Diffeomorphic Atlas Estimation using Karcher Mean and Geodesic Shooting on Volumetric Images

In this paper, we propose a new algorithm to estimate diffeomorphic organ atlases out of 3D medical images. More precisely, we explore the feasibility of Karcher means by using large deformations by diffeomorphisms (LDDMM). This framework preserves organs topology and has interesting properties to quantitatively describe their anatomical variability. We also use a new registration algorithm based on an optimal control method to satisfy the geodesicity of the deformations at any step of the optimisation process. Initial tangent vectors to the shapes, which are used to compute the Karcher mean, are therefore estimated accurately. Our methodology is tested on different groups of 3D images representing organs with a large anatomical variability.