Boundary and shape complexity of a digital object

Abstract

The orthogonal convex hull is the minimal area convex polygon covering a digital object whereas an orthogonal convex skull is the maximal area convex polygon inscribing the digital object. A quantitative approach to analyse the complexity of a given hole-free digital object is presented in this paper. The orthogonal convex hull and an orthogonal convex skull are used together to derive the complexity of an object. The analysis is performed based on the regions added while deriving the orthogonal convex hull and the regions deleted while obtaining an orthogonal convex skull. Another measure for shape complexity using convexity tree derived from the orthogonal convex skull is also presented. The simple and novel approach presented in this paper is useful to derive several shape features of a digital object.