Measuring elongation from shape boundary

Abstract

Shape elongation is one of the basic shape descriptors that has a very clear intuitive meaning. That is the reason for its applicability in many shape classification tasks. In this paper we define a new method for computing shape elongation. The new measure is boundary based and uses all the boundary points. We start with shapes having polygonal boundaries. After that we extend the method to shapes with arbitrary boundaries. The new elongation measure converges when the assigned polygonal approximation converges toward a shape. We express the measure with closed formulas in both cases: for polygonal shapes and for arbitrary shapes. The new measure finds the elongation for shapes whose boundary is not extracted completely, which is impossible to achieve with area based measures.