Shape Similarity Based on a Treelet Kernel with Edition

  • Sébastien Bougleux
  • François-Xavier Dupé
  • Luc Brun
  • Myriam Mokhtari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7626)


Several shape similarity measures, based on shape skeletons, are designed in the context of graph kernels. State-of-the-art kernels act on bags of walks, paths or trails which decompose the skeleton graph, and take into account structural noise through edition mechanisms. However, these approaches fail to capture the complexity of junctions inside skeleton graphs due to the linearity of the patterns. To overcome this drawback, tree patterns embedded in the plane have been proposed to decompose the skeleton graphs. In this paper, we reinforce the behaviour of kernel based on tree patterns by explictly incorporating an edition mechanism adapted to tree patterns.


shape similarity kernel methods tree patterns edition 


  1. 1.
    Pelillo, M., Siddiqi, K., Zucker, S.: Matching hierarchical structures using association graphs. IEEE Trans. on PAMI 21(11), 1105–1120 (1999)CrossRefGoogle Scholar
  2. 2.
    Kashima, H., Tsuda, K., Inokuchi, A.: Marginalized kernels between labeled graphs. In: Proc. of the 20st Int. Conf. on Machine Learning, pp. 321–328 (2003)Google Scholar
  3. 3.
    Goh, W.B.: Strategies for shape matching using skeletons. Computer Vision and Image Understanding 110(3), 326–345 (2008)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Dupé, F.X., Brun, L.: Edition within a Graph Kernel Framework for Shape Recognition. In: Torsello, A., Escolano, F., Brun, L. (eds.) GbRPR 2009. LNCS, vol. 5534, pp. 11–20. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Dupé, F.X., Brun, L.: Tree Covering within a Graph Kernel Framework for Shape Classification. In: Foggia, P., Sansone, C., Vento, M. (eds.) ICIAP 2009. LNCS, vol. 5716, pp. 278–287. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Shervashidze, N., Vishwanathan, S.V.N., Petri, T.H., Mehlhorn, K., Borgwardt, K.M.: Efficient graphlet kernels for large graph comparison. In: Proc. of the 12th Int. Conf. on Artificial Intelligence and Statistics, pp. 488–495 (2009)Google Scholar
  7. 7.
    Mahé, P., Vert, J.P.: Graph kernels based on tree patterns for molecules. Machine Learning 75, 3–35 (2009)CrossRefGoogle Scholar
  8. 8.
    Gaüzère, B., Brun, L., Villemin, D.: Two New Graph Kernels and Applications to Chemoinformatics. In: Jiang, X., Ferrer, M., Torsello, A. (eds.) GbRPR 2011. LNCS, vol. 6658, pp. 112–121. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Bougleux, S., Dupé, F.X., Brun, L., Gaüzère, B., Mokhtari, M.: Shape similarity based on combinatorial maps and a tree pattern kernel. In: 21st Int. Conf. on Pattern Recognition (2012)Google Scholar
  10. 10.
    Brun, L., Mokhtari, M., Domenger, J.P.: Incremental modifications on segmented image defined by discrete maps. Journal of Visual Communication and Image Representation 14, 251–290 (2003)CrossRefGoogle Scholar
  11. 11.
    Cori, R.: Computation of the automorphism group of a topological graph embedding. Technical Report I-8612, Université Bordeaux 1, France (1985)Google Scholar
  12. 12.
    Bougleux, S., Brun, L.: Symmetry group of 2d combinatorial maps. Technical report, GREYC, France (2012)Google Scholar
  13. 13.
    Neuhaus, M., Bunke, H.: Edit-distance based kernel for structural pattern classification. Pattern Recognition 39, 1852–1863 (2006)zbMATHCrossRefGoogle Scholar
  14. 14.
    Sharvit, D., Chan, J., Tek, H., Kimia, B.B.: Symmetry-based indexing of image databases. Journal of Visual Communication and Image Representation 9(4), 366–380 (1998)CrossRefGoogle Scholar
  15. 15.
    Gdalyahu, Y., Weinshall, D.: Flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes. IEEE Trans. on PAMI 21(2), 1312–1328 (1999)CrossRefGoogle Scholar
  16. 16.
    Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE Trans. on PAMI 24(4), 509–522 (2002)CrossRefGoogle Scholar
  17. 17.
    Ling, H., Jacobs, D.W.: Shape classification using the inner-distance. IEEE Trans. on PAMI 29(2), 286–299 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sébastien Bougleux
    • 1
  • François-Xavier Dupé
    • 2
  • Luc Brun
    • 3
  • Myriam Mokhtari
    • 3
  1. 1.GREYC CNRS UMR 6072Université de Caen Basse-NormandieFrance
  2. 2.CNRS UMR 7279 - LIFAix-Marseille UniversitéFrance

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