features, which is highly computationally extensive. Instead, our
method estimates the entire local feature field by a single feedforward network
by formulating this problem as a tensor completion problem on the feature
volume of the object. Due to the redundancy of local feature volumes, this
tensor completion problem can be further reduced to estimating the canonical
factors of the feature volume. A hierarchical variational autoencoder (VAE)
with tiny MLPs is used to probabilistically estimate the canonical factors of
the complete feature volume. The effectiveness of the proposed method is
validated by comparing it with the state-of-the-art method quantitatively and
qualitatively. Further ablation studies also show the need to adopt a
hierarchical architecture to capture the multimodal distribution of possible
shapes.
