Résumé en anglais

Thanks to the use of a 3D homogeneous representation of a picture, we present a multiscale analysis (TtP), t∈R+, P∈≃S2, which is invariant under the projective group: let g be a picture in the plane; for every projective transformation A, there exist t'=t'(A, t), Q=Q(A, P) such that A(Tt'Qg)=TtP(Ag). Moreover, this study allows us to propose simplified multiscale analysis, which are given by a unique PDE, for subgroups of the projective group: the subgroups of the projective transformations which leave invariant a line in the plane; the subgroup of the projective transformations associated, up to a non-zero scalar factor, to an orthogonal 3,3 matrix.