Analysis situs and image processing

Abstract

In the paper a topological approach to approximation of planar Jordan curves and arcs is described. The approximation is based on the basic notions of intrinsic geometry of metric spaces: on the notion of a shortest path in a polygonaly bounded compact set and on the notion of a geodesic diameter of a polygon. Furthermore, a new linear time algorithm for the shortest path problem solution is described, and the approximation of the most important characteristic set in image processing is shown.