Projective invariant multiscale analysis

Thanks to the use of a 3D homogeneous representation of a picture, we present a multiscale analysis (T/sub t//sup P/), t/spl isin/R/sup +/, P/spl isin//spl sime/S/sup 2/, 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(T/sub t'//sup Q/g)=T/sub t//sup P/(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.