GradICON: Approximate Diffeomorphisms via Gradient Inverse Consistency

Many registration approaches exist with early work focusing on optimization-based approaches for image pairs. Recent work focuses on deep registration networks to predict spatial transformations. In both cases, commonly used non-parametric registration models, which estimate transformation functions instead of low-dimensional transformation parameters, require choosing a suitable regularizer (to encourage smooth transformations) and its parameters. This makes models difficult to tune and restricts deformations to the deformation space permissible by the chosen regularizer. While deep-learning models for optical flow exist that do not regularize transformations and instead entirely rely on the data these might not yield diffeomorphic transformations which are desirable for medical image registration. In this work, we therefore develop GradICON building upon the unsupervised ICON deep-learning registration approach, which only uses inverse-consistency for regularization. However, in contrast to ICON, we prove and empirically verify that using a gradient inverse-consistency loss not only significantly improves convergence, but also results in a similar implicit regularization of the resulting transformation map. Synthetic experiments and experiments on magnetic resonance (MR) knee images and computed tomography (CT) lung images show the excellent performance of GradICON. We achieve state-of-the-art (SOTA) accuracy while retaining a simple registration formulation, which is practically important.