Computing a Family of Skeletons of Volumetric Models for Shape Description

  • Tao Ju
  • Matthew L. Baker
  • Wah Chiu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4077)


Skeletons are important shape descriptors in object representation and recognition. Typically, skeletons of volumetric models are computed via an iterative thinning process. However, traditional thinning methods often generate skeletons with complex structures that are unsuitable for shape description, and appropriate pruning methods are lacking. In this paper, we present a new method for computing skeletons on volumes by alternating thinning and a novel skeleton pruning routine. Our method creates a family of skeletons parameterized by two user-specified numbers that determine respectively the size of curve and surface features on the skeleton. As demonstrated on both real-world models and medical images, our method generates skeletons with simple and meaningful structures that are particularly suitable for describing cylindrical and plate-like shapes.


Medial Axis Object Point Image Denoising Pruning Method Object Versus 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Blum, H.: A transformation for extracting new descriptors of shape. In: Wathen-Dunn, W. (ed.) Models for the Perception of Speech and Visual Forms, pp. 362–380. MIT Press, Amsterdam (1967)Google Scholar
  2. 2.
    Lam, L., Lee, S.-W., Suen, C.Y.: Thinning methodologies-a comprehensive survey. IEEE Trans. Pattern Anal. Mach. Intell. 14, 869–885 (1992)CrossRefGoogle Scholar
  3. 3.
    Lee, T.-C., Kashyap, R.L., Chu, C.-N.: Building skeleton models via 3-d medial surface/axis thinning algorithms. CVGIP: Graph. Models Image Process. 56, 462–478 (1994)CrossRefGoogle Scholar
  4. 4.
    Saha, P.K., Chaudhuri, B.B.: Detection of 3-d simple points for topology preserving transformations with application to thinning. IEEE Trans. Pattern Anal. Mach. Intell. 16, 1028–1032 (1994)CrossRefGoogle Scholar
  5. 5.
    Bertrand, G.: Simple points, topological numbers and geodesic neighborhoods in cubic grids. Pattern Recogn. Lett. 15, 1003–1011 (1994)CrossRefGoogle Scholar
  6. 6.
    Tsao, Y.F., Fu, K.S.: A parallel thinning algorithm for 3-d pictures. Comput. Graphics Image Process. 17, 315–331 (1981)CrossRefGoogle Scholar
  7. 7.
    Gong, W., Bertrand, G.: A simple parallel 3d thinning algorithm. In: ICPR 1990, pp. 188–190 (1990)Google Scholar
  8. 8.
    Bertrand, G., Aktouf, Z.: A 3d thinning algorithms using subfields. In: Proceedings, SPIE Conference on Vision Geometry III, vol. 2356, pp. 113–124 (1994)Google Scholar
  9. 9.
    Bertrand, G.: A parallel thinning algorithm for medial surfaces. Pattern Recogn. Lett. 16, 979–986 (1995)CrossRefGoogle Scholar
  10. 10.
    Ma, C.M.: A 3d fully parallel thinning algorithm for generating medial faces. Pattern Recogn. Lett. 16, 83–87 (1995)CrossRefGoogle Scholar
  11. 11.
    Saito, T., Toriwaki, J.: A sequential thinning algorithm for three-dimensional digital pictures using the euclidean distance transformation. In: Proceedings of the 9th Scandinavian Conference on Image Analysis, pp. 507–516 (1995)Google Scholar
  12. 12.
    Palágyi, K., Kuba, A.: A parallel 3d 12-subiteration thinning algorithm. Graph. Models Image Process. 61, 199–221 (1999)CrossRefGoogle Scholar
  13. 13.
    Attali, D., Sanniti di Baja, G., Thiel, E.: Pruning discrete and semicontinuous skeletons. In: Braccini, C., Vernazza, G., DeFloriani, L. (eds.) ICIAP 1995. LNCS, vol. 974, pp. 488–493. Springer, Heidelberg (1995)Google Scholar
