Advertisement

“Shape-Curvature-Graph”: Towards a New Model of Representation for the Description of 3D Meshes

  • Arnaud PoletteEmail author
  • Jean Meunier
  • Jean-Luc Mari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10325)

Abstract

This paper presents a new shape descriptor for 3D meshes, that aims at representing an arbitrary triangular polyhedron using a graph, called SCG for “Shape-Curvature-Graph”. This entity can be used to perform self-similarity detection, or more generally to extract patterns within a shape. Our method uses discrete curvature maps and divides the meshes into eight categories of patches (peak, ridge, saddle ridge, minimal, saddle valley, valley, pit and flat). Then an adjacency graph is constructed with a node for each patch. All categories of patches cannot be neighbors in a continuous context, thus additional intermediary patches are added as boundaries to ensure a continuous consistency at the transitions between areas. To validate the relevance of this modular structure, an approach based of these shape descriptor graphs is developed in order to extract similar patterns within a surface mesh. It illustrates that these “augmented” graphs obtained using differential properties on meshes can be used to analyze shape and extract features.

Keywords

Pattern Extraction Discrete Object Continuous Object Discrete Curvature Mesh Segmentation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). The Bunny and the Happy Buddha data sets were provided courtesy of the Stanford University Computer Graphics Laboratory. The Gargoyle and the Chinese dragon data sets were provided courtesy of the AIM@SHAPE consortium.

