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On the Use of the Tree Structure of Depth Levels for Comparing 3D Object Views

  • Fabio Bracci
  • Ulrich Hillenbrand
  • Zoltan-Csaba Marton
  • Michael H. F. Wilkinson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10424)

Abstract

Today the simple availability of 3D sensory data, the evolution of 3D representations, and their application to object recognition and scene analysis tasks promise to improve autonomy and flexibility of robots in several domains. However, there has been little research into what can be gained through the explicit inclusion of the structural relations between parts of objects when quantifying similarity of their shape, and hence for shape-based object category recognition. We propose a Mathematical Morphology inspired hierarchical decomposition of 3D object views into peak components at evenly spaced depth levels, casting the 3D shape similarity problem to a tree of more elementary similarity problems. The matching of these trees of peak components is here compared to matching the individual components through optimal and greedy assignment in a simple feature space, trying to find the maximum-weight-maximal-match assignments. The matching thus achieved provides a metric of total shape similarity between object views. The three matching strategies are evaluated and compared through the category recognition accuracy on objects from a public set of 3D models. It turns out that all three methods yield similar accuracy on the simple features we used, while the greedy method is fastest.

Keywords

3D shape similarity Tree matching Mathematical Morphology Object recognition Scene analysis 

References

  1. 1.
    Aldoma, A., Blodow, N., Gossow, D., Gedikli, S., Rusu, R., Vincze, M., Bradski, G.: CAD-model recognition and 6DOF pose estimation using 3D cues. In: ICCV Workshop on 3D Representation and Recognition (3dRR 2011), Barcelona (2011)Google Scholar
  2. 2.
    Belongie, S., Malik, J., Puzicha, J.: Shape context: a new descriptor for shape matching and object recognition. In: Proceedings of the 13th International Conference on Neural Information Processing Systems (NIPS 2000), pp. 798–804. MIT Press, Cambridge (2000). http://portal.acm.org/citation.cfm?id=3008867
  3. 3.
    Boscaini, D., Masci, J., Melzi, S., Bronstein, M.M., Castellani, U., Vandergheynst, P.: Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks. Comput. Graph. Forum 34(5), 13–23 (2015). http://dx.doi.org/10.1111/cgf.12693 CrossRefGoogle Scholar
  4. 4.
    Graham, M.W., Higgins, W.E.: Optimal graph-theoretic approach to 3D anatomical tree matching. In: 3rd IEEE International Symposium on Biomedical Imaging: Macro to Nano, pp. 109–112. IEEE, April 2006. http://dx.doi.org/10.1109/isbi.2006.1624864
  5. 5.
    Graham, M.W., Higgins, W.E.: Globally optimal model-based matching of anatomical trees. In: Medical Imaging, vol. 6144, pp. 614415-1–614415-15 (2006). http://dx.doi.org/10.1117/12.651719
  6. 6.
    Huber, D., Kapuria, A., Donamukkala, R.R., Hebert, M.: Parts-based 3D object classification. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR 04), July 2004Google Scholar
  7. 7.
    Jacobs, D.W.: Perceptual organization as generic object recognition, North-Holland, vol. 130, pp. 295–329, December 2001. http://www.sciencedirect.com/science/article/pii/S0166411501800303
  8. 8.
    Jiantao, P., Yi, L., Guyu, X., Hongbin, Z., Weibin, L., Uehara, Y.: 3D model retrieval based on 2D slice similarity measurements. In: Proceedings of the 2nd International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT 2004), pp. 95–101 (2004). http://dx.doi.org/10.1109/3dpvt.2004.3
  9. 9.
    Jonker, R., Volgenant, A.: A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing 38(4), 325–340 (1987). http://dx.doi.org/10.1007/bf02278710 MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Jouili, S., Mili, I., Tabbone, S.: Attributed graph matching using local descriptions. In: Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2009. LNCS, vol. 5807, pp. 89–99. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-04697-1_9 CrossRefGoogle Scholar
  11. 11.
    Körtgen, M., Novotni, M., Klein, R.: 3D shape matching with 3D shape contexts. In: The 7th Central European Seminar on Computer Graphics (2003). http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.67.9266
