3D Shape Matching through Topological Structures

  • Silvia Biasotti
  • Simone Marini
  • Michela Mortara
  • Giuseppe Patanè
  • Michela Spagnuolo
  • Bianca Falcidieno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)


This paper introduces a framework for the matching of 3D shapes represented by topological graphs. The method proposes as comparison algorithm an error tolerant graph isomorphism that includes a structured process for identifying matched areas on the input objects. Finally, we provide a series of experiments showing its capability to automatically compare complex objects starting from different skeletal representations used in Shape Modeling.


Topological Structure Geodesic Distance Node Pair Input Graph Topological Graph 
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.


  1. 1.
    Attene, M., Biasotti, S., Spagnuolo, M.: Shape understanding by contour driven retiling. The Visual Computer 19(2-3), 128–137 (2003)Google Scholar
  2. 2.
    Biasotti, S., Marini, S., Mortara, M., Patané, G.: An overview on properties and efficacy of topological skeletons in shape modelling. In: Proc. of Shape Modelling and Applications 2003, Seoul, pp. 245–254. IEEE Press, Los Alamitos (2003)Google Scholar
  3. 3.
    Bunke, H., Shearer, K.: A graph distance metric based on the maximal common subgraph. Pattern Recognition Letters 19, 255–259 (1998)zbMATHCrossRefGoogle Scholar
  4. 4.
    Gold, S., Rangarajan, A.: A Graduated Assignment Algorithm for Graph Matching. IEEE Trans. on Patt. Anal. Mach. Intell. 18(4), 377–388 (1996)CrossRefGoogle Scholar
  5. 5.
    Hétroy, F., Attali, D.: Topological Quadrangulations of Closed Triangulated Surfaces using the Reeb Graph. Graphical Models 65, 131–148 (2003)zbMATHCrossRefGoogle Scholar
  6. 6.
    Hilaga, M., Shinagawa, Y., Komura, T., Kunii, T.L.: Topology Matching for Fully Automatic Similarity Estimation of 3D Shapes. In: ACM Computer Graphics (Proc. of SIGGRAPH 2001), Los Angeles, pp. 203–212 (2001)Google Scholar
  7. 7.
    Kimia, B., Tannenbaum, A., Zucker, S.: Shapes, shocks, and deformations, I. Computer Vision 15, 189–224 (1995)CrossRefGoogle Scholar
  8. 8.
    Koo, K.G., Suganthan, P.N.: Multiple Relational Graphs Mapping Using Genetic Algorithms. In: Proc. of Congr. on Evolutionary Comp, pp. 727–733 (2001)Google Scholar
  9. 9.
    Jones, R.: Connected Filtering and Segmentation Using Component Trees. Computer Vision and Image Understanding 75(3), 215–228 (1999)CrossRefGoogle Scholar
  10. 10.
    Sundar, H., Silver, D., Gagvani, N., Dickinson, S.: Skeleton Based Shape Matching and retrieval. In: Proc. of Shape Modelling and Applications 2003, Seoul, pp. 130–139. IEEE Press, Los Alamitos (2003)Google Scholar
  11. 11.
    Lazarus, F., Verroust, A.: Level Set Diagrams of Polyhedral Objects. ACM Solid Modeling 1999, Ann Arbor, Michigan, pp. 130–140 (1999)Google Scholar
  12. 12.
    Luo, B., Hancock, E.R.: Symbolic Graph Matching using the EM Algorithm and Singular Value Decomposition. In: Proc. of Int. Conf. on Pattern Recognition, vol. 2, pp. 2141–2144 (2000)Google Scholar
  13. 13.
    Medasani, S., Krishnapuram, R., Choi, Y.: Graph Matching by Relaxation of Fuzzy Assignements. IEEE Trans. on Fuzzy Systems 9(1), 173–182 (2001)CrossRefGoogle Scholar
  14. 14.
    Mortara, M., Patanè, G., Spagnuolo, M., Falcidieno, B., Rossignac, J.: Blowing bubbles for multi-scale analysis and decomposition of triangle meshes. In: Algorithmica, Special Issue on Shape Algorithmics. Springer, Heidelberg (to appear)Google Scholar
  15. 15.
    Messmer, B.T., Bunke, H.: A New Algorithm for Error Tolerant Subgraph Isomorphism Detection. IEEE Trans. Patt. Anal. Mach. Intell. 20(5), 493–504 (1998)CrossRefGoogle Scholar
  16. 16.
    Milnor, J.: Morse Theory. Princeton University Press, New Jersey (1963)zbMATHGoogle Scholar
  17. 17.
    Mortara, M., Patané, G.: Shape-Covering for Skeleton Extraction. Int. J. of Shape Modelling 8(2), 245–252 (2002)Google Scholar
  18. 18.
    Reeb, G.: Sur les points singuliers d’une forme de Pfaff complètement intégrable ou d’une fonction numérique. Comptes Rendu Acad. Sciences 222, 847–849 (1946)zbMATHMathSciNetGoogle Scholar
  19. 19.
    Salembier, P., Oliveras, A., Garrido, L.: Anti-extensive connected operators for image and sequence processing. IEEE Trans. on Image Processing 7(4), 555–570 (1998)CrossRefGoogle Scholar
  20. 20.
    Shattuck, D., Leahy, R.: Automated graph based analysis and correction of cortical vaolume topology. IEEE Trans. on Medical Imaging 20(11), 1167–1177 (2001)CrossRefGoogle Scholar
  21. 21.
    Siddiqi, K., Shokoufandeh, A., Dickenson, S.J., Zucker Shock, S.W.: graphs and shape matching. In: Proc. of 6th Int. Conf on Computer Vision, pp. 222–229 (1998)Google Scholar
  22. 22.
    Veltkamp, R.C., Hagendoorn, M.: State-of-Art in Shape Matching. In: Lew, M. (ed.) IN Principles of Visual Information Retrieval, pp. 87–119. Springer, Heidelberg (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Silvia Biasotti
    • 1
  • Simone Marini
    • 1
  • Michela Mortara
    • 1
  • Giuseppe Patanè
    • 1
  • Michela Spagnuolo
    • 1
  • Bianca Falcidieno
    • 1
  1. 1.Istituto di Matematica Applicata e Tecnologie InformaticheConsiglio Nazionale delle Ricerche 

Personalised recommendations