  We introduce an unsupervised technique for encoding point clouds into a
canonical shape representation, by disentangling shape and pose. Our encoder is
stable and consistent, meaning that the shape encoding is purely
pose-invariant, while the extracted rotation and translation are able to
semantically align different input shapes of the same class to a common
canonical pose. Specifically, we design an auto-encoder based on Vector Neuron
Networks, a rotation-equivariant neural network, whose layers we extend to
provide translation-equivariance in addition to rotation-equivariance only. The
resulting encoder produces pose-invariant shape encoding by construction,
enabling our approach to focus on learning a consistent canonical pose for a
class of objects. Quantitative and qualitative experiments validate the
superior stability and consistency of our approach.
