Polyhedral Representation and Adjacency Graph in n-dimensional Digital Images

In this paper we generalize the concept of digital topology to arbitrary dimension n, in the context of (2n, 3n−1)-adjacency. We define an n-digital image P as an uplet (Zn, R, H), where H is a finite subset of Zn and R represents the adjacency relation in the whole lattice in a specific way. We give a natural and simple construction of polyhedral representation of P based on cubical-complex decomposition. We develop general properties which provide a link between connectivity in digital and Euclidean space. This enables us to use methods of continuous topology in studying properties related to the connectivity, adjacency graph, and borders connectivity in n-digital images.