Skeleton Extraction of Vertex Sets Lying on Arbitrary Triangulated 3D Meshes

  • Dimitri Kudelski
  • Sophie Viseur
  • Jean-Luc Mari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7749)

Abstract

Complex models can be simply described by notions such as skeletons. These robust shape descriptors faithfully characterize the geometry and the topology of an object. Several methods have been developed yet to obtain the skeleton from regular object representations (e.g. 2D images or 3D volumes) but only a few attempt to extract the skeleton from unstructured 3D mesh patches. In this article, we extract a skeleton by topological thinning from vertex sets lying on arbitrary triangulated surface meshes in 3D. The key idea comes down to eroding a 2D set located on a discrete 2-manifold. The main difficulty is to transpose the notion of neighborhood from the classical thinning algorithms where the adjacency is constant (e.g. 26-adjacency in digital volumes, 8-adjacency in 2D images) to the mesh domain where the neighborhood is variable due to the adjacency of each vertex. Thus we propose a thinning operator dedicated to irregular meshes in order to extract the skeleton of a vertex set. To estimate the robustness of our technique, several tests and an application to the feature line detection are presented as a case-study.

Keywords

surface skeleton extraction topological thinning irregular mesh 

References

  1. 1.
    Au, O.K.C., Tai, C.L., Chu, H.K., Cohen-Or, D., Lee, T.Y.: Skeleton extraction by mesh contraction. ACM Transaction on Graphics 27(3), 1–10 (2008)CrossRefGoogle Scholar
  2. 2.
    Bertrand, G.: Simple points, topological numbers and geodesic neighborhoods in cubic grids. Patterns Recognition Letters 15, 1003–1011 (1994)CrossRefGoogle Scholar
  3. 3.
    Bertrand, G.: A boolean characterization of three-dimensional simple points. Pattern Recognition Letters 17, 115–124 (1996)CrossRefGoogle Scholar
  4. 4.
    Gall, J., Stoll, C., De Aguiar, E., Theobalt, C., Rosenhahn, B., Seidel, H.: Motion capture using joint skeleton tracking and surface estimation. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2009), pp. 1746–1753. IEEE Computer Society (June 2009)Google Scholar
  5. 5.
    Goldfeather, J., Interrante, V.: A novel cubic-order algorithm for approximating principal direction vectors. ACM Transaction on Graphics 23(1), 45–63 (2004)CrossRefGoogle Scholar
  6. 6.
    Kudelski, D., Mari, J.L., Viseur, S.: 3D feature line detection based on vertex labeling and 2D skeletonization. In: IEEE International Conference on Shape Modeling and Applications (SMI 2010), pp. 246–250. IEEE Computer Society (June 2010)Google Scholar
  7. 7.
    Kudelski, D., Mari, J.L., Viseur, S.: Extraction of feature lines with connectivity preservation. In: Computer Graphics International (CGI 2011 Electronic Proceedings) (June 2011)Google Scholar
  8. 8.
    Lee, T., Kashyap, R., Chu, C.: Building skeleton models via 3-D medial surface/axis thinning algorithms. Graphical Models and Image Processing 56(6), 462–478 (1994)CrossRefGoogle Scholar
  9. 9.
    Mari, J.-L.: Surface Sketching with a Voxel-Based Skeleton. In: Brlek, S., Reutenauer, C., Provençal, X. (eds.) DGCI 2009. LNCS, vol. 5810, pp. 325–336. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Rössl, C., Kobbelt, L., Seidel, H.P.: Extraction of feature lines on triangulated surfaces using morphological operators. In: AAAI Spring Symposium on Smart Graphics, vol. 00-04, pp. 71–75 (March 2000)Google Scholar
  11. 11.
    Siddiqi, K., Pizer, S.: Medial Representations. Mathematics, Algorithms and Applications. Computational Imaging and Vision, vol. 37. Springer (2008)Google Scholar
  12. 12.
    Yu, K., Wu, J., Zhuang, Y.: Skeleton-Based Recognition of Chinese Calligraphic Character Image. In: Huang, Y.-M.R., Xu, C., Cheng, K.-S., Yang, J.-F.K., Swamy, M.N.S., Li, S., Ding, J.-W. (eds.) PCM 2008. LNCS, vol. 5353, pp. 228–237. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Zhang, T.Y., Suen, C.Y.: A fast parallel algorithm for thinning digital patterns. Communications of the ACM 27(3), 236–239 (1984)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dimitri Kudelski
    • 1
    • 2
    • 3
  • Sophie Viseur
    • 1
    • 3
  • Jean-Luc Mari
    • 1
    • 2
  1. 1.Aix-Marseille UniversityFrance
  2. 2.UMR CNRS 7296Information and System Science Laboratory (LSIS)France
  3. 3.European Center for Research and Teaching in Environmental Geoscience (CEREGE)France

Personalised recommendations