A geodesic based approach for an accurate and invariant 3D surfaces representation

Abstract

In this paper, we propose a novel 3D invariant surface representation under the 3D motion group M(3). It is obtained by combining two main representations: the three-polar representation and the one defined by the radial line curves from a starting point. The retained invariant points correspond to the geometrical locations of the intersection between the two last representations. The approximation of the novel surfaces description method on the 3D discrete meshes is studied. Its accuracy for the 3D faces description and retrieval is evaluated in the mean of the Hausdorff shape distance.