Measuring the Similarity of Geometric Graphs

  • Otfried Cheong
  • Joachim Gudmundsson
  • Hyo-Sil Kim
  • Daria Schymura
  • Fabian Stehn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5526)

Abstract

What does it mean for two geometric graphs to be similar? We propose a distance for geometric graphs that we show to be a metric, and that can be computed by solving an integer linear program. We also present experiments using a heuristic distance function.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alt, H., Guibas, L.J.: Discrete geometric shapes: Matching, interpolation, and approximation. In: Handbook of Computational Geometry, pp. 121–153. Elsevier B.V., Amsterdam (2000)CrossRefGoogle Scholar
  2. 2.
    Fu, K.S.: Syntactic Pattern Recognition and Applications. Prentice-Hall, Englewood Cliffs (1982)MATHGoogle Scholar
  3. 3.
    Imai, H., Iri, M.: Polygonal approximations of a curve - formulations and algorithms. In: Toussaint, G.T. (ed.) Computational Morphology, pp. 71–86. Elsevier B.V., Amsterdam (1988)Google Scholar
  4. 4.
    Itai, A., Papadimitriou, C.H., Szwarcfiter, J.L.: Hamilton paths in grid graphs. SIAM Journal on Computing 11(4), 676–686 (1982)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Justice, D., Hero, A.: A binary linear programming formulation of the graph edit distance. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(8), 1200–1214 (2006)CrossRefGoogle Scholar
  6. 6.
    Lucas, S., Vidal, E., Amiri, A., Hanlon, S., Amengual, J.C.: A comparison of syntactic and statistical techniques for off-line OCR. In: 2nd International Colloquium Grammatical Inference and Applications, pp. 168–179. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  7. 7.
    Pavlidis, T.: Structural Pattern Recognition. Springer, New York (1977)CrossRefMATHGoogle Scholar
  8. 8.
    Rubner, Y., Tomasi, C., Guibas, L.J.: The earth mover’s distance as a metric for image retrieval. International Journal of Computer Vision 40(2) (2000), http://robotics.stanford.edu/~rubner

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Otfried Cheong
    • 1
  • Joachim Gudmundsson
    • 2
  • Hyo-Sil Kim
    • 1
  • Daria Schymura
    • 3
  • Fabian Stehn
    • 3
  1. 1.KAISTKorea
  2. 2.NICTAAustralia
  3. 3.FU BerlinGermany

Personalised recommendations