A distance for elastic matching in object recognition

We define distances between geometric curves by the square root of the minimal energy required to transform one curve into the other. The energy is formally defined from a left invariant Riemannian distance on an infinite dimensional group acting on the curves, which can be explicitely computed. The obtained distance boils down to a variational problem for which an optimal matching between the curves has two be computed. An analysis of the distance when the curves are polygonal leads to a numerical procedure for the solution of the variational problem, which can eflciently be implemented, as illustrated by experiments. Acknowledgements : This work comes as a part of a project on object recognition, supported by the D.R.E.T. helded at SUDIMAGE research laboratory under the direction of R. Azencott. Publication is courtesy of the D.R.ET.