Convexity and Freezing Sets in Digital Topology
Laurence Boxer
TL;DR
This paper investigates the properties of freezing sets in digital topology, focusing on identifying minimal freezing sets for convex disks in the digital plane and highlighting the importance of convexity assumptions.
Contribution
It introduces methods to find minimal freezing sets for convex disks in digital topology and emphasizes the role of convexity in these sets.
Findings
Minimal freezing sets can be determined for convex disks in Z^2
Convexity is crucial for the properties of freezing sets
Examples demonstrate the significance of convexity assumptions
Abstract
We continue the study of freezing sets in digital topology, introduced in [2]. We show how to find a minimal freezing set for a "thick" convex disk X in the digital plane Z^2. We give examples showing the significance of the assumption that X is convex.
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Taxonomy
TopicsDigital Image Processing Techniques · Topological and Geometric Data Analysis · Medical Image Segmentation Techniques