[Show abstract][Hide abstract] ABSTRACT: Summary form only given. In this work we study the diffeomorphic landmark matching problem central to the emerging field of computational anatomy (2002, Annual Review of Biomedical Engineering) for the study of finite dimensional face orbits. We present a new approach based on recent derivation of a conservation of momentum law for the geodesics of diffeomorphic flow. Once a template is fixed, the space of initial momentum - and Nd finite dimensional space for N d-dimensional landmarks - becomes an appropriate space for studying shape via geodesic flow since the flow at any point along the geodesic is completely determined by the momentum at the origin. We solve for the extremal paths (geodesics) of the kinetic energy by computing its variation with respect to the initial momentum and by applying a gradient descent scheme. Statistical analysis of a landmarked database of 100 faces is presented and we suggest a finite dimensional diffeomorphic active shape model.