An Efficient Euclidean Distance Transform

  • Donald G Bailey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3322)


Within image analysis the distance transform has many applications. The distance transform measures the distance of each object point from the nearest boundary. For ease of computation, a commonly used approximate algorithm is the chamfer distance transform. This paper presents an efficient linear- time algorithm for calculating the true Euclidean distance-squared of each point from the nearest boundary. It works by performing a 1D distance transform on each row of the image, and then combines the results in each column. It is shown that the Euclidean distance squared transform requires fewer computations than the commonly used 5x5 chamfer transform.


Voronoi Diagram Lookup Table Background Pixel City Block Current Pixel 
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.
    Rosenfeld, A., Pfaltz, J.: Sequential Operations in Digital Picture Processing. Journal of the ACM 13(4), 471–494 (1966)zbMATHCrossRefGoogle Scholar
  2. 2.
    Russ, J.C.: Image Processing Handbook, 2nd edn. CRC Press, Boca Raton (1995)Google Scholar
  3. 3.
    Huang, C.T., Mitchell, O.R.: A Euclidean Distance Transform Using Grayscale Morphology Decomposition. IEEE Transactions on Pattern Analysis and Machine Intelligence 16(4), 443–448 (1994)CrossRefGoogle Scholar
  4. 4.
    Waltz, F.M., Garnaoui, H.H.: Fast Computation of the Grassfire Transform Using SKIPSM. In: SPIE Conf. on Machine Vision Applications, Architectures and System Integration III, vol. 2347, pp. 396–407 (1994)Google Scholar
  5. 5.
    Creutzburg, R., Takala, J.: Optimising Euclidean Distance Transform Values by Number Theoretic Methods. In: IEEE Nordic Signal Processing Symposium, pp. 199–203 (2000)Google Scholar
  6. 6.
    Butt, M.A., Maragos, P.: Optimal Design of Chamfer Distance Transforms. IEEE Transactions on Image Processing 7(10), 1477–1484 (1998)CrossRefGoogle Scholar
  7. 7.
    Danielsson, P.E.: Euclidean Distance Mapping. Computer Graphics and Image Processing 14, 227–248 (1980)CrossRefGoogle Scholar
  8. 8.
    Rangelmam, I.: The Euclidean Distance Transformation in Arbitrary Dimensions. Pattern Recognition Letters 14, 883–888 (1993)CrossRefGoogle Scholar
  9. 9.
    Shih, F.Y., Wu, Y.T.: Fast Euclidean Distance Transformation in 2 Scans Using a 3x3 Neighborhood. Computer Vision and Image Understanding 93, 109–205 (2004)CrossRefGoogle Scholar
  10. 10.
    Breu, H., Gil, J., Kirkatrick, D., Werman, M.: Linear Time Euclidean Distance Transform Algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(5), 529–533 (1995)CrossRefGoogle Scholar
  11. 11.
    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(7), 757–761 (1998)CrossRefGoogle Scholar
  12. 12.
    Cuisenaire, O., Macq, B.: Fast Euclidean Distance Transformation by Propagation using Multiple Neighbourhoods. Computer Vision and Image Understanding 76, 163–172 (1999)CrossRefGoogle Scholar
  13. 13.
    Vincent, L.: Exact Euclidean distance function by chain propagations. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 520–525 (1991)Google Scholar
  14. 14.
    Eggers, H.: Two Fast Euclidean Distance Transformations in Z2 Based on Sufficient Propagation. Computer Vision and Image Understanding 69, 106–116 (1998)CrossRefGoogle Scholar
  15. 15.
    Saito, T., Toriwaki, J.I.: New Algorithms for Euclidean Distance Transformations of an N-dimensional Digitised Picture with Applications. Pattern Recognition 27, 1551–1565 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Donald G Bailey
    • 1
  1. 1.Institute of Information Sciences and TechnologyMassey UniversityPalmerston NorthNew Zealand

Personalised recommendations