  As in other areas of medical image analysis, e.g. semantic segmentation, deep
learning is currently driving the development of new approaches for image
registration. Multi-scale encoder-decoder network architectures achieve
state-of-the-art accuracy on tasks such as intra-patient alignment of abdominal
CT or brain MRI registration, especially when additional supervision, such as
anatomical labels, is available. The success of these methods relies to a large
extent on the outstanding ability of deep CNNs to extract descriptive visual
features from the input images. In contrast to conventional methods, the
explicit inclusion of geometric information plays only a minor role, if at all.
In this work we take a look at an exactly opposite approach by investigating a
deep learning framework for registration based solely on geometric features and
optimisation. We combine graph convolutions with loopy belief message passing
to enable highly accurate 3D point cloud registration. Our experimental
validation is conducted on complex key-point graphs of inner lung structures,
strongly outperforming dense encoder-decoder networks and other point set
registration methods. Our code is publicly available at
https://github.com/multimodallearning/deep-geo-reg.
