Advertisement

Multi-scale Approximation of the Matching Distance for Shape Retrieval

  • Andrea Cerri
  • Barbara Di Fabio
  • Filippo Medri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7309)

Abstract

This paper deals with the concepts of persistence diagrams and matching distance. They are two of the main ingredients of Topological Persistence, which has proven to be a promising framework for shape comparison. Persistence diagrams are descriptors providing a signature of the shapes under study, while the matching distance is a metric to compare them. One drawback in the application of these tools is the computational costs for the evaluation of the matching distance. The aim of the present paper is to introduce a new framework for the approximation of the matching distance, which does not affect the reliability of the entire approach in comparing shapes, and extremely reduces computational costs. This is shown through experiments on 3D-models.

Keywords

Persistence diagram shape analysis dissimilarity criterion 

References

  1. 1.
    Biasotti, S., De Floriani, L., Falcidieno, B., Frosini, P., Giorgi, D., Landi, C., Papaleo, L., Spagnuolo, M.: Describing shapes by geometrical-topological properties of real functions. ACM Comput. Surv. 40(4), 1–87 (2008)CrossRefGoogle Scholar
  2. 2.
    Biasotti, S., Cerri, A., Frosini, P., Giorgi, D.: A new algorithm for computing the 2-dimensional matching distance between size functions. Pattern Recognition Letters 32(14), 1735–1746 (2011)CrossRefGoogle Scholar
  3. 3.
    Bronstein, A., Bronstein, M., Kimmel, R.: Numerical Geometry of Non-Rigid Shapes, 1st edn. Springer Publishing Company, Incorporated (2008)Google Scholar
  4. 4.
    Carlsson, G., Zomorodian, A., Collins, A., Guibas, L.J.: Persistence barcodes for shapes. IJSM 11(2), 149–187 (2005)zbMATHGoogle Scholar
  5. 5.
    Chazal, F., Cohen-Steiner, D., Guibas, L.J., Mémoli, F., Oudot, S.: Gromov-Hausdorff stable signatures for shapes using persistence. Computer Graphics Forum 28(5), 1393–1403 (2009)CrossRefGoogle Scholar
  6. 6.
    d’Amico, M., Frosini, P., Landi, C.: Using matching distance in size theory: A survey. Int. J. Imag. Syst. Tech. 16(5), 154–161 (2006)CrossRefGoogle Scholar
  7. 7.
    d’Amico, M., Frosini, P., Landi, C.: Natural pseudo-distance and optimal matching between reduced size functions. Acta. Appl. Math. 109, 527–554 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Di Fabio, B., Landi, C., Medri, F.: Recognition of Occluded Shapes Using Size Functions. In: Foggia, P., Sansone, C., Vento, M. (eds.) ICIAP 2009. LNCS, vol. 5716, pp. 642–651. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Edelsbrunner, H., Harer, J.: Computational Topology: An Introduction. American Mathematical Society (2009)Google Scholar
  10. 10.
    Frosini, P., Landi, C.: Size theory as a topological tool for computer vision. Pattern Recogn. and Image Anal. 9, 596–603 (1999)Google Scholar
  11. 11.
    Smeulders, A.W.M., Worring, M., Santini, S., Gupta, A., Jain, R.: Content-based image retrieval at the end of the early years. IEEE Trans. PAMI 22(12) (2000)Google Scholar
  12. 12.
    Tangelder, J.W.H., Veltkamp, R.C.: A survey of content-based 3D shape retrieval methods. Multimedia Tools and Applications 39(3), 441–471 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andrea Cerri
    • 1
  • Barbara Di Fabio
    • 1
  • Filippo Medri
    • 2
  1. 1.ARCESUniversità di BolognaItalia
  2. 2.Dipartimento di Scienze dell’InformazioneUniversità di BolognaItalia

Personalised recommendations