Connectivity Preserving Multivalued Functions in Digital Topology
This work addresses a theoretical problem in digital topology for researchers in image processing and computer vision, but it appears incremental as it builds on existing concepts of continuous multivalued functions.
The paper tackles the problem of modeling digital morphological operations by introducing connectivity preserving multivalued functions, which generalize continuous multivalued functions and are shown to be appropriate models, with properties like composition preservation and easy generalization to higher dimensions and arbitrary adjacency relations.
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.