Advertisement

Euclidean Distance Transform of Digital Images in Arbitrary Dimensions

  • Dong Xu
  • Hua Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4261)

Abstract

A new algorithm for Euclidean distance transform is proposed in this paper. It propagates from the boundary to the inner of object layer by layer, like the inverse propagation of water wave. It can be applied in every dimensional space and has linear time complexity. Euclidean distance transformations of digital images in 2-D and 3-D are conducted in the experiments. Voronoi diagram and Delaunay triangulation can also be produced by this method.

Keywords

Euclidean Distance Voronoi Diagram Delaunay Triangulation Arbitrary Dimension Active Contour Model 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ye, Q.Z.: The Signed Euclidean Distance Transform and Its Applications. In: Proc. ninth Int. Conf. Pattern Recognition, pp. 495–499 (1988)Google Scholar
  2. 2.
    Huang, C.T., Mitchell, O.R.: A Euclidean Distance Transform Using Grayscale Morphology Decomposition. IEEE Trans. Pattern Analysis and Machine Intelligence 16, 443–448 (1994)CrossRefGoogle Scholar
  3. 3.
    Shih, F.Y., Mitchell, O.R.: A Mathematical Morphology Approach to Euclidean Distance Transformation. IEEE Trans. Image Processing. 1, 197–204 (1992)CrossRefGoogle Scholar
  4. 4.
    Shih, F.Y., Liu, J.J.: Size-invariant Four-scan Euclidean Distance Transformation. Pattern Recognition 31, 1761–1766 (1998)CrossRefGoogle Scholar
  5. 5.
    Shih, F.Y., Wu, Y.T.: The Efficient Algorithms for Achieving Euclidean Distance Transformation. IEEE Trans. Image Processing. 13, 1078–1091 (2004)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Vincent, L.: Exact Euclidean Distance Function by Chain Propagations. In: IEEE Proc. Computer Vision and Pattern Recognition, pp. 520–525 (1991)Google Scholar
  7. 7.
    Cuisenaire, O., Macq, B.: Fast and Exact Signed Euclidean Distance Transformation with Linear Complexity. In: Proc. Int. Conf. Acoustics, Speech, and Signal Processing, pp. 3293–3296 (1990)Google Scholar
  8. 8.
    Schouten, T., Broek, E.V.D.: Fast Exact Euclidean Distance (FEED) Transformation. In: Int. Conf. Pattern Recognition, pp. 594–597 (2004)Google Scholar
  9. 9.
    Breu, H., Gil, J., Kirkpatrick, D., Werman, M.: Linear Time Euclidean Distance Transform Algorithms. IEEE Trans. Pattern Analysis and Machine Intelligence 17, 529–533 (1995)CrossRefGoogle Scholar
  10. 10.
    Guan, W.G., Ma, S.D.: A List-Processing Approach to Compute Voronoi Diagrams and the Euclidean Distance Transform. IEEE Trans. Pattern Analysis and Machine Intelligence 20, 757–761 (1998)CrossRefGoogle Scholar
  11. 11.
    Maurer Jr., C.R., Qi, R.S., Raghavan, V.: A Linear Time Algorithm for Computing Exact Euclidean Distance Transforms of Binary Images in Arbitrary Dimensions. IEEE Trans. Pattern Analysis and Machine Intelligence 25, 265–270 (2003)CrossRefGoogle Scholar
  12. 12.
    Ragnemalm, I.: The Euclidean Distance Transform in Arbitrary Dmensions. In: Int. Conf. Image Processing and its Applications, pp. 290–293 (1992)Google Scholar
  13. 13.
    Zhang, S., Karim, M.A.: Euclidean Distance Transform by Stack Filters. IEEE Signal Processing Letters 6, 253–256 (1999)CrossRefGoogle Scholar
  14. 14.
    Capson, D.W., Fung, A.C.: Connected Skeletons from 3D Distance Transforms. In: Southwest Symposium on Image Analysis and Interpretation, pp. 174–179 (1998)Google Scholar
  15. 15.
    Golland, P., Grimson, W.E.L.: Fixed Topology Skeletons. In: IEEE Proc. Computer Vision and Pattern Recognition, pp. 10–17 (2000)Google Scholar
  16. 16.
    Choi, W.P., Lam, K.M., Siu, W.C.: Extraction of the Euclidean Skeleton Based on a Connectivity Criterion. Pattern Recognition 36, 721–729 (2003)MATHCrossRefGoogle Scholar
  17. 17.
    Shih, F.Y., Wu, Y.-T.: Three-dimensional Euclidean Distance Transformation and its Application to Shortest Path Planning. Pattern Recognition 37, 79–92 (2004)MATHCrossRefGoogle Scholar
  18. 18.
    Leymarie, F., Levine, M.D.: Simulating the Grassfire Transform Using an Active Contour Model. IEEE Trans. Pattern Analysis and Machine Intelligence 14, 56–75 (1992)CrossRefGoogle Scholar
  19. 19.
    Toriwaki, J., Mori, K.: Distance Transformation and Skeletonization of 3D Pictures and Their Applications to Medical Images. Digital and Image Geometry: Advanced Lectures, 412–429 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Dong Xu
    • 1
    • 2
  • Hua Li
    • 1
  1. 1.Key Laboratory of Intelligent Information Processing, Institute of Computing TechnologyChinese Academy of SciencesBeijingP.R. China
  2. 2.Graduate University of Chinese Academy of Sciences 

Personalised recommendations