Résumé en anglais

This paper presents a proof of a derivation lemma on the space of BV functions. The origin of this question can be found in the context of the image matching in the framework of large deformation diffeomorphisms. To compute the geodesic equations on the space of diffeomorphisms, one needs this derivation lemma. It gives also the structure of the initial momentum, which is the central tool in the Hamiltonian formulation of geodesic equations.