On polygonal measures with vanishing harmonic moments

In this note we show the existence of large families of signed polygonal measures having all harmonic moments vanishing, where by a polygonal measures we understand a signed measure supported on a finite collection of disjoint polygons and having constant real density in each of them

Numerical reconstruction of convex polytopes from directional moments

International audienceWe reconstruct an n-dimensional convex polytope from the knowledge of its directional moments up to a certain order. The directional moments are related to the projection of the polytope's vertices on a particular direction. To extract the vertex coordinates from the moment information we combine established numerical algorithms such as generalized eigenvalue computation and linear interval interpolation. Numerical illustrations are given for the reconstruction of 2-d and 3-d objects