Computing an average anatomical atlas using LDDMM and geodesic shooting

Average 3D digital atlas construction from a set of images is an important task for registration and assessment of intra- and inter-population differences in structural and functional imagery. In this paper, we describe the computation of an average atlas using LDDMM and geodesic shooting where the velocity vector fields transforming a provisional template to the ensemble are averaged and evolved via shooting using the equation for the geodesic conservation of momentum to give the average atlas. This guarantees that the averaged atlas so computed remains within the permissible shape space of the anatomical ensemble being averaged