A similarity index for convex polygons (abstract only)

A new method for quantifying the shape similarity of two arbitrary convex polygons is presented. The intuitive notion of similarity is captured by computing the maximum area of intersection over every possible superposition of one polygon on the other. Polygons are defined as regions bounded by conjunctive linear constraints of the form: a * x1 + a * x2 + a > = 0.0 (for i = 1,2,…, k). The problem is then reduced to one of non-differential optimization of three dimensions with an integral objective function. The maximum is taken over every possible rotation and translation of one polygon relative to the other. An extension of the method to arbitrary polygons is given where figures are partitioned into convex polygonal components. The results of classification experiments are presented as a comparison of this procedure with existing techniques.