The Hausdorff distance between some sets of points

Tomislav Marošević

Vol. 23 No. 2 (2018)

Regular Articles

The Hausdorff distance between some sets of points

Published 2018-04-03

Tomislav Marošević

Tomislav Marošević
Department of Mathematics, University of Osijek

Submission of an original manuscript to the Mathematical Communications will be taken to mean that it represents original work not previously published, that it is not being considered elsewhere for publication; and, if accepted for publication, it will be published in print and online form and it will not be published elsewhere in the same form, for commercial purposes, in any language, without the consent of the publisher. The journal takes the stance that the publication of scholarly research is meant to disseminate knowledge and, in a not-for-profit regime, benefits neither publisher nor author financially. It sees itself as having an obligation to its authors and to society to make content available online now that the technology allows for such a possibility.

Abstract

Hausdorff distance can be used in various areas, where the problems of shape matching and comparison appear. We look at the Hausdorff distance between two hyperspheres in $\mathbb{R}^n$. With respect to different geometric objects, the Hausdorff distance between a segment and a hypersphere in $\mathbb{R}^n$ is given, too. Using the Mahalanobis distance, a modified Hausdorff distance between a segment and an ellipse in the plane, and generally between a segment and a hyper-ellipsoid in $\mathbb{R}^n$ is adopted. Finally, the modified Hausdorff distance between ellipses is obtained.

Keywords

Hausdorff distance, segment, circle, ellipse

PDF

Supplementary File(s)

FigHDb.eps FigHDa.eps FigHDc.eps FigHDd.eps Fig2n.eps Fig31n.eps Fig32n.eps Fig4n.eps LaTeX file

Author Biography

Tomislav Marošević

Assistant Professor