Ronse deletability conditions and (N,k)-retractions

► We consider retractions defined by digitally continuous multivalued maps. ► A special kind of retractions, called (N,k)-retractions, is considered. ► Deletion of simple points and many thinning algorithms are (N,k)-retractions. ► We characterize thinning algorithms that can be modeled as (N,k)-retractions. ► Characterization in terms of Ronse-like conditions for topology preservation.