Computing the Hausdorff Distance of Geometric Patterns and Shapes

Abstract

A very natural distance measure for comparing shapes and patterns is the Hausdorff distance. In this article we develop algorithms for computin the Hausdorff distance en a very gneral case in which geometric objects are represented by finite collections of k-dimensional simplices in d-dimensional space. The algorithms are polynomial in the size of the input, assuming d is a constant. In addition, we present more efficient algorithms for special cases like sets of points, or line segments, or triangulated surfaces in three dimensions.