Connectivity Preserving Multivalued Functions in Digital Topology

TL;DR

This paper introduces and analyzes connectivity preserving multivalued functions in digital topology, showing they generalize continuous functions and are suitable for digital morphological operations, with advantages like compositionality and higher-dimensional applicability.

Contribution

The paper defines connectivity preserving multivalued functions, demonstrating their suitability for digital morphology and their advantages over continuous functions, including compositionality and higher-dimensional generalization.

Findings

Connectivity preserving functions generalize continuous functions.

These functions are preserved under composition.

They extend naturally to higher dimensions and various adjacency relations.

Abstract

We study connectivity preserving multivalued functions between digital images. This notion generalizes that of continuous multivalued functions studied mostly in the setting of the digital plane $Z^2$. We show that connectivity preserving multivalued functions, like continuous multivalued functions, are appropriate models for digital morpholological operations. Connectivity preservation, unlike continuity, is preserved by compositions, and generalizes easily to higher dimensions and arbitrary adjacency relations.