Discrete 3D Tools Applied to 2D Grey-Level Images

  • Gabriella Sanniti di Baja
  • Ingela Nyström
  • Gunilla Borgefors
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3617)


2D grey-level images are interpreted as 3D binary images, where the grey-level plays the role of the third coordinate. In this way, algorithms devised for 3D binary images can be used to analyse 2D grey-level images. Here, we present three such algorithms. The first algorithm smoothes a 2D grey-level image by flattening its geometrical and grey-level peaks while simultaneously filling in geometrical and grey-level valleys, regarded as non significant in the problem domain. The second algorithm computes an approximation of the convex hull of a 2D grey-level object, by building a covering polyhedron closely fitting the corresponding object in a 3D binary image. The result obtained is convex both from the geometrical and grey-level points of view. The third algorithm skeletonizes a 2D grey-level object by skeletonizing the top surface of the object in the corresponding 3D binary image.


Convex Hull Hollow Space Skeletonization Algorithm Skeleton Branch Local Concavity 
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.
    Sanniti di Baja, G., Svensson, S.: Editing 3D binary images using distance transforms. In: Proc. 15th ICPR, Barcelona, Spain, pp. 1034–1037 (2000)Google Scholar
  2. 2.
    Serra, J.: Image Analysis and Mathematical Morphology, vol. I. Academic Press, London (1982)zbMATHGoogle Scholar
  3. 3.
    Borgefors, G., Nyström, I., Sanniti di Baja, G.: Computing covering polyhedra of non-convex objects. In: Proc. of BMVC 1994, York, pp. 275–284 (1994)Google Scholar
  4. 4.
    Nyström, I., Borgefors, G., Sanniti di Baja, G.: 2D Grey-level Convex Hull Computation: A Discrete 3D Approach. In: Bigun, J., Gustavsson, T. (eds.) SCIA 2003. LNCS, vol. 2749, pp. 763–770. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Svensson, S., Nyström, I., Sanniti di Baja, G.: Curve skeletonization of surface-like objects in 3D images guided by voxel classification. Pattern Recognition Letters 23(12), 1419–1426 (2002)zbMATHCrossRefGoogle Scholar
  6. 6.
    Sanniti di Baja, G., Nyström, I.: 2D Grey-level Skeleton Computation: A Discrete 3D Approach. In: Proc. 17 ICPR, Cambridge, UK, pp. 455–458 (2004)Google Scholar
  7. 7.
    Borgefors, G.: On digital distance transforms in three dimensions. Computer Vision Image Understanding 64(3), 368–376 (1996)CrossRefGoogle Scholar
  8. 8.
    Preparata, F.P., Shamos, M.I.: Computational Geometry. An Introduction. Springer, New York (1985)Google Scholar
  9. 9.
    Lam, L., Lee, S.-W., Suen, C.Y.: Thinning methodologies. A comprehensive survey. IEEE Trans. on PAMI 14(9), 869–885 (1992)Google Scholar
  10. 10.
    Verwer, B.J.H., Van Vliet, L.J., Verbeek, P.W.: Binary and grey-value skeletons: Metrics and algorithms. IJPRAI 7, 1287–1308 (1993)Google Scholar
  11. 11.
    Saha, P.K., Chaudhuri, B.B.: Detection of 3-D simple points for topology preserving transformations with application to thinning. IEEE Trans. on PAMI 16(10), 1028–1032 (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Gabriella Sanniti di Baja
    • 1
  • Ingela Nyström
    • 2
  • Gunilla Borgefors
    • 3
  1. 1.Institute of Cybernetics "E.Caianiello", CNRPozzuoliItaly
  2. 2.Centre for Image AnalysisUUUppsalaSweden
  3. 3.Centre for Image AnalysisSLUUppsalaSweden

Personalised recommendations