  12. 12.
    Kuhn, H.W.: The Hungarian method for the assignment problem. Nav. Res. Logist. 2(1–2), 83–97 (1955). http://dx.doi.org/10.1002/nav.3800020109 MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Lai, K., Fox, D.: Object recognition in 3D point clouds using web data and domain adaptation. Int. J. Robot. Res. 29(8), 1019–1037 (2010). http://ijr.sagepub.com/cgi/doi/10.1177/0278364910369190 CrossRefGoogle Scholar
  14. 14.
    Marton, Z.C., Balint-Benczedi, F., Mozos, O., Blodow, N., Kanezaki, A., Goron, L., Pangercic, D., Beetz, M.: Part-based geometric categorization and object reconstruction in cluttered table-top scenes. J. Intell. Robot. Syst. 76(1), 35–56 (2014). http://dx.doi.org/10.1007/s10846-013-0011-8 CrossRefGoogle Scholar
  15. 15.
    Masci, J., Rodolà, E., Boscaini, D., Bronstein, M.M., Li, H.: Geometric deep learning. In: SIGGRAPH ASIA 2016 Courses (SA 2016), NY, USA (2016). http://dx.doi.org/10.1145/2988458.2988485
  16. 16.
    Munkres, J.: Algorithms for the assignment and transportation problems. J. Soc. Ind. Appl. Math. 5(1), 32–38 (1957)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Pratikakis, I., Spagnuolo, M., Theoharis, T., Editors, R.V., Dutagaci, H., Godil, A., Cheung, C.P., Furuya, T., Hillenbrand, U., Ohbuchi, R.: SHREC 2010 - shape retrieval contest of range scans. In: Proceedings of Eurographics (2010). http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.361.8068
  18. 18.
    Richtsfeld, A., Morwald, T., Prankl, J., Zillich, M., Vincze, M.: Segmentation of unknown objects in indoor environments. In: 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 4791–4796 (2012)Google Scholar
  19. 19.
    Rusu, R.B., Bradski, G., Thibaux, R., Hsu, J.: Fast 3D recognition and pose using the viewpoint feature histogram. In: 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2155–2162. IEEE (2004). http://dx.doi.org/10.1109/iros.2010.5651280
  20. 20.
    Salembier, P., Serra, J.: Flat zones filtering, connected operators, and filters by reconstruction. IEEE Trans. Image Process. 4(8), 1153–1160 (1995). http://dx.doi.org/10.1109/83.403422 CrossRefGoogle Scholar
  21. 21.
    Sundar, H., Silver, D., Gagvani, N., Dickinson, S.: Skeleton based shape matching and retrieval. In: Shape Modeling International, pp. 130–139. IEEE (2003)Google Scholar
  22. 22.
    Tangelder, J.W.H., Veltkamp, R.C.: A survey of content based 3D shape retrieval methods. In: Shape Modeling International, pp. 145–156 (2004). http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.97.8133
  23. 23.
    Torsello, A., Hidovic, D., Pelillo, M.: Four metrics for efficiently comparing attributed trees. In: Proceedings of the 17th International Conference on Pattern Recognition (ICPR 2004), vol. 2, pp. 467–470. IEEE, August 2004. http://dx.doi.org/10.1109/icpr.2004.1334263
  24. 24.
    Torsello, A., Hidovic-Rowe, D., Pelillo, M.: Polynomial-time metrics for attributed trees. IEEE Trans. Pattern Anal. Mach. Intell. 27(7), 1087–1099 (2005). http://dx.doi.org/10.1109/tpami.2005.146 CrossRefGoogle Scholar
  25. 25.
    Urbach, E.R., Roerdink, J.B.T.M., Wilkinson, M.H.F.: Connected shape-size pattern spectra for rotation and scale-invariant classification of gray-scale images. IEEE Trans. Pattern Anal. Mach. Intell. 29(2), 272–285 (2007). http://dx.doi.org/10.1109/tpami.2007.28 CrossRefGoogle Scholar
  26. 26.
    Wu, Z., Song, S., Khosla, A., Yu, F., Zhang, L., Tang, X., Xiao, J.: 3D ShapeNets: a deep representation for volumetric shapes - IEEE Xplore Document. In: The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2015. http://ieeexplore.ieee.org/abstract/document/7298801/
  27. 27.
    Zuckerberger, E., Tal, A., Shlafman, S.: Polyhedral surface decomposition with applications. Comput. Graph. 26(5), 733–743 (2002). http://dx.doi.org/10.1016/s0097-8493(02)00128--0

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Fabio Bracci
    • 1
  • Ulrich Hillenbrand
    • 1
  • Zoltan-Csaba Marton
    • 1
  • Michael H. F. Wilkinson
    • 2
  1. 1.Institute of Robotics and Mechatronics, German Aerospace Center (DLR)WeßlingGermany
  2. 2.Johann Bernoulli Institute for Mathematics and Computer ScienceUniversity of Groningen (RuG)GroningenThe Netherlands

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