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Zbl 1104.68792
Alt, Helmut; Bra\ss, Peter; Godau, Michael; Knauer, Christian; Wenk, Carola
Computing the Hausdorff distance of geometric patterns and shapes. (English)
[A] Aronov, Boris (ed.) et al., Discrete and computational geometry. The Goodman-Pollack Festschrift. Berlin: Springer. Algorithms Comb. 25, 65-76 (2003). ISBN 3-540-00371-1/hbk

Summary: 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.

MSC 2000:: *68U05 Computational geometry, etc.

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Zentralblatt MATH Berlin [Germany]