STRONG AND WEAK CONVEX HULLS IN NON-EUCLIDEAN METRIC - THEORY AND APPLICATION

The notion of convexity is usually defined in the plane supplied with the Euclidean metric. This paper examines what remains if we equip the plane with a distance induced by a norm which is not necessarily the Euclidean one. The basic properties of the geodesic arcs according to these non-Euclidean metrics are stated. In some cases there exists mor e than one geodesic arc between two points. The two associated notions of convexity, both strong and weak, are the presented. The relationsh ips between the notion of weak convex hull and the limit of closings o f increasing size are stated. Finally an application in binary image p attern recognition is described.