Tackles the general problem of surface tracking. The authors present a new method based on the computation of geodesic distance maps between a source and a destination surface. The method used in this case is a generalization to the case of surfaces of a 2D matching process introduced by Cohen and Herlin (1998). It relies on a level-set formulation, thus providing stable and robust resolution schemes. The obtained matching method accommodates both small and large deformations. Actually, the matching constraints are explicitly expressed by the definition of a hypersurface. The connecting paths between the two surfaces lie on this hypersurface. The authors construct a hypersurface that allows the matching process to preserve geometric similarities in the case of small deformations, and loosen these geometric constraints when large deformations occur. The applicative framework is the study of the Earth's crustal evolution to characterize the deformation of digital elevation models