Essential concepts of digital topology\\ (digital $k$-connectivity and $k$-adjacencis for digital products)

TL;DR

This paper reviews fundamental concepts in digital topology such as digital $k$-connectivity and adjacency, clarifies their origins, and discusses their application to digital products, correcting inaccuracies in prior literature.

Contribution

It provides a clear explanation of digital $k$-connectivity and adjacency, and addresses inaccuracies in previous references, enhancing understanding of digital topology concepts.

Findings

Clarification of digital $k$-connectivity and adjacency concepts

Correction of historical inaccuracies in prior literature

Enhanced understanding of digital topology fundamentals

Abstract

The paper refers to several concepts which are essential to studying digital objects from the viewpoint of digital topology: digital $k$-connectivity or digital $k$-adjacency, $C$-compatible and normal $k$-adjacency for a digital product. Since L. Boxer has often mentioned the origins of these concepts in an inaccurate way, we discuss something incorrectly cited or mentioned in Boxer's papers according to the facts.