Open AccessBeyond the Hausdorff metric in digital topology
Author(s) -
Laurence Boxer
Publication year - 2022
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 13
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2022.15893
Subject(s) - mathematics , hausdorff distance , metric (unit) , hausdorff space , urysohn and completely hausdorff spaces , topology (electrical circuits) , metric space , hausdorff measure , pure mathematics , hausdorff dimension , mathematical analysis , combinatorics , operations management , economics
Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that objects close in each of these measures have some similar geometric or topological property. Such measures may be combined with the Hausdorff metric to yield a metric in which close images are similar with respect to multiple properties.