  In the square root velocity framework, the computation of shape space
distances and the registration of curves requires solution of a non-convex
variational problem. In this paper, we present a new PDE-based method for
solving this problem numerically. The method is constructed from numerical
approximation of the Hamilton-Jacobi-Bellman equation for the variational
problem, and has quadratic complexity and global convergence for the distance
estimate. In conjunction, we propose a backtracking scheme for approximating
solutions of the registration problem, which additionally can be used to
compute shape space geodesics. The methods have linear numerical convergence,
and improved efficiency compared previous global solvers.
