Gauss-Newton optimization in Diffeomorphic registration

In this article, we propose a numerical implementation of Gauss-Newton's method for optimization in diffeomorphic registration in the large deformation diffeomorphic metric mapping framework. The computations of the Gateaux derivatives of the objective function are performed in the tangent space of the Riemannian manifold of diffeomorphisms. The resulting algorithm has been compared to gradient descent optimization in brain MRI anatomical images. The experiments have shown similar accuracy for both techniques at steady-state while Gauss-Newton has resulted to be more robust with a faster rate of convergence.