A survey of algebraic methods in digital topology

Abstract

Digital topology is the study of the topological properties of digital images. In most of the literature, a digital image has been endowed with a graph structure; the vertices being the points of the image, and the edges giving the connectivity between the points. This has enabled the use of combinatorial methods to provide theorems and proofs for basic topological results. However, these methods have been shown to be inadequate for a full discussion of object thinning in three dimensions, and also for the development of a topological theory in dimensions higher than three. This has led to the investigation of algebraic topology as a means of providing results in digital topology; this paper surveys the results so far obtained, and shows how they relate to classical algebraic topology, and to digital topology as it has developed over the last two decades.