Primal-Dual convex optimization in large deformation diffeomorphic registration with robust regularizers

Abstract

This paper proposes a method for primal-dual convex optimization in variational Large Deformation Diffeomorphic Metric Mapping (LDDMM) problems formulated with robust regularizers and image similarity metrics. The method is based on Chambolle and Pock primal-dual algorithm for solving general convex optimization problems. Diagonal preconditioning is used to ensure the convergence of the algorithm to the global minimum. We study three robust regularizers liable to provide acceptable results in diffeomorphic registration: Huber, V -Huber and Total Generalized Variation. Experiments in a 2D MRI data set with complex geometry show that, for all the considered regularizers, the proposed method is able to converge to diffeomorphic solutions. The method performs similarly to state of the art stationary LDDMM and log-domain diffeomorphic Demons in terms of the image similarity achieved after registration. In addition, evaluation in the 3D Non-Rigid Image Registration Project (NIREP) database shows an acceptable performance for second-order robust regularizers, close to the performance of the state of the art diffeomorphic registration methods.