Closed Curves and Elementary Visual Object Identification

For two closed curves on a plane (discrete version) and local criteria for similarity of points on the curves one gets a potential, which describes the similarity between curve points. This is the base for a global similarity measure of closed curves (Fr\'echet distance). I use borderlines of handwritten digits to demonstrate an area of application. I imagine, measuring the similarity of closed curves is an essential and elementary task performed by a visual system. This approach to similarity measures may be used by visual systems.