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Algorithmica

, Volume 21, Issue 1, pp 89–103 | Cite as

Matching Convex Shapes with Respect to the Symmetric Difference

  • H. Alt
  • U. Fuchs
  • G. Rote
  • G. Weber

Abstract.

This paper deals with questions from convex geometry related to shape matching. In particular, we consider the problem of moving one convex figure over another, minimizing the area of their symmetric difference. We show that if we just let the two centers of gravity coincide, the resulting symmetric difference is within a factor of 11/3 of the optimum. This leads to efficient approximate matching algorithms for convex figures.

Key words. Computational geometry, Convex geometry, Shape matching, Centroid. 

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Copyright information

© Springer-Verlag New York Inc. 1998

Authors and Affiliations

  • H. Alt
    • 1
  • U. Fuchs
    • 2
  • G. Rote
    • 3
  • G. Weber
    • 4
  1. 1.Institut für Informatik, Freie Universität Berlin, Takustraße 9, D-14195 Berlin, Germany. alt@inf.fu-berlin.deDE
  2. 2.Institut für Informatik, Freie Universität Berlin, Takustraße 9, D-14195 Berlin, Germany. fuchs@inf.fu-berlin.de.DE
  3. 3.Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, {A-8010 Graz}, Austria. rote@opt.math.tu-graz.ac.at.AT
  4. 4.Institut für Informatik, Freie Universität Berlin, Takustraße 9, D-14195 Berlin, Germany. weber@inf.fu-berlin.de.DE

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