A novel curved surface representation which is relatively invariant under the transformations of the 3D motion group is introduced in this paper. It is computed from the superposition of the two geodesic potentials generated from a given couple of surface points. By considering a levels set of such geodesic potentials, finite invariant points are obtained. Two numerical methods are implemented and compared in order to find an efficient approximation of this representation in the sense of the Hausdorff shape distance. Its robustness under an imprecision of reference points positions is studied. Experimentations are performed on the 3D real faces of the database Bosphorus.
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