An Invariant Three-polar Representation for R3 Surfaces: Robustness and Accuracy for 3D Faces Description

Abstract

In this paper, we intend to introduce a new curved surface representation that we qualify by three-polar. It is constructed by the superposition of the three geodesic potentials generated from three reference points of the surface. By considering a pre-selected levels set of this superposition, invariant points are obtained. The accuracy of the three-polar representation for 3D human faces description is performed in the mean of the Hausdorff distance. A comparison between this representation and the one based on the level curves around the nose tip is established in the sense of the robustness under errors on the nose tip positions.