Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces

Classical deformable registration techniques achieve impressive results andoffer a rigorous theoretical treatment, but are computationally intensive sincethey solve an optimization problem for each image pair. Recently,learning-based methods have facilitated fast registration by learning spatialdeformation functions. However, these approaches use restricted deformationmodels, require supervised labels, or do not guarantee a diffeomorphic(topology-preserving) registration. Furthermore, learning-based registrationtools have not been derived from a probabilistic framework that can offeruncertainty estimates. In this paper, we build a connection between classical and learning-basedmethods. We present a probabilistic generative model and derive an unsupervisedlearning-based inference algorithm that uses insights from classicalregistration methods and makes use of recent developments in convolutionalneural networks (CNNs). We demonstrate our method on a 3D brain registrationtask for both images and anatomical surfaces, and provide extensive empiricalanalyses. Our principled approach results in state of the art accuracy and veryfast runtimes, while providing diffeomorphic guarantees. Our implementation isavailable at http://voxelmorph.csail.mit.edu.