  Learning discriminative shape representation directly on point clouds is
still challenging in 3D shape analysis and understanding. Recent studies
usually involve three steps: first splitting a point cloud into some local
regions, then extracting corresponding feature of each local region, and
finally aggregating all individual local region features into a global feature
as shape representation using simple max pooling. However, such pooling-based
feature aggregation methods do not adequately take the spatial relationships
between local regions into account, which greatly limits the ability to learn
discriminative shape representation. To address this issue, we propose a novel
deep learning network, named Point2SpatialCapsule, for aggregating features and
spatial relationships of local regions on point clouds, which aims to learn
more discriminative shape representation. Compared with traditional max-pooling
based feature aggregation networks, Point2SpatialCapsule can explicitly learn
not only geometric features of local regions but also spatial relationships
among them. It consists of two modules. To resolve the disorder problem of
local regions, the first module, named geometric feature aggregation, is
designed to aggregate the local region features into the learnable cluster
centers, which explicitly encodes the spatial locations from the original 3D
space. The second module, named spatial relationship aggregation, is proposed
for further aggregating clustered features and the spatial relationships among
them in the feature space using the spatial-aware capsules developed in this
paper. Compared to the previous capsule network based methods, the feature
routing on the spatial-aware capsules can learn more discriminative spatial
relationships among local regions for point clouds, which establishes a direct
mapping between log priors and the spatial locations through feature clusters.
