  We present multiresolution tree-structured networks to process point clouds
for 3D shape understanding and generation tasks. Our network represents a 3D
shape as a set of locality-preserving 1D ordered list of points at multiple
resolutions. This allows efficient feed-forward processing through 1D
convolutions, coarse-to-fine analysis through a multi-grid architecture, and it
leads to faster convergence and small memory footprint during training. The
proposed tree-structured encoders can be used to classify shapes and outperform
existing point-based architectures on shape classification benchmarks, while
tree-structured decoders can be used for generating point clouds directly and
they outperform existing approaches for image-to-shape inference tasks learned
using the ShapeNet dataset. Our model also allows unsupervised learning of
point-cloud based shapes by using a variational autoencoder, leading to
higher-quality generated shapes.
