  A complete representation of 3D objects requires characterizing the space of
deformations in an interpretable manner, from articulations of a single
instance to changes in shape across categories. In this work, we improve on a
prior generative model of geometric disentanglement for 3D shapes, wherein the
space of object geometry is factorized into rigid orientation, non-rigid pose,
and intrinsic shape. The resulting model can be trained from raw 3D shapes,
without correspondences, labels, or even rigid alignment, using a combination
of classical spectral geometry and probabilistic disentanglement of a
structured latent representation space. Our improvements include more
sophisticated handling of rotational invariance and the use of a diffeomorphic
flow network to bridge latent and spectral space. The geometric structuring of
the latent space imparts an interpretable characterization of the deformation
space of an object. Furthermore, it enables tasks like pose transfer and
pose-aware retrieval without requiring supervision. We evaluate our model on
its generative modelling, representation learning, and disentanglement
performance, showing improved rotation invariance and intrinsic-extrinsic
factorization quality over the prior model.
