The Hausdorff distance between some sets of points

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.