Curves Matching Using Geodesic Paths

We present a method for matching curves which accommodates large and small deformation. The method preserves geometric similarities in the case of small deformation, and loosens these geometric constraints when large deformations occur. The approach is based on the computation of a set of geodesic paths connecting the curves. These two curves are defined as a source area and a destination area which can have an arbitrary number of connected components and different topologies. The applicative framework of the presented method is the study of the crustal deformation from a set of iso-elevation curves. An experiment with real curves demonstrates that the approach can be successfully applied to characterize deformation of Digital Elevation Models.