In this paper, we propose a new algorithm to compute intrinsic means of organ shapes from 3D medical images. More specifically, we explore the feasibility of Karcher means in the framework of the large deformations by diffeomorphisms (LDDMM). This setting preserves the topology of the averaged shapes and has interesting properties to quantitatively describe their anatomical vari- ability. Estimating Karcher means requires to perform multiple registrations between the averaged template image and the set of reference 3D images. Here, we use a recent algorithm based on an optimal control method to satisfy the geodesicity of the deformations at any step of each registra- tion. We also combine this algorithm with organ specific metrics. We demonstrate the efficiency of our methodology with experimental results on different groups of anatomical 3D images. We also extensively discuss the convergence of our method and the bias due to the initial guess. A direct perspective of this work is the computation of 3D+time atlases.