Computable Elastic Distances Between Shapes

We deene distances between geometric curves by the square root of the minimal energy required to transform one curve into the other. The energy is formally deened from a left invariant Riemannian distance on an innnite 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 eeciently be implemented, as illustrated by experiments.