A suggested generalization for the lacunarity index

Nowadays, lacunarity is a well-accepted concept to complement fractality studies of complex sets. Lacunarity features are used to assess the largeness of gaps or holes of complex signals and images. As it stands, the lacunarity analysis used is an index averaging the behavior of small- and large-size structures in a given set. The aim of this work is to propose a generalized lacunarity concept on the basis of generalized moments. In this form, the lacunarity index, depending on a discrimination parameter, is oriented to quantify lacunarity associated with objects of different size. Textbook and real images are used to illustrate the ability of the generalized lacunarity index for displaying interesting features of real complex sets.