Adaptive gradient descent optimization of initial momenta for geodesic shooting in diffeomorphisms

Diffeomorphic image registration algorithms are widely used in medical imaging, and require optimization of a high-dimensional nonlinear objective function. The function being optimized has many characteristics that are relevant for optimization but are typically not well understood. Due to that complexity, most authors have used a simple gradient descent, but it is not often discussed how step sizes are chosen or if line searches are used. Further, if a system is to be robust to a range of input images, that may differ to varying degrees, the optimization must be adaptable. Here, we present two methods of adaptable gradient descent with line searches, and test how they affect image registration. The optimization schemes are deployed for geodesic shooting in diffeomorphisms - an approach that is used to quantify anatomical changes, such as atrophy, in longitudinal image pairs. We evaluate the optimization schemes on their convergence characteristics and based on how well the resulting atrophy scores correlate with diagnostic group and mini mental state exam (MMSE) scores. We find that the Barzilai-Borwein method with a backtracking line search outperforms other optimization schemes in convergence time and adaptability by a wide margin. We also find that the variable optimization schemes do not significantly affect the ability to measure atrophy with clinical significance.