Matching shapes with a reference point

Authors:
Helmut Alt;Oswin Aichholzer;Günter Rote
Affiliations:
Freie Universität Berlin, Fachbereich Mathematik und Informatik, Takustraβe 9, D-14195 Berlin, Germany;Institut fur Grundlagen der Informationsverarbeitung, Technische Universität Graz, Schieβstattgasse 4, A-8010 Graz, Austria;Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria
Venue:
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Year:
1994

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Abstract

For two given point sets, we present a very simple (almost trivial) algorithm to translate one set so that the Hausdorff distance between the two sets is not larger than a constant factor times the minimum Hausdorff distance which can be achieved in this way. The algorithm just matches the so-called Steiner points of the two sets.The focus of our paper is the general study of reference points (like the Steiner point) and their properties with respect to shape matching.For more general transformations than translations, our method eliminates several degrees of freedom from the problem and thus yields good matchings with improved time bounds.