  14. 14.
    Shaked, D., Bruckstein, A.M.: Pruning medial axes. Comput. Vis. Image Underst. 69, 156–169 (1998)CrossRefGoogle Scholar
  15. 15.
    Ogniewicz, R.L., Kübler, O.: Hierarchic Voronoi skeletons. Pattern Recognition 28, 343–359 (1995)CrossRefGoogle Scholar
  16. 16.
    Attali, D., Montanvert, A.: Computing and simplifying 2d and 3d continuous skeletons. Comput. Vis. Image Underst. 67, 261–273 (1997)CrossRefGoogle Scholar
  17. 17.
    Amenta, N., Choi, S., Kolluri, R.K.: The power crust. In: SMA 2001: Proceedings of the sixth ACM symposium on Solid modeling and applications, pp. 249–266. ACM Press, New York (2001)CrossRefGoogle Scholar
  18. 18.
    Dey, T.K., Zhao, W.: Approximate medial axis as a voronoi subcomplex. In: SMA 2002: Proceedings of the seventh ACM symposium on Solid modeling and applications, pp. 356–366. ACM Press, New York (2002)CrossRefGoogle Scholar
  19. 19.
    Foskey, M., Lin, M.C., Manocha, D.: Efficient computation of a simplified medial axis. In: SM 2003: Proceedings of the eighth ACM symposium on Solid modeling and applications, pp. 96–107. ACM Press, New York (2003)CrossRefGoogle Scholar
  20. 20.
    Tam, R., Heidrich, W.: Shape simplification based on the medial axis transform. In: Proceedings of IEEE Visualization (2003)Google Scholar
  21. 21.
    Sud, A., Foskey, M., Manocha, D.: Homotopy-preserving medial axis simplification. In: SPM 2005: Proceedings of the 2005 ACM symposium on Solid and physical modeling, pp. 39–50. ACM Press, New York (2005)CrossRefGoogle Scholar
  22. 22.
    Mekada, Y., Toriwaki, J.: Anchor point thinning using a skeleton based on the euclidean distance transformation. In: ICPR 2002: Proceedings of the 16 th International Conference on Pattern Recognition (ICPR 2002), Washington, DC, USA, vol. 3, p. 30923. IEEE Computer Society Press, Los Alamitos (2002)Google Scholar
  23. 23.
    Svensson, S., Sanniti di Baja, G.: Simplifying curve skeletons in volume images. Comput. Vis. Image Underst. 90, 242–257 (2003)MATHCrossRefGoogle Scholar
  24. 24.
    Saha, P., Gomberg, B., Wehrli, F.: Three-dimensional digital topological characterization of cancellous bone architecture. IJIST 11, 81–90 (2000)Google Scholar
  25. 25.
    Bonnassie, A., Peyrin, F., Attali, D.: Shape description of three-dimensional images based on medial axis. In: Proc. 10th Int. Conf. on Image Processing, Thessaloniki, Greece (2001)Google Scholar
  26. 26.
    Lorensen, W.E., Cline, H.E.: Marching cubes: A high resolution 3d surface construction algorithm. In: SIGGRAPH 1987: Proceedings of the 14th annual conference on Computer graphics and interactive techniques, pp. 163–169. ACM Press, New York (1987)CrossRefGoogle Scholar
  27. 27.
    Natarajan, B.K.: On generating topologically consistent isosurfaces from uniform samples. The Visual Computer 11, 52–62 (1994)CrossRefGoogle Scholar
  28. 28.
    Ju, T.: Robust repair of polygonal models. ACM Trans. Graph. 23, 888–895 (2004)CrossRefGoogle Scholar
  29. 29.
    Chiu, W., Baker, M., Jiang, W., Zhou, Z.: Deriving the folds of macromolecular complexes through electron cryomicroscopy and bioinformatics approaches. Curr. Opin. Struct. Biol. 2, 263–269 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tao Ju
    • 1
  • Matthew L. Baker
    • 2
  • Wah Chiu
    • 2
  1. 1.Washington UniversitySt. Louis
  2. 2.Baylor College of MedicineHouston

Personalised recommendations