Beyond the Hausdorff Metric in Digital Topology

TL;DR

This paper explores alternative measures for comparing digital images that better capture geometric and topological similarities than the Hausdorff metric alone, aiming to develop a more comprehensive image comparison framework.

Contribution

It introduces methods to compare digital objects based on properties beyond the Hausdorff metric, potentially combining multiple measures for enhanced similarity assessment.

Findings

Proposes alternative measures capturing geometric and topological properties

Suggests combining measures with Hausdorff metric for improved comparison

Highlights differences between Hausdorff closeness and property similarity

Abstract

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.