  This paper presents a generalization to image matching of the Hamiltonian
approach for planar curve matching developed in the context of group of
diffeomorphisms. We propose an efficient framework to deal with discontinuous
images in any dimension, for example 2D or 3D. In this context, we give the
structure of the initial momentum (which happens to be decomposed in a smooth
part and a singular part) thanks to a derivation lemma interesting in itself.
The second part develops a Hamiltonian interpretation of the variational
problem, derived from the optimal control theory point of view.
