  We propose a deformable registration algorithm based on unsupervised learning
of a low-dimensional probabilistic parameterization of deformations. We model
registration in a probabilistic and generative fashion, by applying a
conditional variational autoencoder (CVAE) network. This model enables to also
generate normal or pathological deformations of any new image based on the
probabilistic latent space. Most recent learning-based registration algorithms
use supervised labels or deformation models, that miss important properties
such as diffeomorphism and sufficiently regular deformation fields. In this
work, we constrain transformations to be diffeomorphic by using a
differentiable exponentiation layer with a symmetric loss function. We
evaluated our method on 330 cardiac MR sequences and demonstrate robust
intra-subject registration results comparable to two state-of-the-art methods
but with more regular deformation fields compared to a recent learning-based
algorithm. Our method reached a mean DICE score of 78.3% and a mean Hausdorff
distance of 7.9mm. In two preliminary experiments, we illustrate the model's
abilities to transport pathological deformations to healthy subjects and to
cluster five diseases in the unsupervised deformation encoding space with a
classification performance of 70%.
