Digital Hausdorff distance on a connected digital image


Vergili T.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, vol.69, no.2, pp.76-88, 2020 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.31801/cfsuasmas.620674
  • Title of Journal : COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Page Numbers: pp.76-88
  • Keywords: digital topology, Hausdorff distance, MULTIVALUED FUNCTIONS

Abstract

A digital image X can be considered as a subset of Zn together with an adjacency relation where Z is the set of the integers and n is a natural number. The aim of this study is to measure the closeness of two subsets of a connected digital image. To do this, we adapt the Hausdorff distance in the topological setting to its digital version. In this paper, we define a metric on a connected digital image by using the length of the shortest digital simple path. Then we use this metric to de.ne the r-thickening of the subsets of a connected digital image and de.ne the digital Hausdorff distance between them.