Abstract
Given an n×n binary image of white and black pixels, we present an optimal parallel algorithm for computing the distance transform and the nearest feature transform using the Euclidean metric. The algorithm employs the systolic computation to achieve O(n) running time on a linear array of n processors.
Similar content being viewed by others
References
G. Borgefors. Distance transformations in digital images. Computer Vision, Graphics and Image Processing, 34:344-371, 1986.
H. Breu, J. Gil, D. Kirkpatrick, and M. Werman. Linear time Euclidean distance transform algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17 5:529-533, 1995.
P. Danielsson. Euclidean distance mapping. Computer Graphics and Image Processing, 14:227-248, 1980.
A. Fujiwara, M. Inoue, T. Masuzawa, and H. Fujiwara. A simple parallel algorithm for the medial axis transform of binary images. In Proceedings of the IEEE 2nd International Conference on Algorithms and Architecture for Parallel Processing, 1-8, 1996.
W. Guan and S. Ma. A line-processing approach to compute Voronoi diagrams and the Euclidean distance transform. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(7):757-761, 1998.
T. Hirata. A unified linear-time algorithm for computing distance maps. Information Processing Letters, 58:129-133, 1996.
Y.-H. Lee and S.-J. Horng. Fast parallel chessboard distance transform algorithms. In Proceedings of the 1996 International Conference Parallel and Distribution Systems, 488-493, 1992.
I. Ragnemalm. Neighborhoods for distance transformation using ordered propogation. Computer Vision, Graphics and Image Processing, 56:399-409, 1992.
A. Rosenfeld and J. L. Pfalz. Sequential operations in digital picture processing. Journal of the ACM, 13:471-494, 1966.
O. Schwarzkopf. Parallel computation of distance transform. Algorithmica, 6:685-697, 1991.
H. Yamada. Complete Euclidean distance transformation by parallel operation. Proceedings of the 7th International Conference on Pattern Recognition, 69-71, 1984.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gavrilova, M.L., Alsuwaiyel, M.H. Computing the Euclidean Distance Transform on a Linear Array of Processors. The Journal of Supercomputing 25, 177–185 (2003). https://doi.org/10.1023/A:1023948712732
Issue Date:
DOI: https://doi.org/10.1023/A:1023948712732