Computational anatomy: computing metrics on anatomical shapes

An important area of research in Computational Anatomy is to assign a metric space structure to 2D/3D images of anatomical structures. The images are registered in the non-rigid dense large deformation setting by computing a diffeomorphic transformation between the given images. The metric distance on the images follows from the Lie Group structure of diffeomorphisms, which allows measurement of lengths of curves on the manifold of diffeomorphisms. We present here a gradient-based method to compute the diffeomorphism matching the given images and estimating the metric distance for the pair. We show results for matching 2D sections of canine heart images.