Segmenting Simplified Surface Skeletons

  • Dennie Reniers
  • Alexandru Telea
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)

Abstract

A novel method for segmenting simplified skeletons of 3D shapes is presented. The so-called simplified Y-network is computed, defining boundaries between 2D sheets of the simplified 3D skeleton, which we take as our skeleton segments. We compute the simplified Y-network using a robust importance measure which has been proved useful for simplifying complex 3D skeleton manifolds. We present a voxel-based algorithm and show results on complex real-world objects, including ones containing large amounts of boundary noise.

Keywords

Feature Point Geodesic Distance Medial Axis Importance Measure Pruning Strategy 
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.

References

  1. 1.
    Zhang, J., Siddiqi, K., Macrini, D., Shokoufandeh, A., Dickinson, S.: Retrieving articulated 3-d models using medial surfaces and their graph spectra. In: Int. Workshop On Energy Minimization Methods in Computer Vision and Pattern Recognition, pp. 285–300 (2005)Google Scholar
  2. 2.
    Damon, J.: Global medial structure of regions in R 3. Geometry and Topology 10, 2385–2429 (2006)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Reniers, D., Van Wijk, J.J., Telea, A.: Computing multiscale curve and surface skeletons of genus 0 shapes using a global importance measure. IEEE TVCG 14(2), 355–368 (2008)Google Scholar
  4. 4.
    Malandain, G., Bertrand, G., Ayache, N.: Topological segmentation of discrete surfaces. International Journal of Computer Vision 10(2), 183–197 (1993)CrossRefGoogle Scholar
  5. 5.
    Reniers, D., Telea, A.: Tolerance-based feature transforms. In: Advances in Computer Graphics and Computer Vision, CCIS, vol. 4, pp. 187–200. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Cornea, N.D., Silver, D., Min, P.: Curve-skeleton properties, applications and algorithms. IEEE Transactions on Visualization and Computer Graphics 13(3), 530–548 (2007)CrossRefGoogle Scholar
  7. 7.
    Lieutier, A.: Any open bounded subset of ℝ3 has the same homotopy type as its medial axis. In: Proc. of the 8th ACM symposium on Solid modeling and applications, pp. 65–75 (2003)Google Scholar
  8. 8.
    Giblin, P., Kimia, B.B.: A formal classification of 3d medial axis points and their local geometry. IEEE Trans. on Pattern Analysis and Machine Intelligence 26(2), 238–251 (2004)CrossRefGoogle Scholar
  9. 9.
    Chazala, F., Lieutier, A.: The λ-medial axis. Graphical Models 67(5), 304–331 (2005)CrossRefGoogle Scholar
  10. 10.
    Shaked, D., Bruckstein, A.M.: Pruning medial axes. Computer Vision and Image Understanding 69(2), 156–169 (1998)CrossRefGoogle Scholar
  11. 11.
    Malandain, G., Fernández-Vidal, S.: Euclidean skeletons. Image and Vision Computing 16(5), 317–327 (1998)CrossRefGoogle Scholar
  12. 12.
    Siddiqi, K., Bouix, S., Tannenbaum, A., Zucker, S.W.: The hamilton-jacobi skeleton. In: Proc. of the Int. Conference on Computer Vision (ICCV 1999), pp. 828–834 (1999)Google Scholar
  13. 13.
    Ogniewicz, R.L., Kübler, O.: Hierarchic voronoi skeletons. Pattern Recognition 28(3), 343–359 (1995)CrossRefGoogle Scholar
  14. 14.
    Costa, L.F., Cesar Jr, R.M.: Shape analysis and classification, pp. 416–419. CRC Press, Boca Raton (2001)Google Scholar
  15. 15.
    Telea, A., Van Wijk, J.J.: An augmented fast marching method for computing skeletons and centerlines. In: Proc. of the Symposium on Data Visualisation (VisSym 2002), pp. 251–259 (2002)Google Scholar
  16. 16.
    Dey, T.K., Sun, J.: Defining and computing curve-skeletons with medial geodesic function. In: Proc. of Eurographics Symposium on Geometry Processing, pp. 143–152 (2006)Google Scholar
  17. 17.
    Mullikin, J.C.: The vector distance transform in two and three dimensions. CVGIP: Graphical Models and Image Processing 54(6), 526–535 (1992)CrossRefGoogle Scholar
  18. 18.
    Kiryati, N., Székely, G.: Estimating shortest paths and minimal distances on digitized three-dimensional surfaces. Pattern Recognition 26, 1623–1637 (1993)CrossRefGoogle Scholar
  19. 19.
    Reniers, D., Telea, A.C.: Skeleton-based hierarchical shape segmentation. In: Proc. of the IEEE Int. Conf. on Shape Modeling and Applications (SMI 2007), pp. 179–188 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Dennie Reniers
    • 1
  • Alexandru Telea
    • 2
  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Institute for Mathematics and Computing ScienceUniversity of GroningenGroningenThe Netherlands

Personalised recommendations