Linear Time Euclidean Distance Transform Algorithms

Heinz Breu; David Kirkpatrick; Joseph Gil; Michael Werman

doi:10.1109/34.391389

Linear Time Euclidean Distance Transform Algorithms

Heinz Breu, David Kirkpatrick, Joseph Gil, Michael Werman

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

406 Scopus citations

Abstract

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 language	English
Pages (from-to)	529-533
Number of pages	5
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	17
Issue number	5
DOIs	https://doi.org/10.1109/34.391389
State	Published - 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.

Keywords

Distance transform
Euclidean distance
Voronoi diagram
algorithm

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10.1109/34.391389

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title = "Linear Time Euclidean Distance Transform Algorithms",

abstract = "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.",

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AU - Gil, Joseph

AU - Werman, Michael

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N2 - 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.

AB - 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.

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Linear Time Euclidean Distance Transform Algorithms

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Keywords

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