A Contour-Oriented Approach to Shape Analysis via the Slope Chain Code

We present a noncircularity measure for 2D (two-dimensional) shapes and an approach to the computation of the Euler number based on the Slope Chain Code (SCC). The SCC was developed for representing and analyzing open and closed curves in the 2D domain. Now, in this paper we describe more properties of the SCC, such as: the independence of scaling and starting point for simple closed curves, arithmetic operations among convex shapes, the minimum and maximum values of the proposed noncircularity measure, the computation of the number of holes in a picture, and the computation of the Euler number. Finally, in order to illustrate the capabilities of the proposed method, we present the computation of topological properties of an example of a picture of the real world.