Advertisement

The Visual Computer

, Volume 30, Issue 11, pp 1233–1245 | Cite as

A sparse coding approach for local-to-global 3D shape description

  • Davide Boscaini
  • Umberto Castellani
Original Article

Abstract

The definition of reliable shape descriptors is an essential topic for 3D object retrieval. In general, two main approaches are considered: global, and local. Global approaches are effective in describing the whole object, while local ones are more suitable to characterize small parts of the shape. Recently some strategies to combine these two approaches have been proposed which are mainly concentrated to the so-called bag of words paradigm. With this paper we address this problem and propose an alternative strategy that goes beyond the bag of word approach. In particular, a sparse coding technique is exploited for the 3D domain: a set of local shape descriptors are collected from the shape, and then a dictionary is trained as generative model. In this fashion the dictionary is used as global shape descriptor for shape retrieval purposes. Several experiments are performed on standard databases in order to evaluate the proposed method in challenging situations like the case of ‘SHREC 2011: robustness benchmark’ where strong shape transformations are included, and the case of ‘SHREC 2007: partial matching track’ where composite models are considered in the query phase. A drastic improvement of the proposed method is observed by showing that sparse coding approach is particularly suitable for local-to-global description and outperforms other approaches such as the bag of words.

Keywords

3D object retrieval Sparse coding  Bag of words  Partial shape matching 

Notes

Acknowledgments

We would like to thank Alex and Michael Bronstein for useful suggestions and fruitful discussions.

