. Currently I am interested in the analysis of biomedical and other images using the mathematical structure induced on the infinite-dimensional space of shapes by the action of groups of diffeomorphisms, equipped with a right invariant metric. This framework induces a metric in the space of shapes allowing their analytic and statistical study.

Recently, singular solutions of the geodesic Euler-Poincarè equation on diffeomorphisms (EPDiff) have been studied as evolutions of the generalized momentum of diffeomorphic flow of least energy. In particular, the momentum map for singular solutions of the EPDiff yields a Hamiltonian formulation which provides a complete parametrization of members of deformable object classes by their canonical positions and initial momenta.