3D surfaces representation using geodesic computation and spectral analysis coupled approach: Application to 3D faces

In this paper, we intend to introduce a 3D surface representation defined around a given reference point already taken on the surface. Such representation is obtained from a coordinate system which is composed by a set of indexed levels of geodesic curves and radial lines. A sampling criterion through a generalized version of the Shannon theorem allows the determination of the minimum resolution of both curves that describes faithfully the surface. The obtained representation relatively to a unique landmark with the suited resolution is then computed around several reference points to overcome the instability due to landmarks detection errors. Thus, its robustness under small reference points positions distortion is analyzed. Experimentations are performed on the 3D facial database Bosphorus [8]. Results show also the discrimination power of such representation.