The Euclidean Distance Transform Applied to the FCC and BCC Grids

  • Robin Strand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3522)


The discrete Euclidean distance transform is applied to grids with non-cubic voxels, the face-centered cubic (fcc) and body-centered cubic (bcc) grids. These grids are three-dimensional generalizations of the hexagonal grid. Raster scanning and contour processing techniques are applied using different neighbourhoods. When computing the Euclidean distance transform, some voxel configurations produce errors. The maximum errors for the two different grids and neighbourhood sizes are analyzed and compared with the cubic grid.


Euclidean Distance Grid Point Maximum Error Voronoi Diagram Maximum Relative Error 
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.
    Bell, S.B.M., Holroyd, F.C., Mason, D.C.: A digital geometry for hexagonal pixels. Image and Vision Computing 7, 194–204 (1989)CrossRefGoogle Scholar
  2. 2.
    Herman, G.T.: Geometry of Digital Spaces. Birkhäuser, Basel (1998)zbMATHGoogle Scholar
  3. 3.
    Borgefors, G.: On digital distance transforms in three dimensions. Computer Vision and Image Understanding 64, 368–376 (1996)CrossRefGoogle Scholar
  4. 4.
    Danielsson, P.E.: Euclidean distance mapping. Computer Graphics and Image Processing 14, 227–248 (1980)CrossRefGoogle Scholar
  5. 5.
    Ragnemalm, I.: The Euclidean distance transform and its implementation on SIMD architectures. In: Proceedings of 6th Scandinavian Conference on Image Analysis, Oulu, Finland, pp. 379–384 (1989)Google Scholar
  6. 6.
    Ragnemalm, I.: The Euclidean distance transform in arbitrary dimensions. Pattern Recognition Letters 14, 883–888 (1993)zbMATHCrossRefGoogle Scholar
  7. 7.
    Strand, R., Borgefors, G.: Distance transforms for three-dimensional grids with non-cubic voxels (2004) (Submitted for publication)Google Scholar
  8. 8.
    Vincent, L.: Exact Euclidean distance function by chain propagations. In: Proceedings IEEE Conference on Computer Vision and Pattern Recognition, Maui, Hawaii, pp. 520–525 (1991)Google Scholar
  9. 9.
    Ragnemalm, I.: Neighborhoods for distance transformations using ordered propagation. Computer Vision, Graphics, and Image Processing 56, 399–409 (1992)zbMATHGoogle Scholar
  10. 10.
    Cuisenaire, O., Macq, B.: Fast Euclidean distance transformation by propagation using multiple neighborhoods. Computer Vision and Image Understanding 76, 163–172 (1999)CrossRefGoogle Scholar
  11. 11.
    Yamada, H.: Complete Euclidean distance transformation by parallel operation. In: Proceedings 7th international Conference on Pattern Recognition, Montreal, pp. 69–71 (1984)Google Scholar
  12. 12.
    Maurer, C.R., Qi, R., Raghavan, V.: A linear time algorithm for computing exact Euclidean distance transforms of binary images in arbitrary dimensions. IEEE Transactions on Pattern Analysis and Machine Intelligence 25, 265–270 (2003)CrossRefGoogle Scholar
  13. 13.
    Breu, H., Gil, J., Kirkpatrick, D., Werman, M.: Linear time Euclidean distance transform algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence 17, 529–533 (1995)CrossRefGoogle Scholar
  14. 14.
    Guan, W., Ma, S.: A list-processing approach to compute Voronoi diagrams and the Euclidean distance transform. IEEE Transactions on Pattern Analysis and Machine Intelligence 20, 757–761 (1998)CrossRefGoogle Scholar
  15. 15.
    Mullikin, J.C.: The vector distance transform in two and three dimensions. CVGIP: Graphical Models and Image Processing 54, 526–535 (1992)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Robin Strand
    • 1
  1. 1.Centre for Image AnalysisUppsala UniversityUppsalaSweden

Personalised recommendations