The <3,4,5> Curvilinear Skeleton

  • Carlo Arcelli
  • Gabriella Sanniti di Baja
  • Luca Serino
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)


A new skeletonization algorithm is presented to compute the curvilinear skeleton of 3D objects. The algorithm is based on the use of the <3,4,5> distance transform, on the detection of suitable anchor points, and on iterated topology preserving voxel removal. The obtained skeleton is topologically correct, is symmetrically placed within the object and its structure reflects the morphology of the represented object.


Anchor Point Pruning Step Skeletonization Algorithm Maximal Disc Maximal Ball 
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.


  1. 1.
    Siddiqi, K., Pizer, S.M. (eds.): Medial Representations. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  2. 2.
    De Floriani, L., Spagnuolo, M. (eds.): Shape Analysis and Structuring. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  3. 3.
    Arcelli, C., Sanniti di Baja, G.: A width-independent fast thinning algorithm. IEEE Trans. on PAMI 7, 463–474 (1985)CrossRefGoogle Scholar
  4. 4.
    Klein, F.: Euclidean skeletons. In: Proc. 5th Scandinavian Conf. Image Anal., pp. 443–450 (1987)Google Scholar
  5. 5.
    Arcelli, C., Sanniti di Baja, G.: A one-pass two-operations process to detect the skeletal pixels on the 4-distance transform. IEEE Trans. PAMI 11, 411–414 (1989)CrossRefGoogle Scholar
  6. 6.
    Xia, Y.: Skeletonization via the realization of the fire front’s propagation and extinction in digital binary shapes. IEEE Trans. PAMI 11(10), 1076–1086 (1989)CrossRefGoogle Scholar
  7. 7.
    Arcelli, C., Sanniti di Baja, G.: Euclidean skeleton via center-of-maximal-disc extraction. Image and Vision Computing 11, 163–173 (1993)CrossRefGoogle Scholar
  8. 8.
    Kimmel, R., Shaked, D., Kiryati, N.: Skeletonization via distance maps and level sets. Computer Vision and Image Understanding 62(3), 382–391 (1995)CrossRefGoogle Scholar
  9. 9.
    Sanniti di Baja, G., Thiel, E.: Skeletonization algorithm running on path-based distance maps. Image and Vision Computing 14, 47–57 (1996)CrossRefGoogle Scholar
  10. 10.
    Pudney, C.: Distance-ordered homotopic thinning: a skeletonization algorithm for 3D digital images. Computer Vision and Image Understanding 72(3), 404–413 (1998)CrossRefGoogle Scholar
  11. 11.
    Zhou, Y., Kaufman, A., Toga, A.W.: Three-dimensional skeleton and centerline generation based on an approximate minimum distance field. The Visual Computer 14(7), 303–314 (1998)CrossRefGoogle Scholar
  12. 12.
    Borgefors, G., Nystrom, I., Sanniti di Baja, G.: Computing skeletons in three dimensions. Pattern Recognition 32(7), 1225–1236 (1999)CrossRefGoogle Scholar
  13. 13.
    Sanniti di Baja, G., Svensson, S.: Surface skeletons detected on the d6 distance transform. In: Amin, A., Pudil, P., Ferri, F., Iñesta, J.M. (eds.) SPR 2000 and SSPR 2000. LNCS, vol. 1876, pp. 387–396. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  14. 14.
    Blum, H.: Biological shape and visual science. Journal of Theoretical Biology 38, 205–287 (1973)CrossRefGoogle Scholar
  15. 15.
    Leymarie, F., Levine, M.D.: Simulating the grassfire transform using an active contour model. IEEE Trans. PAMI 14(1), 56–75 (1992)CrossRefGoogle Scholar
  16. 16.
    Kimia, B.B., Tannenbaum, A., Zucker, S.W.: Shape, shocks, and deformations I: the components of two-dimensional shape and the reaction-diffusion space. International Journal of Computer Vision 15, 189–224 (1995)CrossRefGoogle Scholar
  17. 17.
    Siddiqi, K., Bouix, S., Tannenbaum, A., Zucker, S.W.: Hamilton-Jacobi skeletons. International Journal of Computer Vision 48(3), 215–231 (2002)CrossRefzbMATHGoogle Scholar
  18. 18.
    Dimitrov, P., Damon, J.N., Siddiqi, K.: Flux invariants for shape. In: Proc. IEEE Conf. CVPR 2003, Madison, WI, vol. 1, pp. 835–841 (2003)Google Scholar
  19. 19.
    Giblin, P.J., Kimia, B.B.: A formal classification of 3D medial axis points and their local geometry. IEEE Trans. PAMI 26(2), 238–251 (2004)CrossRefGoogle Scholar
  20. 20.
    Saha, P.K., Chaudhuri, B.B.: Detection of 3D simple points for topology preserving transformations with application to thinning. IEEE Trans. PAMI 16(10), 1028–1032 (1994)CrossRefGoogle Scholar
  21. 21.
    Bertrand, G., Malandain, G.: A new characterization of three-dimensional simple points. Pattern Recognition Letters 15(2), 169–175 (1994)CrossRefzbMATHGoogle Scholar
  22. 22.
    Borgefors, G.: Digital distance transforms in 2D, 3D, and 4D. In: Chen, C.H., Wang, P.P.S. (eds.) Handbook of Pattern Recognition and Computer Vision, pp. 157–176. World Scientific, Singapore (2005)CrossRefGoogle Scholar
  23. 23.
    Svensson, S., Sanniti di Baja, G.: Using distance transforms to decompose 3D discrete objects. Image and Vision Computing 20, 529–540 (2002)CrossRefGoogle Scholar
  24. 24.
    Shaked, D., Bruckstein, A.M.: Pruning medial axes. Computer Vision and Image Understanding 69(2), 156–169 (1998)CrossRefGoogle Scholar
  25. 25.
    Svensson, S., Sanniti di Baja, G.: Simplifying curve skeletons in volume images. Computer Vision and Image Understanding 90(3), 242–257 (2003)CrossRefzbMATHGoogle Scholar
  26. 26.
    AIM@SHAPE Shape Repository,
  27. 27.
    Shilane, P., Min, P., Kazhdan, M., Funkhouser, T.: The Princeton Shape Benchmark. In: Shape Modeling International, Genova, Italy (June 2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Carlo Arcelli
    • 1
  • Gabriella Sanniti di Baja
    • 1
  • Luca Serino
    • 1
  1. 1.Institute of Cybernetics “E. Caianiello”CNRPozzuoli (Naples)Italy

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