Advertisement

Machine Vision and Applications

, Volume 24, Issue 2, pp 435–445 | Cite as

Retrieving 2D shapes using caterpillar decomposition

  • M. Fatih DemirciEmail author
Short Paper

Abstract

Graphs provide effective data structures modeling complex relations and schemaless data such as images, XML documents, circuits, compounds, and proteins. Given a query graph, finding sufficiently similar database graphs without performing a sequential search is an important problem arising in different domains. In this paper, we propose a new method for indexing tree structures based on a graph-theoretic concept called caterpillar decomposition. Our algorithm starts by representing each tree along with its subtrees in the geometric space using its caterpillar decomposition. After representing the query in the same fashion, similar database trees are retrieved efficiently by means of nearest neighbor searches. We have successfully evaluated the proposed algorithm on two shape databases and include a set of perturbation experiments that establish the algorithm’s robustness to noise. We have also shown that the approach compares favorably to previous approaches for shape retrieval on these datasets.

Keywords

Shape retrieval Indexing Caterpillar decomposition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berretti S., Del Bimbo A., Vicario E.: Efficient matching and indexing of graph models in content-based retrieval. IEEE Trans. Pattern Anal. Mach. Intell. 23, 1089–1105 (2001)CrossRefGoogle Scholar
  2. 2.
    Bicego, M., Lagorio, A., Grosso, E., Tistarelli, M.: On the use of sift features for face authentication. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshop, CVPRW ’06, IEEE Computer Society, Washington, DC (2006)Google Scholar
  3. 3.
    Blum H.: Biological shape and visual science (Part I). J. Theor. Biol. 38(2), 205–287 (1973)CrossRefGoogle Scholar
  4. 4.
    Chen, Q., Lim, A., Ong, K.: D(k)-index: an adaptive structural summary for graph-structured data. In: Proceedings of the 2003 ACM SIGMOD international conference on Management of data, pp. 134–144, ACM, New York (2003)Google Scholar
  5. 5.
    Demirci, M.F.:Graph-based shape indexing. Mach. Vis. Appl. pp. 1–15, (2010) doi: 10.1007/s00138-010-0290-z
  6. 6.
    Demirci M.F., van Leuken R.H., Veltkamp R.C.: Indexing through Laplacian spectra. Comput. Vis. Image Understand. 110(3), 312–325 (2008)CrossRefGoogle Scholar
  7. 7.
    Fergus, R., Perona, P., and Zisserman, A.: Object class recognition by unsupervised scale-invariant learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 264–271. IEEE Comput. Soc. (2003)Google Scholar
  8. 8.
    Garey M.R., Johnson D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)zbMATHGoogle Scholar
  9. 9.
    Geusebroek J., Burghouts G., Smeulders A.: The Amsterdam library of object images. Int. J. Comput. Vis. 61(1), 103–112 (2005)CrossRefGoogle Scholar
  10. 10.
    Giblin P., Kimia B.: On the local form and transitions of symmetry sets, medial axes, and shocks. Int. J. Comput. Vis. 54(1–3), 143–156 (2003)zbMATHCrossRefGoogle Scholar
  11. 11.
    Goedemé T., Nuttin M., Tuytelaars T., Van Gool L.: Omnidirectional vision based topological navigation. Int. J. Comput. Vis. 74, 219–236 (2007)CrossRefGoogle Scholar
  12. 12.
    Gupta, A.: Embedding tree metrics into low dimensional euclidean spaces. In: Proceedings of the Thirty-first Annual ACM symposium on Theory of computing, pp. 694–700, ACM, New York (1999)Google Scholar
  13. 13.
    Lowe D.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60, 91–110 (2004)CrossRefGoogle Scholar
  14. 14.
    Matousek J.: On embedding trees into uniformly convex banach spaces. Isr. J. Math. 237, 221–237 (1999)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Messmer B.T., Bunke H.: A new algorithm for error-tolerant subgraph isomorphism detection. IEEE Trans. Pattern Anal. Mach. Intell. 20, 493–504 (1998)CrossRefGoogle Scholar
  16. 16.
    Messmer B.T., Bunke H.: A decision tree approach to graph and subgraph isomorphism detection. Pattern Recognit. 32(12), 1979–1998 (1999)CrossRefGoogle Scholar
  17. 17.
    Min J., Chung C., Shim K.: An adaptive path index for xml data using the query workload. Inf. Syst. 30(6), 467–487 (2005)CrossRefGoogle Scholar
  18. 18.
    Nister, D., Stewenius, H.:Scalable recognition with a vocabulary tree. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2161–2168, IEEE Computer Society, Washington, DC (2006)Google Scholar
  19. 19.
    Petrakis E.G.M., Faloutsos C.: Similarity searching in medical image databases. IEEE Trans. Knowl. Data Eng. 9, 435–447 (1997)CrossRefGoogle Scholar
  20. 20.
    Se S., Lowe D., Little J.: Mobile robot localization and mapping with uncertainty using scale-invariant visual landmarks. Int. J. Robot. Res. 21, 735–758 (2002)CrossRefGoogle Scholar
  21. 21.
    Shasha, D., Wang, J., Giugno, R.: Algorithmics and applications of tree and graph searching. In: Proceedings of the 21st ACM SIGMOD-SIGACT-SIGART symposium on Principles of Database Systems, pp. 39–52, ACM, New York (2002)Google Scholar
  22. 22.
    Shih F., Kowalski A.: Computing unique three-dimensional object aspects representation. Inf. Sci. 132, 13–22 (2001)zbMATHCrossRefGoogle Scholar
  23. 23.
    Shilane, P., Min, P., Kazhdan, M., Funkhouser, T.: The Princeton shape benchmark. In: Proceedings of the Shape Modeling International, pp. 167–178, IEEE Computer Society, Washington, DC (2004)Google Scholar
  24. 24.
    Shokoufandeh A., Macrini D., Dickinson S., Siddiqi K., Zucker S.W.: Indexing hierarchical structures using graph spectra. IEEE Trans. Pattern Anal. Mach. Intell. 27(7), 1125–1140 (2005)CrossRefGoogle Scholar
  25. 25.
    Uhlmann J.K.: Satisfying general proximity/similarity queries with metric trees. Inf. Process. Lett. 40, 175–179 (1991)zbMATHCrossRefGoogle Scholar
  26. 26.
    Yan, X., Yu, P., Han, J.: Graph indexing: a frequent structure-based approach. In: Proceedings of the 2004 ACM SIGMOD International Conference on Management of Data, pp. 335–346, ACM, New York (2004)Google Scholar
  27. 27.
    Yilmaz, F., Demirci, M.F.: Indexing tree structures through caterpillar decomposition. In: Heyden, A., Kahl, F. (eds.) SCIA volume 6688 of Lecture Notes in Computer Science, pp. 687–696. Springer (2011)Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Computer EngineeringTOBB University of Economics and TechnologyAnkaraTurkey

Personalised recommendations