Extension of a one-dimensional convexity measure to two dimensions

In this paper we propose a new idea to design a measure for shape descriptors based on the concept of Q-convexity. The new measure extends the directional convexity measure defined in [2] to a two-dimensional convexity measure. The derived shape descriptors have the following features: (1) their values range from 0 to 1; (2) their values equal 1 if and only if the binary image is Q-convex; (3) they are invariant by reflection and point symmetry; (4) their computation can be easily and efficiently implemented.