Linear Time Euclidean Distance Transform Algorithms

Heinz Breu, David Kirkpatrick, Joseph Gil, Michael Werman

Research output: Contribution to journalArticlepeer-review

400 Scopus citations


Two linear time (and hence asymptotically optimal) algorithms for computing the Euclidean distance transform of a two-dimensional binary image are presented. The algorithms are based on the construction and regular sampling of the Voronoi diagram whose sites consist of the unit (feature) pixels in the image. The first algorithm, which is of primarily theoretical interest, constructs the complete Voronoi diagram. The second, more practical, algorithm constructs the Voronoi diagram where it intersects the horizontal lines passing through the image pixel centers. Extensions to higher dimensional images and to other distance functions are also discussed.

Original languageAmerican English
Pages (from-to)529-533
Number of pages5
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number5
StatePublished - May 1995

Bibliographical note

Funding Information:
This work has been supported by the Center for Systems Science at Simon Fraser University and the Natural Sciences and Engineering Research Council of Canada. We also wish to thank Michael Swain for providing us with his image database.


  • Distance transform
  • Euclidean distance
  • Voronoi diagram
  • algorithm


Dive into the research topics of 'Linear Time Euclidean Distance Transform Algorithms'. Together they form a unique fingerprint.

Cite this