Curve matching on brain surfaces using Frenet distances.

This paper describes methods for diffeomorphic matching of curves on brain surfaces. Distances between curves are defined by Frenet representation via speed, curvature, and torsion. The curvematching algorithm is based on bipartite graph matching, with weights defined by the Frenet distance over diffeomorphic maps of one curve onto the other (Sedgewick [1983]: Algorithms). We follow Khaneja ([1996]: Statistics and Geometry of Cortical Features) and define fundus curves on the brain surfaces as extremal curvature lines generated using dynamic programming. Examples are shown for fundus curve matchings on macaque brain surfaces.