$m-$homotopic Distances in Digital Images

TL;DR

This paper introduces the concept of digital m-homotopic distance and explores its properties, including invariance, while relating it to notions like m-category and m-complexity in digital topology and robotics.

Contribution

It defines new digital homotopic distance measures and investigates their invariance, connecting them with existing topological concepts in digital image analysis.

Findings

Defined digital m-homotopic distance and higher versions

Established homotopy invariance properties of these measures

Linked these concepts to m-category and m-complexity in digital topology

Abstract

We define digital $m-$homotopic distance and its higher version. We also mention related notions such as $m-$category in the sense of Lusternik-Schnirelmann and $m-$complexity in topological robotics. Later, we examine the homotopy invariance or $m-$homotopy invariance property of these concepts.