  We propose to learn a probabilistic motion model from a sequence of images
for spatio-temporal registration. Our model encodes motion in a low-dimensional
probabilistic space - the motion matrix - which enables various motion analysis
tasks such as simulation and interpolation of realistic motion patterns
allowing for faster data acquisition and data augmentation. More precisely, the
motion matrix allows to transport the recovered motion from one subject to
another simulating for example a pathological motion in a healthy subject
without the need for inter-subject registration. The method is based on a
conditional latent variable model that is trained using amortized variational
inference. This unsupervised generative model follows a novel multivariate
Gaussian process prior and is applied within a temporal convolutional network
which leads to a diffeomorphic motion model. Temporal consistency and
generalizability is further improved by applying a temporal dropout training
scheme. Applied to cardiac cine-MRI sequences, we show improved registration
accuracy and spatio-temporally smoother deformations compared to three
state-of-the-art registration algorithms. Besides, we demonstrate the model's
applicability for motion analysis, simulation and super-resolution by an
improved motion reconstruction from sequences with missing frames compared to
linear and cubic interpolation.
