Skip to main content
SpringerLink
Log in

Scalable 3D shape retrieval using local features and the signature quadratic form distance

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

We present a scalable and unsupervised approach for content-based retrieval on 3D model collections. Our goal is to represent a 3D shape as a set of discriminative local features, which is important to maintain robustness against deformations such as non-rigid transformations and partial data. However, this representation brings up the problem on how to compare two 3D models represented by feature sets. For solving this problem, we apply the signature quadratic form distance (SQFD), which is suitable for comparing feature sets. Using SQFD, the matching between two 3D objects involves only their representations, so it is easy to add new models to the collection. A key characteristic of the feature signatures, required by the SQFD, is that the final object representation can be easily obtained in a unsupervised manner. Additionally, as the SQFD is an expensive distance function, to make the system scalable we present a novel technique to reduce the amount of features by detecting clusters of key points on a 3D model. Thus, with smaller feature sets, the distance calculation is more efficient. Our experiments on a large-scale dataset show that our proposed matching algorithm not only performs efficiently, but also its effectiveness is better than state-of-the-art matching algorithms for 3D models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Beecks, C.: Distance-based similarity models for content-based multimedia retrieval. In: Dissertation, Fakultt fr Mathematik, Informatik und Naturwissenschaften, RWTH Aachen University (2013)

  2. Beecks, C., Uysal, M.S., Seidl, T.: Signature quadratic form distances for content-based similarity. In: Proc. ACM Int. Conf. on Multimedia, MM ’09, pp. 697–700. ACM, New York (2009)

  3. Bronstein, A., Bronstein, M., Guibas, L., Ovsjanikov, M.: Shape google: geometric words and expressions for invariant shape retrieval. ACM Trans. Comput. Graph. 30(1), 1:1–1:20 (2011)

    Google Scholar 

  4. Abdelrahman, M., Farag, A., Swanson, D., El-Melegy, M.T.: Heat Diffusion over weighted manifolds: a new descriptor for textured 3D non-rigid shapes. In: Proc. IEEE Conf. Comput. Vision and Pattern Recognit., CVPR, pp. 187–195 (2015)

  5. Tabia, H., Laga, H., Picard, D., Gosselin, P.H.: Covariance descriptors for 3d shape matching and retrieval. In: Proc. IEEE Conf. Comput. Vision and Pattern Recognit., pp. 4185–4192. IEEE Computer Society, Washington, DC (2014)

  6. Bai, X., Bai, S., Zhu, Z., Latecki, L.: 3D shape matching via two layer coding. IEEE Trans. Pattern Anal. Mach. Intell. 37(12), 2361–2373 (2015)

    Article  Google Scholar 

  7. Savelonas, M.A., Pratikakis, I., Sfikas, K.: Partial 3D object retrieval combining local shape descriptors with global fisher vectors. In: Pratikakis, I., Spagnuolo, M., Theoharis, T., Gool, L.V., Veltkamp, R. (eds.) Proc. Eurographics Workshop on 3D Object Retr., pp. 23–30. The Eurographics Association (2015)

  8. Litman, R., Bronstein, A.M., Bronstein, M.M., Castellani, U.: Supervised learning of bag-of-features shape descriptors using sparse coding. Comput. Graph. Forum 33(5), 127–136 (2014)

    Article  Google Scholar 

  9. Liu, Z., Bu, S., Han, J.: Locality-constrained sparse patch coding for 3d shape retrieval. Neurocomputing 151, Part 2, 583–592 (2015)

    Article  Google Scholar 

  10. Fang, Y., Xie, J., Dai, G., Wang, M., Zhu, F., Xu, T., Wong, E.: 3D deep shape descriptor. In: Proc. IEEE Conf. Comput. Vision and Pattern Recognit., pp. 2319–2328 (2015)

  11. Bu, S., Cheng, S., Liu, Z., Han, J.: Multimodal feature fusion for 3D shape recognition and retrieval. IEEE Multimed. 21(4), 38–46 (2014)

    Article  Google Scholar 

  12. Xie, J., Fang, Y., Zhu, F., Wong, E.: DeepShape: deep learned shape descriptor for 3D shape matching and retrieval. In: Proc. IEEE Conf. Comput. Vision and Pattern Recognit., CVPR, pp. 1275–1283 (2015)

  13. Bustos, B., Keim, D.A., Saupe, D., Schreck, T., Vranic, D.V.: Feature-based similarity search in 3D object databases. ACM Comput. Surv. 37(4), 345–387 (2005)

    Article  Google Scholar 

  14. Chang, A.X., Funkhouser, T., Guibas, L., Hanrahan, P., Huang, Q., Li, Z., Savarese, S., Savva, M., Song, S., Su, H., Xiao, J., Yi, L., Yu, F.: Shapenet: An information-rich 3d model repository. CoRR arxiv:1512.03012 (2015)

  15. Sun, J., Ovsjanikov, M., Guibas, L.J.: A concise and provably informative multi-scale signature based on heat diffusion. Comput. Graph. Forum 28(5), 1383–1392 (2009)

    Article  Google Scholar 

  16. Belkin, M., Sun, J., Wang, Y.: Discrete laplace operator on meshed surfaces. In: Proc. Symposium on Comput. Geom., pp. 278–287. ACM (2008)

  17. Bronstein, M., Kokkinos, I.: Scale-invariant heat kernel signatures for non-rigid shape recognition. In: Proc. IEEE Conf. Comput. Vision and Pattern Recognit., pp. 1704–1711 (2010)

