  Deep neural networks are increasingly used for pair-wise image registration.
We propose to extend current learning-based image registration to allow
simultaneous registration of multiple images. To achieve this, we build upon
the pair-wise variational and diffeomorphic VoxelMorph approach and present a
general mathematical framework that enables both registration of multiple
images to their geodesic average and registration in which any of the available
images can be used as a fixed image. In addition, we provide a likelihood based
on normalized mutual information, a well-known image similarity metric in
registration, between multiple images, and a prior that allows for explicit
control over the viscous fluid energy to effectively regularize deformations.
We trained and evaluated our approach using intra-patient registration of
breast MRI and Thoracic 4DCT exams acquired over multiple time points.
Comparison with Elastix and VoxelMorph demonstrates competitive quantitative
performance of the proposed method in terms of image similarity and reference
landmark distances at significantly faster registration.
