A digital fundamental group

Abstract

A group analogous to the fundamental group is defined for binary digital pictures based on almost arbitrary lattices and adjacency relations. This digital fundamental group has an immediate application to image processing—it can be used to give a precise statement of what it means for a three-dimensional image thinning algorithm to preserve topology. Given any suitably well-behaved digital picture, it is possible to construct a polyhedral set whose fundamental groups are naturally isomorphic to the digital fundamental groups of the digital picture. This result confirms that the digital fundamental group has been appropriately defined.