Characterizations of simple points, simple edges and simple cliques of digital spaces: One method of topology-preserving transformations of digital spaces by deleting simple points and edges

The notion of a simple point plays an important role in topology-preserving thinning, skeletonization and simplification of digital images. This paper presents new dimension-independent characterizations of simple points, simple edges and simple cliques based on the notion of a digital contractible space and contractible transformations of digital spaces. We show that a given digital space can be transformed to a normal digital space by the removal of simple points, edges and cliques while preserving topology. We describe a topology-preserving thinning algorithm, which transforms a given digital image to a normal one.