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Recognition of Occluded Shapes Using Size Functions

  • Barbara Di Fabio
  • Claudia Landi
  • Filippo Medri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5716)

Abstract

The robustness against occlusions and the ability to perform not only global matching, but also partial matching are investigated in computer vision in order to evaluate the performance of shape descriptors. In this paper we consider the size function shape descriptor, and we illustrate some results about size functions of occluded shapes. Theoretical results indicate that size functions are able to detect a partial matching between shapes by showing a common subset of cornerpoints. Experiments are presented which outline the potential of the proposed approach in recognition tasks in the presence of occlusions.

Keywords

Size function shape occlusion cornerpoint Hausdorff distance 

References

  1. 1.
    Biasotti, S., Cerri, A., Frosini, P., Giorgi, D., Landi, C.: Multidimensional Size Functions for Shape Comparison. J. Math. Imaging Vis. 32(2), 161–179 (2008)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Biasotti, S., Cerri, A., Giorgi, D.: k-dimensional size functions for shape description and comparison. In: Proc. of ICIAP 2007, pp. 345–352 (2007)Google Scholar
  3. 3.
    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 Computing Surveys 40(4), 12:1–12:87 (2008)CrossRefGoogle Scholar
  4. 4.
    Biasotti, S., Giorgi, D., Spagnuolo, M., Falcidieno, B.: Reeb graphs for shape analysis and applications. Theor. Comput. Sci. 392(1-3), 5–22 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Biasotti, S., Marini, S., Spagnuolo, M., Falcidieno, B.: Sub-part correspondence by structural descriptors of 3D shapes. Computer-Aided Design 38(9), 1002–1019 (2006)CrossRefGoogle Scholar
  6. 6.
    Carlsson, G., Zomorodian, A., Collins, A., Guibas, L.: Persistence barcodes for shapes. International Journal of Shape Modeling 11, 149–187 (2005)CrossRefzbMATHGoogle Scholar
  7. 7.
    Cazals, F., Chazal, F., Lewiner, T.: Molecular shape analysis based upon the Morse-Smale complex and the Connolly function. In: Proc. of SCG 2003, pp. 351–360 (2003)Google Scholar
  8. 8.
    Cerri, A., Ferri, M., Giorgi, D.: Retrieval of trademarks images by means of size functions. Graphical Models 68, 451–471 (2006)CrossRefGoogle Scholar
  9. 9.
    d’Amico, M.: A New Optimal Algorithm for Computing Size Functions of Shapes. In: Proc. of CVPRIP Algoritms III, pp. 107–110 (2000)Google Scholar
  10. 10.
    d’Amico, M., Frosini, P., Landi, C.: Natural pseudo-distance and optimal matching between reduced size functions. Acta Appl. Math. (digitally available)Google Scholar
  11. 11.
    Di Fabio, B., Landi, C.: Čech homology for shape recognition in the presence of occlusions (preprint), http://arxiv.org/PS_cache/arxiv/pdf/0807/0807.0796v1.pdf
  12. 12.
    Ferri, M., Landi, C.: Representing size functions by complex polynomials. Proc. Math. Met. in Pattern Recognition 9, 16–19 (1999)Google Scholar
  13. 13.
    Landi, C., Frosini, P.: New pseudodistances for the size function space. In: Proc. SPIE, Vision Geometry VI, vol. 3168, pp. 52–60 (1997)Google Scholar
  14. 14.
    Höynck, M., Ohm, J.R.: Shape retrieval with robustness against partial occlusion. In: Proc. of IEEE ICASSP 2003, vol. 3, pp. 593–596 (2003)Google Scholar
  15. 15.
    Huttenlocher, D.P., Klanderman, G.A., Rucklidge, W.J.: Comparing images using the Hausdorff distance. IEEE Trans. PAMI 15, 850–863 (1993)CrossRefGoogle Scholar
  16. 16.
    Intille, S.S., Bobick, A.F.: Disparity-space images and large occlusion stereo. In: Proc. of ECCV 1994, vol. II, pp. 179–186 (1994)Google Scholar
  17. 17.
    Latecki, L.J., Lakämper, R., Wolter, D.: Optimal partial shape similarity. Image Vision Comput. 23(2), 227–236 (2005)CrossRefGoogle Scholar
  18. 18.
    Stanganelli, I., Brucale, A., Calori, L., Gori, R., Lovato, A., Magi, S., Kopf, B., Bacchilega, R., Rapisarda, V., Testori, A., Ascierto, P.A., Simeone, E., Ferri, M.: Computer-aided diagnosis of melanocytic lesions. Anticancer Res. 25, 4577–4582 (2005)Google Scholar
  19. 19.
    Veltkamp, R.C.: Shape matching: similarity measures and algorithms. In: Proc. of Shape Modeling International 2001, pp. 188–197 (2001)Google Scholar
  20. 20.
    Tanase, M., Veltkamp, R.C.: Part-based shape retrieval. In: Proc. of MULTIMEDIA 2005, pp. 543–546 (2005)Google Scholar
  21. 21.
    Uras, C., Verri, A.: Computing size functions from edge maps. Internat. J. Comput. Vis. 23(2), 169–183 (1997)CrossRefGoogle Scholar
  22. 22.
    Wolfson, H.J., Rigoutsos, I.: Geometric Hashing: An Overview. IEEE Computational Science and Engineering 4(4), 10–21 (1997)CrossRefGoogle Scholar
  23. 23.

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Barbara Di Fabio
    • 1
  • Claudia Landi
    • 2
  • Filippo Medri
    • 3
  1. 1.Dipartimento di MatematicaUniversità di BolognaItaly
  2. 2.Di.S.M.I.Università di Modena e Reggio EmiliaItaly
  3. 3.Dipartimento di Scienze dell’InformazioneUniversità di BolognaItaly

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