Dergiler / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2020 / Cilt: 69 - Sayı: 2

DIGITAL HAUSDORFF DISTANCE ON A CONNECTED DIGITAL IMAGE

DIGITAL HAUSDORFF DISTANCE ON A CONNECTED DIGITAL IMAGE

Tane VERGILI

Sayfa
1070–1082
DOI
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Abstract

A digital image E 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 define the r-thickening of the subsets of a connected digital image and define the digital Hausdorff distance between them.