Curve Matching Using the Fast Marching Method

Abstract

Common techniques for curve alignment find a solution in the form of a shortest network path by means of dynamic programming. In this paper we present an approach that employs Sethian’s Fast Marching Method to find the solution with sub-resolution accuracy and in consistence with the underlying continuous problem. We demonstrate how the method may be applied to compare closed curves, morph one curve into another, and compute curve averages. Our method is based on a local curve dissimilarity function F(t,s) that compares the two input curves $\mathcal{C}_{1}(t)$ and $\mathcal{C}_{2}(s)$ at given points t and s. In our experiments, we compare dissimilarity functions based on local curvature information and on shape contexts. We have tested the algorithm on a database of 110 sample curves by performing “best matches” experiments.