Subdivision of Maps of Digital Images

A digital image is a finite set of integer lattice points in an ambient Euclidean space together with a suitable adjacency relation between points. Subdivision, which is a process of enlarging a digital image in the photographic sense, provides a basic tool for operating with digital images. But given a map of digital images, there is as yet no general way to define a map of their subdivisions that might reasonably be called a subdivision of the map. In this paper, we construct such maps of subdivisions when the map of digital images has a 1- or 2-dimensional domain. From our constructions we deduce path covering and homotopy covering results that play a role in our development of the digital fundamental group.