Ronse deletability conditions and (N, k)-retractions

摘要

In some recent papers we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued maps, provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we have characterized the deletion of simple points and some well known parallel thinning algorithm as a particular type of retractions, called (Ν, k)-retrac-tions. In this paper we give a full characterization of the thinning algorithms that can be modeled as (Ν, k retractions. This class agrees, with minor modifications, with the class of thinning algorithms satisfying Ronse sufficient conditions for preservation of topology.