Structuring Digital Plane by Closure Operators Associated with n-ary Relations

Abstract

We associate a closure operator with every n-ary relation (\(n>1\) an integer) on a given set. We focus on certain n-ary relations on the digital line \(\mathbb {Z}\) and study the closure operators on the digital plane \(\mathbb {Z}^2\) that are associated with special products of pairs of the relations. These closure operators, which include the Khalimsky topology, are shown to provide well behaved connectedness, so that they may be used as background structures on the digital plane for the study of digital images.