An efficient parallel algorithm for hierarchical geodesic models in diffeomorphisms

We present a novel algorithm for computing hierarchical geodesic models (HGMs) for diffeomorphic longitudinal shape analysis. The proposed algorithm exploits the inherent parallelism arising out of the independence in the contributions of individual geodesics to the group geodesic. The previous serial implementation severely limits the use of HGMs to very small population sizes due to computation time and massive memory requirements. The conventional method makes it impossible to estimate the parameters of HGMs on large datasets due to limited memory available onboard current GPU computing devices. The proposed parallel algorithm easily scales to solve HGMs on a large collection of 3D images of several individuals. We demonstrate its effectiveness on longitudinal datasets of synthetically generated shapes and 3D magnetic resonance brain images (MRI).