From a 2D Shape to a String Structure Using the Symmetry Set

  • Arjan Kuijper
  • Ole Fogh Olsen
  • Peter Giblin
  • Philip Bille
  • Mads Nielsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3022)


Many attempts have been made to represent families of 2D shapes in a simpler way. These approaches lead to so-called structures as the Symmetry Set (\(\mathcal{SS}\)) and a subset of it, the Medial Axis (\(\mathcal{MA}\)).

In this paper a novel method to represent the \(\mathcal{SS}\) as a string is presented. This structure is related to so-called arc-annotated sequences, and allows faster and simpler query algorithms for comparison and database applications than graph structures, used to represent the \(\mathcal{MA}\).

Example shapes are shown and their data structures derived. They show the stability and robustness of the \(\mathcal{SS}\) and its string representation.


String Representation Graph Structure Medial Axis Cusp Point Circle Tangent 
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 2004

Authors and Affiliations

  • Arjan Kuijper
    • 1
  • Ole Fogh Olsen
    • 1
  • Peter Giblin
    • 2
  • Philip Bille
    • 3
  • Mads Nielsen
    • 1
  1. 1.Image Group, IT-University of CopenhagenCopenhagenDenmark
  2. 2.Department of Mathematical SciencesThe University of LiverpoolLiverpoolUnited Kingdom
  3. 3.Algorithm GroupIT-University of CopenhagenCopenhagenDenmark

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