The Visual Computer

, Volume 33, Issue 12, pp 1571–1585 | Cite as

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

  • Ivan Sipiran
  • Jakub Lokoc̆
  • Benjamin Bustos
  • Tomás̆ Skopal
Original Article


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.


3D shape retrieval Local features Signature quadratic form distance 



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.


  1. 1.
    Beecks, C.: Distance-based similarity models for content-based multimedia retrieval. In: Dissertation, Fakultt fr Mathematik, Informatik und Naturwissenschaften, RWTH Aachen University (2013)Google Scholar
  2. 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)Google Scholar
  3. 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. 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)Google Scholar
  5. 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)Google Scholar
  6. 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)CrossRefGoogle Scholar
  7. 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)Google Scholar
  8. 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)CrossRefGoogle Scholar
  9. 9.
    Liu, Z., Bu, S., Han, J.: Locality-constrained sparse patch coding for 3d shape retrieval. Neurocomputing 151, Part 2, 583–592 (2015)CrossRefGoogle Scholar
  10. 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)Google Scholar
  11. 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)CrossRefGoogle Scholar
  12. 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)Google Scholar
  13. 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)CrossRefGoogle Scholar
  14. 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. 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)CrossRefGoogle Scholar
  16. 16.
    Belkin, M., Sun, J., Wang, Y.: Discrete laplace operator on meshed surfaces. In: Proc. Symposium on Comput. Geom., pp. 278–287. ACM (2008)Google Scholar
  17. 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)Google Scholar
  18. 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 CrossRefGoogle Scholar
  19. 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)Google Scholar
  20. 20.
    Leow, W.K., Li, R.: The analysis and applications of adaptive-binning color histograms. Comput. Vis. Image Underst. 94, 67–91 (2004)CrossRefGoogle Scholar
  21. 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)CrossRefGoogle Scholar
  22. 22.
    Kimmel, R., Sethian, J.A.: Computing geodesic paths on manifolds. In: Proc. Natl. Acad. Sci. USA, pp. 8431–8435 (1998)Google Scholar
  23. 23.
    Borg, I., Groenen, P.: Modern multidimensional scaling: theory and applications. Springer, Berlin (2005)zbMATHGoogle Scholar
  24. 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 CrossRefGoogle Scholar
  25. 25.
    Bronstein, A., Bronstein, M., Kimmel, R.: Numerical geometry of non-rigid shapes, 1st edn. Springer Publishing Company, Berlin (2008)zbMATHGoogle Scholar
  26. 26.
    Sumner, R.W., Popović, J.: Deformation transfer for triangle meshes. ACM Trans. Graph. 23, 399–405 (2004)CrossRefGoogle Scholar
  27. 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)CrossRefGoogle Scholar
  28. 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)Google Scholar
  29. 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)CrossRefGoogle Scholar
  30. 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)Google Scholar
  31. 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)Google Scholar
  32. 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)CrossRefGoogle Scholar
  33. 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)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Sección Ingeniería InformáticaPontificia Universidad Católica del Perú PUCPLimaPeru
  2. 2.SIRET Research Group, Faculty of Mathematics and PhysicsCharles University in PraguePragueCzech Republic
  3. 3.Department of Computer ScienceUniversity of ChileSantiagoChile

Personalised recommendations