A Note on Computable Proximity of $\mathcal{L}_1$-Discs on the Digital Plane

TL;DR

This paper explores how to measure the closeness of digital discs in the 2D digital plane using the $ ext{L}_1$-metric and a Jaccard-like metric, providing numerical characterizations of their intersections.

Contribution

It introduces a method to quantify the proximity of digital discs under the $ ext{L}_1$-metric using a Jaccard-like metric, advancing digital geometry analysis.

Findings

Numerical characterizations of intersecting digital discs

Application of a Jaccard-like metric in digital geometry

Insights into the proximity of digital discs in the $ ext{L}_1$-metric

Abstract

This paper investigates problems in the characterization of the proximity of digital discs. Based on the $\mathcal{L}_1$-metric structure for the 2D digital plane and using a Jaccard-like metric, we determine numerical characters for intersecting digital discs.