Resemblance and symmetries of geometric patterns

  • Helmut Alt
  • Johannes Blömer
Geometric Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 594)


This article is a survey on research done in recent years at FU Berlin applying methods from Computational Geometry to problems in pattern and shape analysis. In particular, algorithms are described for determining the exact and approximate congruence of finite sets of points in the plane. This problem is generalized to polygonal curves in the plane, where variuos cases are considered depending on the set of rigid motions (translations, rotations) allowed to match the given curves. Furthermore, algorithms are given for approximating convex polygons by ”simpler“ curves. In addition, the problem of finding all symmetries of a finite set of points is considered, the approximate version of which turns out to be NP-complete in general.


Symmetry Group Convex Polygon Geometric Object Simple Polygon Polygonal Chain 
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 1992

Authors and Affiliations

  • Helmut Alt
  • Johannes Blömer
    • 1
  1. 1.Fachbereich MathematikFU BerlinBerlin 33Germany

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