  18. Hafner, J., Sawhney, H.S., Equitz, W., Flickner, M., Niblack, W.: Efficient color histogram indexing for quadratic form distance functions. IEEE Trans. Pattern Anal. Mach. Intell. 17(7), 729–736 (1995). doi:10.1109/34.391417

    Article  Google Scholar 

  19. Beecks, C., Uysal, M.S., Seidl, T.: Signature quadratic form distance. In: Proc. ACM Int. Conf. on Image and Video Retr., CIVR ’10, pp. 438–445. ACM, New York (2010)

  20. Leow, W.K., Li, R.: The analysis and applications of adaptive-binning color histograms. Comput. Vis. Image Underst. 94, 67–91 (2004)

    Article  Google Scholar 

  21. Sipiran, I., Bustos, B.: Harris 3D: a robust extension of the Harris operator for interest point detection on 3D meshes. Vis. Comput. 27, 963–976 (2011)

    Article  Google Scholar 

  22. Kimmel, R., Sethian, J.A.: Computing geodesic paths on manifolds. In: Proc. Natl. Acad. Sci. USA, pp. 8431–8435 (1998)

  23. Borg, I., Groenen, P.: Modern multidimensional scaling: theory and applications. Springer, Berlin (2005)

    MATH  Google Scholar 

  24. Sipiran, I., Bustos, B.: Key-components: detection of salient regions on 3d meshes. Vis. Comput. 29(12), 1319–1332 (2013). doi:10.1007/s00371-013-0870-9

    Article  Google Scholar 

  25. Bronstein, A., Bronstein, M., Kimmel, R.: Numerical geometry of non-rigid shapes, 1st edn. Springer Publishing Company, Berlin (2008)

    MATH  Google Scholar 

  26. Sumner, R.W., Popović, J.: Deformation transfer for triangle meshes. ACM Trans. Graph. 23, 399–405 (2004)

    Article  Google Scholar 

  27. Reuter, M., Wolter, F.E., Peinecke, N.: Laplace-Beltrami spectra as Shape-DNA of surfaces and solids. Comput. Aided Des. 38(4), 342–366 (2006)

    Article  Google Scholar 

  28. Beecks, C., Lokoč, J., Seidl, T., Skopal, T.: Indexing the signature quadratic form distance for efficient content-based multimedia retrieval. In: Proc. 1st ACM Int. Conf. on Multimedia Retr., pp. 24:1–24:8. ACM, New York (2011)

  29. Hetland, M., Skopal, T., Lokoč, J., Beecks, C.: Ptolemaic access methods: challenging the reign of the metric space model. Inf. Syst. 38, 989–1006 (2013)

    Article  Google Scholar 

  30. Lokoč, J., Grošup, T., Skopal, T.: On scalable approximate search with the signature quadratic form distance. In: Brisaboa, N., Pedreira, O., Zezula, P. (eds.) Proc. 7th Int. Conf. on Similarity Search and Applications, Lecture Notes in Computer Science, vol. 8199, pp. 312–318. Springer, Berlin, Heidelberg (2013)

  31. Navarro, G.: Analyzing metric space indexes: what for? In: Proc. 2nd Int. Workshop on Similarity Search and Applications, pp. 3–10. IEEE Computer Society (2009)

  32. Mico, M.L., Oncina, J., Vidal, E.: A new version of the nearest-neighbour approximating and eliminating search algorithm (aesa) with linear preprocessing time and memory requirements. Pattern Recognit. Lett. 15(1), 9–17 (1994)

    Article  Google Scholar 

  33. Sipiran, I., Bustos, B., Schreck, T., Bronstein, A.M., Bronstein, M., Castellani, U., Choi, S., Lai, L., Li, H., Litman, R., Sun, L.: Scalability of Non-Rigid 3D Shape Retrieval. In: Pratikakis, I., Spagnuolo, M., Theoharis, T., Gool, L.V., Veltkamp, R. (eds.) Proc. Eurographics Workshop on 3D Object Retr. The Eurographics Association (2015)

Download references

Acknowledgments

This work has been partially supported by Programa Nacional de Innovación para la Competitividad y Productividad, INNOVATE Perú, Grant Nr. 280-PNICP-BRI-2015. This work has been also supported by Charles University projects P46 and SVV-2016-260331. Benjamin Bustos has been funded by FONDECYT (Chile) Project 1140783 and the Millennium Nucleus Center for Semantic Web Research, Grant Nr. NC120004.

Author information

Authors and Affiliations

  1. Sección Ingeniería Informática, Pontificia Universidad Católica del Perú PUCP, Lima, Peru

    Ivan Sipiran

  2. SIRET Research Group, Faculty of Mathematics and Physics, Charles University in Prague, Prague, Czech Republic

    Jakub Lokoc̆ & Tomás̆ Skopal

  3. Department of Computer Science, University of Chile, Santiago, Chile

    Benjamin Bustos

Authors
  1. Ivan Sipiran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jakub Lokoc̆
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Benjamin Bustos
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tomás̆ Skopal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ivan Sipiran.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sipiran, I., Lokoc̆, J., Bustos, B. et al. Scalable 3D shape retrieval using local features and the signature quadratic form distance. Vis Comput 33, 1571–1585 (2017). https://doi.org/10.1007/s00371-016-1301-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-016-1301-5

Keywords

Search

Navigation