Chapter

Discrete and Computational Geometry

Volume 25 of the series Algorithms and Combinatorics pp 65-76

Computing the Hausdorff Distance of Geometric Patterns and Shapes

  • Helmut AltAffiliated withInstitute for Computer Science, Free University of Berlin
  • , Peter BraßAffiliated withInstitute for Computer Science, Free University of Berlin
  • , Michael GodauAffiliated withInstitute for Computer Science, Free University of Berlin
  • , Christian KnauerAffiliated withInstitute for Computer Science, Free University of Berlin
  • , Carola WenkAffiliated withInstitute for Computer Science, Free University of Berlin

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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,a ssuming d is a constant. In addition,w e present more efficient algorithms for special cases like sets of points,or line segments,or triangulated surfaces in three dimensions.