Skip to main content

An Efficient Euclidean Distance Transform

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3322))

Abstract

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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Rosenfeld, A., Pfaltz, J.: Sequential Operations in Digital Picture Processing. Journal of the ACM 13(4), 471–494 (1966)

    Article  MATH  Google Scholar 

  2. Russ, J.C.: Image Processing Handbook, 2nd edn. CRC Press, Boca Raton (1995)

    Google Scholar 

  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)

    Article  Google Scholar 

  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. 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. Butt, M.A., Maragos, P.: Optimal Design of Chamfer Distance Transforms. IEEE Transactions on Image Processing 7(10), 1477–1484 (1998)

    Article  Google Scholar 

  7. Danielsson, P.E.: Euclidean Distance Mapping. Computer Graphics and Image Processing 14, 227–248 (1980)

    Article  Google Scholar 

  8. Rangelmam, I.: The Euclidean Distance Transformation in Arbitrary Dimensions. Pattern Recognition Letters 14, 883–888 (1993)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  12. Cuisenaire, O., Macq, B.: Fast Euclidean Distance Transformation by Propagation using Multiple Neighbourhoods. Computer Vision and Image Understanding 76, 163–172 (1999)

    Article  Google Scholar 

  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. Eggers, H.: Two Fast Euclidean Distance Transformations in Z2 Based on Sufficient Propagation. Computer Vision and Image Understanding 69, 106–116 (1998)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bailey, D.G. (2004). An Efficient Euclidean Distance Transform. In: Klette, R., Žunić, J. (eds) Combinatorial Image Analysis. IWCIA 2004. Lecture Notes in Computer Science, vol 3322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30503-3_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30503-3_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23942-0

  • Online ISBN: 978-3-540-30503-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics