  Diffeomorphic deformable image registration is crucial in many medical image
studies, as it offers unique, special properties including topology
preservation and invertibility of the transformation. Recent deep
learning-based deformable image registration methods achieve fast image
registration by leveraging a convolutional neural network (CNN) to learn the
spatial transformation from the synthetic ground truth or the similarity
metric. However, these approaches often ignore the topology preservation of the
transformation and the smoothness of the transformation which is enforced by a
global smoothing energy function alone. Moreover, deep learning-based
approaches often estimate the displacement field directly, which cannot
guarantee the existence of the inverse transformation. In this paper, we
present a novel, efficient unsupervised symmetric image registration method
which maximizes the similarity between images within the space of diffeomorphic
maps and estimates both forward and inverse transformations simultaneously. We
evaluate our method on 3D image registration with a large scale brain image
dataset. Our method achieves state-of-the-art registration accuracy and running
time while maintaining desirable diffeomorphic properties.
