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The Visual Computer

, Volume 29, Issue 3, pp 203–216 | Cite as

Skeleton growing: an algorithm to extract a curve skeleton from a pseudonormal vector field

  • Natapon PantuwongEmail author
  • Masanori Sugimoto
Original Article

Abstract

A curve skeleton is used to represent a 3D object in many different applications. It is a 1D curve that captures topology of the 3D object. The proposed method extracts a curve skeleton from the vector field inside the 3D object. A vector at each voxel of the 3D object is calculated using a pseudonormal vector. By using such a calculation, the computation time is significantly reduced compared with using a typical potential field. A curve skeleton is then extracted from the pseudonormal vector field by using a skeleton-growing algorithm. The proposed algorithm uses high-curvature boundary voxels to search for a set of critical points and skeleton branches near high-curvature areas. The set of detected critical points is then used to grow a curve skeleton in the next step. All parameters of our algorithms are calculated from the 3D object itself, without user intervention. The effectiveness of our method is demonstrated in our experiments.

Keywords

Skeleton growing Curve skeleton Vector field Curvature Topology 

Notes

Acknowledgements

The authors thank Dr. Yasuyuki Matsushita (Microsoft Research Asia) for his constructive duscussions and valuable suggestions. The research is sponsored by Microsoft Research Collaborative Research Projects (MSR CORE7).

Supplementary material

(MPG 20.0 MB)

