An invariant descriptor map for 3D objects matching

  • Authors

    • Abdallah El Chakik Beirut Arab University
    • Abdul Rahman El Sayed
    • Hassan Alabboud
    • Amer Bakkach
    2020-01-23
    https://doi.org/10.14419/ijet.v9i1.29918
  • 3D Mesh, Descriptor Map Detection, Multi-Scale Computation, 3D Surface Segmentation, 3D Models Matching.

  • Abstract

    Meshes and point clouds are traditionally used to represent and match 3D shapes. The matching prob-lem can be formulated as finding the best one-to-one correspondence between featured regions of two shapes. This paper presents an efficient and robust 3D matching method using vertices descriptors de-tection to define feature regions and an optimization approach for regions matching. To do so, we compute an invariant shape descriptor map based on 3D surface patches calculated using Zernike coef-ficients. Then, we propose a multi-scale descriptor map to improve the measured descriptor map quali-ty and to deal with noise. In addition, we introduce a linear algorithm for feature regions segmentation according to the descriptor map. Finally, the matching problem is modelled as sub-graph isomorphism problem, which is a combinatorial optimization problem to match feature regions while preserving the geometric. Finally, we show the robustness and stability of our method through many experimental re-sults with respect to scaling, noise, rotation, and translation.

     

     

  • References

    1. [1] El Sayed, Abdul Rahman, et al. ‘Efficient 3D mesh salient region detection using local homogeneity measure’, IET Image Processing, 2018, 12,(9), pp.1663 – 1672. https://doi.org/10.1049/iet-ipr.2017.0598.

      [2] A. Nouri, C. Charrier, O. Lézoray, “Multi-scale mesh saliency with local adaptive patches for viewpoint selectionâ€, Signal Processing: Image Communication, 38, (2015), pp.151–166. https://doi.org/10.1016/j.image.2015.08.002.

      [3] Tal, A., Shtrom, E., Leifman, G.: ‘Fast-match: fast affine template matching surface regions of interest for view-point selection’. IEEE Conf. on Computer Vision and Pattern Recognition, 2012, pp. 414–421.

      [4] Wu, J., Shen, X., Zhu, W., et al.: ‘Mesh saliency with global rarity’, Graph.Models, 2013, 75, (5), pp. 255–264. https://doi.org/10.1016/j.gmod.2013.05.002.

      [5] F. R. Schmidt, D. Farin, and D. Cremers. Fast matching of planar shapes in sub-cubic runtime. In IEEE Int. Conf. on Computer Vision, Rio de Janeiro, October 2007. 1, 3, 7. https://doi.org/10.1109/ICCV.2007.4409018.

      [6] T. Windheuser, U. Schlickewei, F. R. Schmidt, & D. Cremers, Geometrically consistent elastic matching of 3d shapes: A linear programming solution. In Computer Vision (ICCV), 2011 IEEE International Conference. (2011, November), (pp. 2134-2141). https://doi.org/10.1109/ICCV.2011.6126489.

      [7] F. M´emoli and G. Sapiro. A theoretical and computational framework for isometry invariant recognition of point cloud data. Foundations of Computational Mathematics, 5(3), (2005), PP. 313–347. https://doi.org/10.1007/s10208-004-0145-y.

      [8] A. Bronstein, M. Bronstein, and R. Kimmel. Efficient computation of isometry-invariant distances between surfaces. SIAM J. Sci. Comput., 28(5), (2006), PP. 1812–1836. https://doi.org/10.1137/050639296.

      [9] S. Kurtek, E. Klassen, Z. Ding, and A. Srivastava. A novel riemannian framework for shape analysis of 3d objects. In CVPR, (2010), pp. 1625–1632. https://doi.org/10.1109/CVPR.2010.5539778.

      [10] Y. Wang, X. Gu, K. Hayashi, T. Chan, P. Thompson, and S. Yau. Brain surface parameterization using riemann surface structure. In MICCAI (2), (2005), pp. 657–665. https://doi.org/10.1007/11566489_81.

      [11] P Tao, J Cao, S Li, X Liu, L Liu. Mesh saliency via ranking unsalient patches in a descriptor space, Comput Graph, 2015, 46(0): 264–274. https://doi.org/10.1016/j.cag.2014.09.023.

      [12] Y. Zeng, C.Wang, Y.Wang, X. Gu, D. Samaras, and N. Paragios. Dense non-rigid surface registration using high-order graph matching. In CVPR, (2010), pp. 382–389. https://doi.org/10.1109/CVPR.2010.5540189.

      [13] L. Torresani, V. Kolmogorov, and C. Rother. Feature correspondence via graph matching: Models and global optimization. In ECCV (2), (2008), pp. 596–609. https://doi.org/10.1007/978-3-540-88688-4_44.

      [14] https://github.com/forsythrosin/cs348aHW4/tree/master/models/MeshsegBenchmark-1.0.

      [15] J. D. Boissonnat and B. Geiger. Three-dimensional reconstruction of complex shapes based on the Delaunay triangulation. In Biomedical Image Processing and Biomedical Visualization, 1905, (1993), pp. 964–975. https://doi.org/10.1117/12.148710.

      [16] Chen, X., Saparov, A., Pang, B., et al. Schelling points on 3D surface meshes. ACM Trans. Graph, 2012, 31, (4), pp.29. https://doi.org/10.1145/2185520.2185525.

      [17] A. El Sayed, A. el Chakik, H. Alabboud, Adnan, A. Yassine. Efficient 3D point clouds classification for face detection using linear programming and data mining. The Imaging Science Journal, 2018, 66, pp. 23-37. https://doi.org/10.1080/13682199.2017.1376772.

      [18] A. Maximo, R. Patro, A. Varshney, R. FariasA robust and rotationally invariant local surface descriptor with applications to non-local mesh processing Graph Models, 73 (5) (2011), pp. 231-242. https://doi.org/10.1016/j.gmod.2011.05.002.

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  • How to Cite

    El Chakik, A., El Sayed, A. R., Alabboud, H., & Bakkach, A. (2020). An invariant descriptor map for 3D objects matching. International Journal of Engineering & Technology, 9(1), 59-68. https://doi.org/10.14419/ijet.v9i1.29918

    Received date: 2019-09-25

    Accepted date: 2019-12-25

    Published date: 2020-01-23