GeoMorph: Geometric Deep Learning for Cortical Surface Registration

We present GeoMorph, a geometric deep learning image registration framework that takes two cortical surfaces on the spherical space and learns a smooth displacement field that aligns the features on the moving surface to those on the target. GeoMorph starts with feature extraction: independently extracting low-dimensional feature representations for each input surface using graph convolutions. These learned features are then registered in a deep-discrete manner by learning the optimal displacement for a set of control points that optimizes the overlap between features across the two surfaces. To ensure a smooth deformation, we propose a regularization network that considers the input sphere structure based on a deep conditional random field (CRF), implemented using a recurrent neural network (RNN). Results show that GeoMorph improves over existing deep learning methods by improving alignment whilst generating smoother and more biologically plausible deformations. Performance is competitive with classical frameworks, generalizing well even for subjects with atypical folding patterns.