Metric subgraphs of the chamfer metrics and the Melter-Tomescu path generated metrics Original Research Article

Chamfer metrics are determined by local distances which are chosen to ensure that each geodesic lies within one of the cones determined by the mask and contains only edges in the directions of the bounding rays of the cone. It is shown that the chamfer distances calculated within a set are the same as those calculated in the whole space if and only if the set is convex in each of the local distance directions. The result does not hold when the local distances allow more general geodesics. The results for chamfer metrics are related to corresponding results for the metrics generated by the two-, three- and four-direction graphs studied by Melter and Tomescu.