Computing the Hausdorff Distance of Geometric Patterns and Shapes Helmut Alt

Abstract

A very natural distance measure for comparing shapes and patterns is the Hausdorff distance. In this article we develop algorithms for computing the Hausdorff distance in a very general 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.