Geometric Deep Learning for Unsupervised Registration of Diffusion Magnetic Resonance Images

Deep learning based models for registration predict a transformation directly from moving and fixed image appearances. These models have revolutionized the field of medical image registration, achieving accuracy on-par with classical registration methods at a fraction of the computation time. Unfortunately, most deep learning based registration methods have focused on scalar imaging modalities such as T1/T2 MRI and CT, with less attention given to more complex modalities such as diffusion MRI. In this paper, to the best of our knowledge, we present the first end-to-end geometric deep learning based model for the non-rigid registration of fiber orientation distribution fields (fODF) derived from diffusion MRI (dMRI). Our method can be trained in a fully-unsupervised fashion using only input fODF image pairs, i.e. without ground truth deformation fields. Our model introduces several novel differentiable layers for local Jacobian estimation and reorientation that can be seamlessly integrated into the recently introduced manifold-valued convolutional network in literature. The results of this work are accurate deformable registration algorithms for dMRI data that can execute in the order of seconds, as opposed to dozens of minutes to hours consumed by their classical counterparts.