Frequency Diffeomorphisms for Efficient Image

This paper presents an e cient algorithm for large deformation di eomorphic metric mapping (LDDMM) with geodesic shooting for image registration. We introduce a novel nite dimensional Fourier representation of di eomorphic deformations based on the key fact that the high frequency components of a di eomorphism remain stationary throughout the integration process when computing the deformation associated with smooth velocity elds. We show that manipulating high dimensional di eomorphisms can be carried out entirely in the bandlimited space by integrating the nonstationary low frequency components of the displacement eld. This insight substantially reduces the computational cost of the registration problem. Experimental results show that our method is signi cantly faster than the state-of-the-art di eomorphic image registration methods while producing equally accurate alignment. We demonstrate our algorithm in two di erent applications of image registration: neuroimaging and in-utero imaging.