Diffeomorphometry is the metric study of imagery, shape and form in the discipline of computational anatomy (CA) in medical imaging. The study of images in computational anatomy rely on high-dimensional diffeomorphism groups which generate orbits of the form , in which images can be dense scalar magnetic resonance or computed axial tomography images. For deformable shapes these are the collection of manifolds , points, curves and surfaces. The diffeomorphisms move the images and shapes through the orbit according to which are defined as the group actions of computational anatomy.