A novel accurate 3D surfaces description using the Arc-length reparametrized level curves of the three-polar representation

Abstract

This paper studies the problem of the 3D surfaces representation. Our starting point is the extraction of the threepolar representation from the 3D shapes. It consists on a level curves set of the superposition of the three geodesic potentials generated from three reference points of the surface. These curves are characterized by their invariance under the M(3) group of R3 displacements. We intend to make the arc-length reparametrization of each level curve to ensure its independence to the initial parametrization. The novel representation is materialized by the points of the arc-length reparametrization of all the level curves. Therefore, we obtain an invariant representation under the M(3) transformations group and independent to the initial parametrization. In this work, we implement it on 3D faces since this type of surfaces knows actually a growing interest for the identities determination especially after the many terrorist acts occurred around the world. We experiment, in this context, the identification scenario on a part of the BU-3DFE database. The obtained results show the accuracy of the novel representation.