Measuring convexity via convex polygons

Abstract

This paper describes a general approach to compute a family of convexity measures. Inspired by the use of geometric primitives (such as circles) which are often fitted to shapes to approximate them, we use convex polygons for this task. Convex polygons can be generated in many ways, and several are demonstrated here. These polygons are scaled and translated to ensure that they fit the input shape and produce a meaningful convexity measure. Subsequently, a convexity measure can be computed based on the degree of overlap between the two shapes.