A linear time algorithm for computing exact Euclidean distance transforms of binary images in arbitrary dimensions

A sequential algorithm is presented for computing the exact Euclidean distance transform (DT) of a k-dimensional binary image in time linear in the total number of voxels N. The algorithm, which is based on dimensionality reduction and partial Voronoi diagram construction, can be used for computing...

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Vydané v:IEEE transactions on pattern analysis and machine intelligence Ročník 25; číslo 2; s. 265 - 270
Hlavní autori: Maurer, C.R., Rensheng Qi, Raghavan, V.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.02.2003
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Algorithms
Anisotropic magnetoresistance
Chamfering
Computer vision
Computing time
Construction
Euclidean distance
Image processing
Image registration
Interpolation
Mathematical analysis
Nearest neighbor searches
Pattern analysis
Pattern matching
Skeleton
Studies
Surface morphology
Transforms
ISSN:0162-8828, 1939-3539
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Popis
Shrnutí:A sequential algorithm is presented for computing the exact Euclidean distance transform (DT) of a k-dimensional binary image in time linear in the total number of voxels N. The algorithm, which is based on dimensionality reduction and partial Voronoi diagram construction, can be used for computing the DT for a wide class of distance functions, including the L/sub p/ and chamfer metrics. At each dimension level, the DT is computed by constructing the intersection of the Voronoi diagram whose sites are the feature voxels with each row of the image. This construction is performed efficiently by using the DT in the next lower dimension. The correctness and linear time complexity are demonstrated analytically and verified experimentally. The algorithm may be of practical value since it is relatively simple and easy to implement and it is relatively fast (not only does it run in O(N) time but the time constant is small). A simple modification of the algorithm computes the weighted Euclidean DT, which is useful for images with anisotropic voxel dimensions. A parallel version of the algorithm runs in O(N/p) time with p processors.
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ISSN:0162-8828
1939-3539
DOI:10.1109/TPAMI.2003.1177156