A chance conversation with Ralph Kopperman in a German woods re-ignited my interest in image analysis and the possibility of using closure as a basic topological concept in digital images. (Recall that a closure operator C need only satisfy 3 basic properties: reflexivity, X \subseteq C(X); order preserving, X \subseteq Y implies C(X) \subseteq C(Y), and idempotency C(C(X)) = C(X). Of course, a particular digital topology may have additional properties of interest.

It has turned out that many of the resulting concepts are congruent to those already developed by Gabor Herman. For example, we have an interesting extension to his Jordan surface theorem.

In this talk, we will illustrate how two old image processing operators developed by Azriel Rosenfeld and myself in the late 60's fit into this newer topological framework. While the talk will be essentially confined to digital images, we will try to demonstrate its much wider applicability to computer science in general.