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A General Algorithm for Computing Distance Transforms in Linear Time

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Part of the Computational Imaging and Vision book series (CIVI,volume 18)

Abstract

A new general algorithm for computing distance transforms of digital images is presented. The algorithm consists of two phases. Both phases consist of two scans, a forward and a backward scan. The first phase scans the image column-wise, while the second phase scans the image row-wise. Since the computation per row (column) is independent of the computation of other rows (columns), the algorithm can be easily parallelized on shared memory computers. The algorithm can be used for the computation of the exact Euclidean, Manhattan (L 1 norm), and chessboard distance (L norm) transforms.

Key words

  • Distance Transforms
  • Row-Column Factorization
  • Parallelization

A. Meijster works at the Computing Centre of the University of Groningen.

J.B.T.M. Roerdink and W.H. Hesselink work at the Institute for Mathematics and Computing Science.

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References

  1. G. Borgefors. Distance transformations in arbitrary dimensions. Computer Vision, Graphics, and Image Processing, 27:321–345, 1984.

    Google Scholar 

  2. G. Borgefors. Distance transformations in digital images. Computer Vision, Graphics, and Image Processing, 34:344–371, 1986.

    Google Scholar 

  3. P. Danielsson. Euclidean distance mapping. Comput. Graphics Image Process., 14:227–248, 1980.

    CrossRef  Google Scholar 

  4. W._H. Hesselink, A. Meijster, and J. B. T. M. Roerdink. An exact Euclidean distance transform in linear time. Technical Report IWI 99-9-04, Institute for Mathematics and Computing Science, University of Groningen, the Netherlands, Apr. 1999.

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  5. M. Kolountzakis and K. Kutulakos. Fast computation of the Euclidean distance maps for binary images. Information Processing Letters, 43:181–184, 1992.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. S. Pavel and A. Akl. Efficient algorithms for the Euclidean distance transform. Parallel Processing Letters, 5:205–212, 1995.

    CrossRef  MathSciNet  Google Scholar 

  7. A. Rosenfeld and J. Pfaltz. Distance functions on digital pictures. Pattern Recognition, 1:33–61, 1968.

    CrossRef  MathSciNet  Google Scholar 

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© 2002 Kluwer Academic/Plenum Publishers

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Meijster, A., Roerdink, J.B.T.M., Hesselink, W.H. (2002). A General Algorithm for Computing Distance Transforms in Linear Time. In: Goutsias, J., Vincent, L., Bloomberg, D.S. (eds) Mathematical Morphology and its Applications to Image and Signal Processing. Computational Imaging and Vision, vol 18. Springer, Boston, MA. https://doi.org/10.1007/0-306-47025-X_36

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  • DOI: https://doi.org/10.1007/0-306-47025-X_36

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-7923-7862-4

  • Online ISBN: 978-0-306-47025-7

  • eBook Packages: Springer Book Archive