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An O(1)Time Algorithm for the 3D Euclidean Distance Transform on the CRCW PRAM Model
October 2003 (vol. 14 no. 10)
pp. 973-982

Abstract—In this paper, we develop a parallel algorithm for the 2D Euclidean distance transform (2D_EDT, for short) of a binary image of size N x N in O(1)time using N^{2+\delta+\epsilon} CRCW processors and a parallel algorithm for the 3D Euclidean distance transform (3D_EDT, for short) of a binary image of size N x N x N in O(1)time using N^{3+\delta+\epsilon} CRCW processors, where \delta= {1\over k}, \epsilon= {1\over 2^{c+1}-1}, k, and c are constants and positive integers. Our 2D_EDT (3D_EDT) parallel algorithm can be used to build up Voronoi diagram and Voronoi polygons (polyhedra) in a 2D (3D) binary image also. All of these parallel algorithms can be performed in O(1) time using N^{2+\delta+\epsilon} (N^{3+\delta+\epsilon}) CRCW processors. To the best of our knowledge, all results derived above are the best O(1) time algorithms known.

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Index Terms:
Computer vision, Euclidean distance transform, image processing, parallel algorithm, Voronoi diagram, CRCW PRAM model.
Citation:
Yuh-Rau Wang, Shi-Jinn Horng, "An O(1)Time Algorithm for the 3D Euclidean Distance Transform on the CRCW PRAM Model," IEEE Transactions on Parallel and Distributed Systems, vol. 14, no. 10, pp. 973-982, Oct. 2003, doi:10.1109/TPDS.2003.1239866
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