  Nonlinear image registration continues to be a fundamentally important tool
in medical image analysis. Diagnostic tasks, image-guided surgery and
radiotherapy as well as motion analysis all rely heavily on accurate
intra-patient alignment. Furthermore, inter-patient registration enables
atlas-based segmentation or landmark localisation and shape analysis. When
labelled scans are scarce and anatomical differences large, conventional
registration has often remained superior to deep learning methods that have so
far mainly dealt with relatively small or low-complexity deformations. We
address this shortcoming by leveraging ideas from probabilistic dense
displacement optimisation that has excelled in many registration tasks with
large deformations. We propose to design a network with approximate
min-convolutions and mean field inference for differentiable displacement
regularisation within a discrete weakly-supervised registration setting. By
employing these meaningful and theoretically proven constraints, our learnable
registration algorithm contains very few trainable weights (primarily for
feature extraction) and is easier to train with few labelled scans. It is very
fast in training and inference and achieves state-of-the-art accuracies for the
challenging inter-patient registration of abdominal CT outperforming previous
deep learning approaches by 15% Dice overlap.
