Subsets and Freezing Sets in the Digital Plane

TL;DR

This paper advances the understanding of freezing sets in digital images, providing new methods to determine minimal freezing sets for subsets of the digital plane, specifically in Z^2.

Contribution

It introduces novel techniques for obtaining and analyzing freezing sets in digital images, focusing on minimal sets in the digital plane Z^2.

Findings

Methods for obtaining freezing sets in Z^2 digital images.

Examples illustrating how to determine minimal freezing sets.

Enhanced understanding of freezing set structures in digital topology.

Abstract

We continue the study of freezing sets for digital images introduced in [4, 2, 3]. We prove methods for obtaining freezing sets for digital images (X, c_i) for X \subset Z^2 and i \in {1, 2}. We give examples to show how these methods can lead to the determination of minimal freezing sets.