  Registration is an essential tool in image analysis. Deep learning based
alternatives have recently become popular, achieving competitive performance at
a faster speed. However, many contemporary techniques are limited to volumetric
representations, despite increased popularity of 3D surface and shape data in
medical image analysis. We propose a one-step registration model for 3D
surfaces that internalises a lower dimensional probabilistic deformation model
(PDM) using conditional variational autoencoders (CVAE). The deformations are
constrained to be diffeomorphic using an exponentiation layer. The one-step
registration model is benchmarked against iterative techniques, trading in a
slightly lower performance in terms of shape fit for a higher compactness. We
experiment with two distance metrics, Chamfer distance (CD) and Sinkhorn
divergence (SD), as specific distance functions for surface data in real-world
registration scenarios. The internalised deformation model is benchmarked
against linear principal component analysis (PCA) achieving competitive results
and improved generalisability from lower dimensions.