References

  1. 1.
    Au, O.K.C., Tai, C.L., Chu, H.K., Cohen-Or, D., Lee, T.Y., Project: Skeleton Extraction by Mesh Contraction. http://visgraph.cse.ust.hk/projects/skeleton/
  2. 2.
    Au, O.K.C., Tai, C.L., Chu, H.K., Cohen-Or, D., Lee, T.Y.: Skeleton extraction by mesh contraction. ACM Trans. Graph. 27, 44:1–44:10 (2008) CrossRefGoogle Scholar
  3. 3.
    Aujay, G., Hétroy, F., Lazarus, F., Depraz, C.: Harmonic skeleton for realistic character animation. In: SCA’07, pp. 151–160 (2007) Google Scholar
  4. 4.
    Baran, I., Popović, J.: Automatic rigging and animation of 3D characters. In: SIGGRAPH’07, p. 72 (2007) Google Scholar
  5. 5.
    Bouix, S., Siddiqi, K.: Divergence-based medial surfaces. In: ECCV’00, pp. 603–618 (2000) Google Scholar
  6. 6.
    Cheng, Z.Q., Xu, K., Li, B., Wang, Y.Z., Dang, G., Jin, S.Y.: A mesh meaningful segmentation algorithm using skeleton and minima-rule. In: ISVC’07, pp. 671–680 (2007) Google Scholar
  7. 7.
    Chuang, J.H., Tsai, C.H., Ko, M.C.: Skeletonization of three-dimensional object using generalized potential field. IEEE Trans. Pattern Anal. Mach. Intell. 22, 1241–1251 (2000) CrossRefGoogle Scholar
  8. 8.
    Cornea, N.D., Demirci, M.F., Silver, D., Shokoufandeh, A., Dickinson, S.J., Kantor, P.B.: 3D object retrieval using many-to-many matching of curve skeletons. In: SMI’05, pp. 368–373 (2005) Google Scholar
  9. 9.
    Cornea, N.D., Silver, D., Min, P.: Curve-skeleton properties, applications, and algorithms. IEEE Trans. Vis. Comput. Graph. 13, 530–548 (2007) CrossRefGoogle Scholar
  10. 10.
    Cornea, N.D., Silver, D., Yuan, X., Balasubramanian, R.: Computing hierarchical curve-skeletons of 3D objects. Vis. Comput. 21(11), 945–955 (2005) CrossRefGoogle Scholar
  11. 11.
    Demarsin, K., Vanderstraeten, D., Roose, D.: Meshless extraction of closed feature lines using histogram thresholding. Comput.-Aided Des. Appl. 5(5), 589–600 (2008) Google Scholar
  12. 12.
    Dey, T.K., Sun, J.: Curve skeletons for 3D shapes. http://www.cse.ohio-states.edu/~tamaldey/cskel.html/
  13. 13.
    Dey, T.K., Sun, J.: Defining and computing curve-skeletons with medial geodesic function. In: SGP’06, pp. 143–152 (2006) Google Scholar
  14. 14.
    Globus, A., Levit, C., Lasinski, T.: A tool for visualizing the topology of three-dimensional vector fields. In: VIS’91, pp. 33–40, 408 (1991) Google Scholar
  15. 15.
    Goh, W.B.: Strategies for shape matching using skeletons. Comput. Vis. Image Underst. 110, 326–345 (2008) CrossRefGoogle Scholar
  16. 16.
    Hadwiger, M., Kniss, J.M., Rezk-salama, C., Weiskopf, D., Engel, K.: Real-Time Volume Graphics. A. K. Peters, Ltd., Natick (2006) Google Scholar
  17. 17.
    Hassouna, M.S., Farag, A.A.: Robust centerline extraction framework using level sets. In: CVPR’05, pp. 458–465 (2005) Google Scholar
  18. 18.
    Katz, S., Tal, A.: Hierarchical mesh decomposition using fuzzy clustering and cuts. ACM Trans. Graph. 22, 954–961 (2003) CrossRefGoogle Scholar
  19. 19.
    Liao, D.: GPU-accelerated multi-valued solid voxelization by slice functions in real time. In: SCCG’08, pp. 113–120 (2010) Google Scholar
  20. 20.
    Lien, J.M., Keyser, J., Amato, N.M.: Simultaneous shape decomposition and skeletonization. In: SPM’06, pp. 219–228 (2006) Google Scholar
  21. 21.
    Liu, P.C., Wu, F.C., Ma, W.C., Liang, R.H., Ouhyoung, M.: Automatic animation skeleton construction using repulsive force field. In: PG’03, p. 409 (2003) Google Scholar
  22. 22.
    Ma, C.M., Wan, S.Y., Lee, J.D.: Three-dimensional topology preserving reduction on the 4-subfields. IEEE Trans. Pattern Anal. Mach. Intell. 24(12), 1594–1605 (2002) CrossRefGoogle Scholar
  23. 23.
    Monga, O., Lengagne, R., Deriche, R.: Extraction of the zero-crossings of the curvature derivatives in volumic 3D medical images: a multi-scale approach. In: CVPR’94, pp. 852–855 (1994) Google Scholar
  24. 24.
    Ogniewicz, R., Ilg, M.: Voronoi skeletons: theory and applications. In: CVPR’92, pp. 63–69 (1992) Google Scholar
  25. 25.
    Pantuwong, N., Sugimoto, M.: 3D Curve-skeleton extraction algorithm using a pseudo-normal vector field. In: VMV’10, pp. 235–242 (2010) Google Scholar
  26. 26.
    Pascucci, V., Scorzelli, G., Bremer, P.T., Mascarenhas, A.: Robust on-line computation of Reeb graphs: simplicity and speed. ACM Trans. Graph. 26 (2007) Google Scholar
  27. 27.
    Poirier, M., Paquette, E.: Rig retargeting for 3D animation. In: GI’09, pp. 103–110 (2009) Google Scholar
  28. 28.
    Schwarz, M., Seidel, H.P.: Fast parallel surface and solid voxelization on GPUs. ACM Trans. Graph. 29, 179:1–179:10 (2010) CrossRefGoogle Scholar
  29. 29.
    She, F.H., Chen, R.H., Gao, W.M., Hodgson, P.H., Kong, L.X., Hong, H.Y.: Improved 3D thinning algorithms for skeleton extraction. In: DICTA’09, pp. 14–18 (2009) Google Scholar
  30. 30.
    Shilane, P., Min, P., Kazhdan, M., Funkhouser, T.: The Princeton shape benchmark. In: SMI’04, pp. 167–178 (2004) Google Scholar
  31. 31.
    Theisel, H., Weinkauf, T., Hege, H.C., Seidel, H.P.: Saddle connectors—an approach to visualizing the topological skeleton of complex 3D vector fields. In: VIS’03, p. 30 (2003) Google Scholar
  32. 32.
    Wang, Y.S., Lee, T.Y.: Curve-skeleton extraction using iterative least squares optimization. IEEE Trans. Vis. Comput. Graph. 14, 926–936 (2008) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.The University of TokyoTokyoJapan

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