References

  1. 1.
    Aubry, M., Schlickewei, U., Cremens, D.: The wave kernel signature: a quantum mechanical approach to shape analysis. In: Proc. of ICCV Workshop Dyn. Shape Capture Anal. (4DMOD) (2011)Google Scholar
  2. 2.
    Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE Trans. Pattern Anal. Mach. Intell. 24(24), 509–522 (2002)CrossRefGoogle Scholar
  3. 3.
    Besl, P.J., McKay, N.D.: A method for registration of 3-D shapes. IEEE Trans. Pattern Anal. Mach. Intell. 14(2), 239–256 (1992)CrossRefGoogle Scholar
  4. 4.
    Boscaini, D., Castellani, U.: Local signature quantization by sparse coding. In: Eurographics Workshop on 3D Object Retr. (2013)Google Scholar
  5. 5.
    Boyer, E., Bronstein, A.M., Bronstein, M.M., Bustos, B., Darom, T., Horaud, R.: SHREC 2011: robust feature detection and description benchmark. Proc. of Eurographics Workshop 3D Object Retr. (3DOR) (2011)Google Scholar
  6. 6.
    Bronstein, A.M., Bronstein, M.M., Guibas, L.J., Ovsjanikov, M.: Shape google: geometric words and expressions for invariant shape retrieval. ACM Trans. Graph. (TOG) 30(1), 1–20 (2011)CrossRefGoogle Scholar
  7. 7.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Numerical Geometry of Non-rigid Shapes, Monographs in Computer Science. Springer, New York (2008)Google Scholar
  8. 8.
    Bronstein, M.M., Kokkinos, I.: Scale-invariant heat kernel signature for non-rigid shape recognition. In: Proc. Comput. Vis. Pattern Recognit. (CVPR), pp. 1704–1711 (2010)Google Scholar
  9. 9.
    Castellani, U., Bartoli, A.: 3D shape registration. 3D Imaging, Analysis, and Applications. Springer, Berlin (2012)Google Scholar
  10. 10.
    Castellani, U., Cristani, M., Murino, V.: Statistical 3D shape analysis by local generative descriptors. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI) 33, 2555–2560 (2011)CrossRefGoogle Scholar
  11. 11.
    Castellani, U., Mirtuono, P., Murino, V., Bellani, M., Rambaldelli, G., Tansella, M., Brambilla, P.: A new shape diffusion descriptor for brain classification. . In: Medical Image Computing and Computer-Assisted Intervention (MICCAI), Lecture Notes in Computer Science, vol 6892. Springer, Berlin, pp 426–433 (2011)Google Scholar
  12. 12.
    Darom, T., Keller, Y.: Scale-invariant features for 3-D mesh models. IEEE Trans. Image Process. 21(5), 2758–2769 (2012)Google Scholar
  13. 13.
    Elad, A., Kimmel, R.: On bending invariant signatures for surfaces. Trans. Pattern Anal. Mach. Intell. 25(10), 1285–1295 (2003)CrossRefGoogle Scholar
  14. 14.
    Funkhouser, T., Kazhdan, M., Min, P., Shilane, P.: Shape-based retrieval and analysis of 3D models. Commun. ACM 48, 58–64 (2005)CrossRefGoogle Scholar
  15. 15.
    Johnson, A.E., Hebert, M.: Using spin images for efficient object recognition in cluttered 3-D scenes. IEEE Trans. Pattern Anal. Mach. Intell. 21(5), 433–449 (1999)CrossRefGoogle Scholar
  16. 16.
    Lavoue, G.: Combination of bag-of-words descriptors for robust partial shape retrieval. Vis. Comput. 26, 1257–1268 (2012)Google Scholar
  17. 17.
    Lévy, B.: Laplace–Beltrami eigenfunctions: towards an algorithm that “understands” geometry. In: IEEE Int. Conf. on Shape Model. Appl. (2006)Google Scholar
  18. 18.
    Lian, Z., Godil, A., Bustos, B., Daoudi, M., et al.: SHREC 2011 track: shape retrieval on non-rigid 3D watertight meshes. In: Proceedings of the Eurographics Workshop on 3D Object Retrieval, pp. 79–88 (2011)Google Scholar
  19. 19.
    Lian, Z., Godil, A., Bustos, B., et al.: A comparison of methods for non-rigid 3D shape retrieval. Pattern Recognit. 46(1), 449–461 (2013)CrossRefGoogle Scholar
  20. 20.
    Lian, Z., Godil, A., Fabry, T., T., F., et al.: SHREC 2010: Non-rigid 3D shape retrieval. In: Proc. Eurographics Workshop 3D Object Retr. (3DOR) (2010)Google Scholar
  21. 21.
    Litman, R., Bronstein, A.M.: Learning spectral descriptors for deformable shape correspondence. IEEE Trans. Pattern Anal. Mach. Intell. 36(1), 171–180 (2014)Google Scholar
  22. 22.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2), 91–110 (2004)CrossRefGoogle Scholar
  23. 23.
    Mairal, J., Bach, F., Ponce, J., Sapiro, G.: Online dictionary learning for sparse coding. In: Proc. Int. Conf. Mach. Learn. (ICML), pp. 689–696 (2009)Google Scholar
  24. 24.
    Mairal, J., Bach, F., Ponce, J., Sapiro, G.: Online learning for matrix factorization and sparse coding. J. Mach. Learn. Res. 11, 19–60 (2010)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Marini, S., Paraboschi, L., Biasotti, S.: Shape retrieval contest 2007 (SHREC07): Partial matching track. technical report 10/07, IMATI (2007)Google Scholar
  26. 26.
    Mitra, N.J., Guibas, L., Giesen, J., Pauly, M.: Probabilistic fingerprints for shapes. In: Symposium on Geometry Processing, pp. 121–130 (2006)Google Scholar
  27. 27.
    Ovsjanikov, M., Ben-Chen, M., Solomon, J., Butscher, A., Guibas, L.: Functional Maps: A flexible representation of maps between shapes. ACM Trans. Graph. 31(4), 30:1–30:11 (2012)Google Scholar
  28. 28.
    Pokrass, J., Bronstein, A.M., Bronstein, M.M., Sprechmann, P., Sapiro, G.: Sparse modeling of intrinsic correspondences. Comput. Graph. Forum 32(2), 459G–468 (2013)Google Scholar
  29. 29.
    Reuter, M., Wolter, F.E., Peinecke, N.: Laplace–Beltrami spectra as ‘shape-DNA’ of surfaces and solids. Comput.-Aided Des. 38, 342–366 (2006)CrossRefGoogle Scholar
  30. 30.
    Rustamov, R.M.: Laplace–Beltrami eigenfunctions for deformation invariant shape representation. In: Eurographics Symp. Geom. Process., pp. 225–233 (2007)Google Scholar
  31. 31.
    Schölkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. The MIT Press, Cambridge (2002)Google Scholar
  32. 32.
    Sumner, R.W., Popović, J.: Deformation transfer for triangle meshes. ACM Trans. Graph. (TOG) 23, 399–405 (2004)CrossRefGoogle Scholar
  33. 33.
    Sun, J., Ovsjanikov, M., Guibas, L.: A concise and provably informative multi-scale signature based on heat diffusion. In: Proc. Symp. Geom. Process., pp. 1383–1392 (2009)Google Scholar
  34. 34.
    Tangelder, J.W., Veltkamp, R.C.: A survey of content based 3D shape retrieval methods. In: Int. Conf. Shape Modell. Appl., pp. 145–156 (2004)Google Scholar
  35. 35.
    Tibshirani, R.: Regression shrinkage and selection via the Lasso. J. R. Stat. Soc. pp. 267–288 (1996)Google Scholar
  36. 36.
    Toldo, R., Castellani, U., Fusiello, A.: The bag of words approach for retrieval and categorization of 3D objects. Vis. Comput. 26, 1257–1268 (2010)CrossRefGoogle Scholar
  37. 37.
    Veltkamp, R.C., Haar, F.B.: Shrec 2007: 3D shape retrieval contest. Tech. Rep. UU-CS-2007-015, Department of Information and Computing Sciences, Utrecht University (2007)Google Scholar
  38. 38.
    Wuhrer, S., Azouz, Z.B., Shu, C.: Posture invariant surface description and feature extraction. In: IEEE Conf. Comput. Vis. Pattern Recognit. (CVPR), pp. 374–381 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.University of LuganoLuganoSwitzerland
  2. 2.University of VeronaVeronaItaly

Personalised recommendations