A unified topological framework for digital imaging

Abstract

In this article, a tractable modus operandi is proposed to model a (binary) digital image (i.e., an image defined on ℤn and equipped with a standard pair of adjacencies) as an image defined in the space of cubical complexes (double-struck Fn). In particular, it is shown that all the standard pairs of adjacencies in ℤn can then be correctly modelled in double-struck Fn. Moreover, it is established that the digital fundamental group of a digital image in ℤn is isomorphic to the fundamental group of its corresponding image in double-struck F n, thus proving the topological correctness of the proposed approach. From these results, it becomes possible to establish links between topology-oriented methods developed either in classical digital spaces (ℤn) or cubical complexes (double-struck Fn). © 2011 Springer-Verlag.