New measure for shape elongation

Abstract

Shape elongation is one of the basic shape descriptors that has a very clear intuitive meaning. That is reason for its applicability in many shape classification tasks. In this paper we define a new method for computing shape elongation for shapes with polygonal boundaries. The measure is the ratio of the maximal and minimal of the sums of squared lengths of the projections of all of the edges of the polygonal boundary onto a line which has a particular slope. We express the measure with a closed formula. This measure finds the elongation for shapes whose boundary is not extracted completely, which is impossible to achieve with existing area based measures.