References

  1. 1.
    Berner, A., Bokeloh, M., Wand, M., Schilling, A., Seidel, H.-P.: A graph-based approach to symmetry detection. In: Proceedings of the Fifth Eurographics/IEEE VGTC Conference on Point-Based Graphics, SPBG 2008, pp. 1–8. Eurographics Association, Aire-la-Ville, Switzerland, Switzerland (2008)Google Scholar
  2. 2.
    Besl, P.J., Jain, R.C.: Segmentation through variable-order surface fitting. IEEE Trans. Pattern Anal. Mach. Intell. 10(2), 167–192 (1988)CrossRefGoogle Scholar
  3. 3.
    Gal, R., Cohen-Or, D.: Salient geometric features for partial shape matching and similarity. ACM Trans. Graph. 25(1), 130–150 (2006)CrossRefGoogle Scholar
  4. 4.
    Gumhold, S., Wang, X., Macleod, R.: Feature extraction from point clouds. In: Proceedings of the 10th International Meshing Roundtable, pp. 293–305 (2001)Google Scholar
  5. 5.
    Hildebrandt, K., Polthier, K., Wardetzky, M.: Smooth feature lines on surface meshes. In: Proceedings of the Third Eurographics Symposium on Geometry Processing, SGP 2005, pp. 085–090. Eurographics Association, Aire-la-Ville, Switzerland, Switzerland (2005)Google Scholar
  6. 6.
    Ho, H.T., Gibbins, D.: Curvature-based approach for multi-scale feature extraction from 3D meshes and unstructured point clouds. IET Comput. Vis. 3(4), 201–212 (2009)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Huang, Q., Guibas, L.J., Mitra, N.J.: Near-regular structure discovery using linear programming. ACM Trans. Graph. 33(3), 23:1–23:17 (2014)zbMATHGoogle Scholar
  8. 8.
    Kudelski, D., Viseur, S., Mari, J.-L.: Skeleton extraction of vertex sets lying on arbitrary triangulated 3D meshes. In: Gonzalez-Diaz, R., Jimenez, M.-J., Medrano, B. (eds.) DGCI 2013. LNCS, vol. 7749, pp. 203–214. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-37067-0_18 CrossRefGoogle Scholar
  9. 9.
    Lavoué, G., Dupont, F., Baskurt, A.: A new CAD mesh segmentation method, based on curvature tensor analysis. Comput.-Aided Des. 37(10), 975–987 (2005)CrossRefzbMATHGoogle Scholar
  10. 10.
    Lee, C.H., Varshney, A., Jacobs, D.W.: Mesh saliency. ACM Trans. Graph. 24(3), 659–666 (2005)CrossRefGoogle Scholar
  11. 11.
    Meyer, M., Desbrun, M., Schröder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. In: Hege, H.-C., Polthier, K. (eds.) Visualization and Mathematics III. Mathematics and Visualization, pp. 35–57. Springer, Berlin (2003)CrossRefGoogle Scholar
  12. 12.
    Nikolić, M.: Measuring similarity of graph nodes by neighbor matching. Intell. Data Anal. 16(6), 865–878 (2012)Google Scholar
  13. 13.
    Polette, A., Meunier, J., Mari, J.-L.: Feature extraction using a shape descriptor graph based on discrete curvature patches. In: Computer Graphics International (CGI 2015), Strasbourg, France (2015)Google Scholar
  14. 14.
    Rodola, E., Rota Bulo, S., Cremers, D.: Robust region detection via consensus segmentation of deformable shapes. Comput. Graph. Forum 33(5), 97–106 (2014)CrossRefGoogle Scholar
  15. 15.
    Simari, P., Kalogerakis, E., Singh, K.: Folding meshes: hierarchical mesh segmentation based on planar symmetry. In: Proceedings of the Fourth Eurographics Symposium on Geometry Processing, SGP 2006, pp. 111–119. Eurographics Association, Aire-la-Ville, Switzerland, Switzerland (2006)Google Scholar
  16. 16.
    Simari, P., Nowrouzezahrai, D., Kalogerakis, E., Singh, K.: Multi-objective shape segmentation and labeling. In: Computer Graphics Forum: Eurographics Symposium on Geometry Processing. Eurographics Association, Switzerland, Aire-la-Ville, Switzerland, March 2009Google Scholar
  17. 17.
    Sundar, H., Silver, D., Gagvani, N., Dickinson, S.: Skeleton based shape matching and retrieval. In: Proceedings of the Shape Modeling International 2003, SMI 2003. IEEE Computer Society, Washington, DC, USA (2003)Google Scholar
  18. 18.
    Tevs, A., Huang, Q., Wand, M., Seidel, H.-P., Guibas, L.: Relating shapes via geometric symmetries and regularities. ACM Trans. Graph. 33(4), 119:1–119:12 (2014)CrossRefGoogle Scholar
  19. 19.
    Xie, Z., Kai, X., Liu, L., Xiong, Y.: 3D shape segmentation and labeling via extreme learning machine. Comput. Graph. Forum 33(5), 85–95 (2014)CrossRefGoogle Scholar
  20. 20.
    Yang, Y.-L., Lai, Y.-K., Hu, S.-M., Pottmann, H.: Robust principal curvatures on multiple scales. In: Polthier, K., Sheffer, A. (eds.) SGP 2006: 4th Eurographics Symposium on Geometry processing, pp. 223–226. Eurographics Association (2006)Google Scholar
  21. 21.
    Yang, Y.-L., Shen, C.-H.: Multi-scale salient features for analyzing 3D shapes. J. Comput. Sci. Technol. 27(6), 1092–1099 (2012)CrossRefGoogle Scholar
  22. 22.
    Yoshizawa, S., Belyaev, A., Seidel, H.-P.: Fast and robust detection of crest lines on meshes. In: Proceedings of the 2005 ACM Symposium on Solid and Physical Modeling, SPM 2005, pp. 227–232. ACM, New York (2005)Google Scholar
  23. 23.
    Zhang, X., Li, G., Xiong, Y., He, F.: 3D mesh segmentation using mean-shifted curvature. In: Chen, F., Jüttler, B. (eds.) GMP 2008. LNCS, vol. 4975, pp. 465–474. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-79246-8_35 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Arts et Métiers ParisTech, CNRS, LSIS UMR 7296Aix-en-provenceFrance
  2. 2.DIROUniversity of MontrealMontrealCanada
  3. 3.Aix-Marseille Université, CNRS, LSIS UMR 7296MarseilleFrance

Personalised recommendations