Decomposing Digital 3D Shapes Using a Multiresolution Structure

  • Gunilla Borgefors
  • Stina Svensson
  • Gabriella Sanniti di Baja
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)


In many applications, e. g. object recognition, decomposition of a shape is of great interest. We present a decomposition algorithm for 3D shape that is based on a multiresolution structure. The shape is hierarchically decomposed according to local thickness. A merging process is introduced for merging of small components to more significant parts. As a side effect of the algorithm, we also obtain a way of smoothing noisy shapes.


Merging Process Local Thickness Distance Transform Merging Algorithm Pattern Recognition Letter 
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.
    C. Arcelli and G. Sanniti di Baja. Finding local maxima in a pseudo-Euclidean distance transform. Computer Vision, Graphics and Image Processing, 43(3):361–367, Sept. 1988.CrossRefGoogle Scholar
  2. 2.
    I. Biederman. Recognition-by-components: A theory of human image understanding. Psychological Review, 94(2):115–147, 1987.CrossRefGoogle Scholar
  3. 3.
    G. Borgefors. On digital distance transform in three dimensions. Computer Vision and Image Understanding, 64(3):368–376, Nov. 1996.CrossRefGoogle Scholar
  4. 4.
    G. Borgefors and I. Nyström. Efficient shape representation by minimizing the set of centres of maximal discs/spheres. Pattern Recognition Letters, 18:465–472, 1997.CrossRefGoogle Scholar
  5. 5.
    G. Borgefors and G. Sanniti di Baja. Parallel smoothing and decomposition of digital shapes using a multiresolution structure. In Proceedings 10th International Conference on Pattern Recognition, pages 745–748. IEEE Computer Society Press, 1990.Google Scholar
  6. 6.
    G. Borgefors, G. Sanniti di Baja, and S. Svensson. Multiresolution representation of shape in binary images ii: Volume images. In E. Ahronovitz and C. Fiorio, editors, Discrete Geometry for Computer Imagery (DGCI’97), pages 75–86. Springer Verlag, Berlin Heidelberg1997. Lecture Notes in Computer Science1347.CrossRefGoogle Scholar
  7. 7.
    A. Held and K. Abe. On decomposition of binary shapes into meaningful parts. Pattern Recognition, 27(5):637–647, 1994.CrossRefGoogle Scholar
  8. 8.
    I. Ragnemalm. The Euclidean distance transform in arbitrary dimensions. Pattern Recognition Letters, 14(11):883–888, Nov. 1993.zbMATHCrossRefGoogle Scholar
  9. 9.
    G. Sanniti di Baja and E. Thiel. (3,4)-weighted skeleton decomposition for pattern representation and description. Pattern Recognition, 27(8):1039–1049, 1994.CrossRefGoogle Scholar
  10. 10.
    K. Siddiqi and B.B. Kimia. Parts of visual form: Computational aspects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(3):239–251, Mar. 1995.CrossRefGoogle Scholar
  11. 11.
    K. Siddiqi, K.J. Tresness, and B.B. Kimia. On the anatomy of visual form. In C. Arcelli, L.P. Cordella, and G. Sanniti di Baja, editors, Aspects of Visual Form Processing, pages 507–521. World Scientific Publishing Co. Pte. Ltd., 1994.Google Scholar
  12. 12.
    J. Xu. Morphological decomposition of 2-D binary shapes into simpler shape parts. Pattern Recognition Letters, 17(7):759–769, 1996.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Gunilla Borgefors
    • 1
  • Stina Svensson
    • 1
  • Gabriella Sanniti di Baja
    • 2
  1. 1.Centre for Image AnalysisSwedish University of Agricultural SciencesUppsalaSWEDEN
  2. 2.Italian National Research CouncilIstituto di CiberneticaArco Felice (Naples)ITALY

Personalised recommendations