  We propose a method to learn object representations from 3D point clouds
using bundles of geometrically interpretable hidden units, which we call
geometric capsules. Each geometric capsule represents a visual entity, such as
an object or a part, and consists of two components: a pose and a feature. The
pose encodes where the entity is, while the feature encodes what it is. We use
these capsules to construct a Geometric Capsule Autoencoder that learns to
group 3D points into parts (small local surfaces), and these parts into the
whole object, in an unsupervised manner. Our novel Multi-View Agreement voting
mechanism is used to discover an object's canonical pose and its pose-invariant
feature vector. Using the ShapeNet and ModelNet40 datasets, we analyze the
properties of the learned representations and show the benefits of having
multiple votes agree. We perform alignment and retrieval of arbitrarily rotated
objects -- tasks that evaluate our model's object identification and canonical
pose recovery capabilities -- and obtained insightful results.
