On the Use of Shape Primitives for Reversible Surface Skeletonization

  • Stina Svensson
  • Pieter P. Jonker
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)


We use a mathematical morphology approach to compute the surface and curve skeletons of a 3D object. We focus on the behaviour of the surface skeleton, in particular the reversibility for the case when the skeleton is, and is not anchored to the set of centres of maximal balls. We elaborate on the difficulties to obtain a reversible surface skeleton that does not depend on the orientation of the original object with respect to the grid, and that has no jagged borders.


Topological erosion mathematical morphology distance transform 


  1. 1.
    Attali, D., Lachaud, J.O.: Delaunay conforming iso-surface, skeleton extraction and noise removal. Computational Geometry 19, 175–189 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Leymarie, F.F., Kimia, B.B.: The shock scaffold for representing 3D shape. In: Arcelli, C., Cordella, L.P., Sanniti di Baja, G. (eds.) IWVF 2001. LNCS, vol. 2059, pp. 216–228. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Ma, C.M., Wan, S.Y.: A medial-surface oriented 3-d two-subfield thinning algorithm. Pattern Recognition Letters 22, 1439–1446 (2001)zbMATHCrossRefGoogle Scholar
  4. 4.
    Palágyi, K., Kuba, A.: A parallel 3D 12-subiteration thinning algorithm. Graphical Models and Image Processing 61, 199–221 (1999)CrossRefGoogle Scholar
  5. 5.
    Jonker, P.P.: Skeletons in N dimensions using shape primitives. Pattern Recognition Letters 23, 677–686 (2002)zbMATHCrossRefGoogle Scholar
  6. 6.
    Svensson, S.: Reversible surface skeletons of 3D objects by iterative thinning of distance transforms. In: Bertrand, G., Imiya, A., Klette, R. (eds.) Digital and Image Geometry. LNCS, vol. 2243, pp. 395–406. Springer, Heidelberg (2002)Google Scholar
  7. 7.
    Rosenfeld, A., Pfaltz, J.L.: Sequential operations in digital picture processing. Journal of the Association for Computing Machinery 13, 471–494 (1966)zbMATHGoogle Scholar
  8. 8.
    Borgefors, G.: Applications using distance transforms. In: Arcelli, C., Cordella, L.P., Sanniti di Baja, G. (eds.) Aspects of Visual Form Processing, pp. 83–108. World Scientific Publishing Co. Pte. Ltd., Singapore (1994)Google Scholar
  9. 9.
    Borgefors, G.: On digital distance transforms in three dimensions. Computer Vision and Image Understanding 64, 368–376 (1996)CrossRefGoogle Scholar
  10. 10.
    Svensson, S., Borgefors, G.: Digital distance transforms in 3D images using information from neighbourhoods up to 5 × 5 × 5. Computer Vision and Image Understanding 88, 24–53 (2002)Google Scholar
  11. 11.
    Danielsson, P.E.: Euclidean distance mapping. Computer Graphics and Image Processing 14, 227–248 (1980)CrossRefGoogle Scholar
  12. 12.
    Ragnemalm, I.: The Euclidean distance transform in arbitrary dimensions. Pattern Recognition Letters 14, 883–888 (1993)zbMATHCrossRefGoogle Scholar
  13. 13.
    Borgefors, G., Ragnemalm, I., Sanniti di Baja, G.: The Euclidean distance transform: Finding the local maxima and reconstructing the shape. In: Johansen, P., Olsen, S. (eds.) Proceedings of Scandinavian Conference on Image Analysis (SCIA 1991), Pattern Recognition Society of Denmark, pp. 974–981 (1991)Google Scholar
  14. 14.
    Nyström, I., Borgefors, G.: Synthesising objects and scenes using the reverse distance transformation in 2D and 3D. In: Braccini, C., Floriani, L.D., Vernazza, G. (eds.) ICIAP 1995. LNCS, vol. 974, pp. 441–446. Springer, Heidelberg (1995)Google Scholar
  15. 15.
    Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, Inc., New York (1982)zbMATHGoogle Scholar
  16. 16.
    Kong, T.Y.: A digital fundamental group. Computers & Graphics 13, 159–166 (1989)CrossRefGoogle Scholar
  17. 17.
    Jonker, P.P.: Morphological operations in recursive neighbourhoods. Accepted for publication in Pattern Recognition Letters (2002)Google Scholar
  18. 18.
    Jonker, P.P.: Lecture notes on mathematical morphology for 2, 3 & 4 dimensional images and its implementation in soft and hardware. In: Wojciechowski, K. (ed.) Summer School on Mathematical Morphology and Signal Processing, Zakopane, Poland, vol. 2, pp. 41–120 (1995) ISBN 83-904743-2-8Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Stina Svensson
    • 1
  • Pieter P. Jonker
    • 2
  1. 1.Centre for Image AnalysisSwedish University of, Agricultural SciencesUppsalaSweden
  2. 2.Pattern Recognition Group, Faculty of Applied SciencesDelft University of TechnologyDelftThe Netherlands

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