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.
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Borgefors. Distance transformations in arbitrary dimensions. Computer Vision, Graphics, and Image Processing, 27:321–345, 1984.
G. Borgefors. Distance transformations in digital images. Computer Vision, Graphics, and Image Processing, 34:344–371, 1986.
P. Danielsson. Euclidean distance mapping. Comput. Graphics Image Process., 14:227–248, 1980.
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.
M. Kolountzakis and K. Kutulakos. Fast computation of the Euclidean distance maps for binary images. Information Processing Letters, 43:181–184, 1992.
S. Pavel and A. Akl. Efficient algorithms for the Euclidean distance transform. Parallel Processing Letters, 5:205–212, 1995.
A. Rosenfeld and J. Pfaltz. Distance functions on digital pictures. Pattern Recognition, 1:33–61, 1968.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Kluwer Academic/Plenum Publishers
About this chapter
Cite this chapter
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
Download citation
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