Matching convex shapes with respect to the symmetric difference

  • Helmut Alt
  • Ulrich Fuchs
  • Günter Rote
  • Gerald Weber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1136)


This paper deals with questions from convex geometry related to shape matching. In particular, we consider the problem of matching convex figures minimizing the area of the symmetric difference. The main theorem of this paper states, that if we just match the two centers of gravity the resulting symmetric difference is within a factor of 11/3 from the optimal one. This leads to efficient approximate matching algorithms for convex figures.


Reference Point Convex Body Convex Polygon Rigid Motion Steiner Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Helmut Alt
    • 1
  • Ulrich Fuchs
    • 1
  • Günter Rote
    • 2
  • Gerald Weber
    • 1
  1. 1.Institut für InformatikFreie Universität BerlinBerlinGermany
  2. 2.Institut für MathematikTechnische Universität GrazGrazAustria

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