Closed Curves and Elementary Visual Object Identification

TL;DR

This paper introduces a method for measuring the similarity of closed curves using local criteria, leading to a global similarity measure like the Fréchet distance, with applications demonstrated on handwritten digit borders.

Contribution

It presents a novel approach to curve similarity measurement based on local criteria, applicable to visual object identification.

Findings

Demonstrated the method on handwritten digit borders

Proposed a potential-based similarity measure for curves

Suggested applications in visual systems

Abstract

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.