A Stable and Invariant Three-polar Surface Representation: Application to 3D Face Description

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. A comparative study between this representation and the unipolar one based on the level curves around one reference point is established in the sense of the stability under errors on the reference points positions. The three-polar representation is applied, finally, for 3D human faces description. Its accuracy is performed in the mean of the Hausdorff shape distance.