IEEE Transactions on Parallel and Distributed Systems
Fast All Nearest Neighbor Algorithms from Image Processing Perspective
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
An efficient O(1) time 3D all nearest neighbor algorithm from image processing perspective
Journal of Parallel and Distributed Computing
3D Block-Based Medial Axis Transform and Chessboard Distance Transform on the CREW PRAM
ICA3PP '08 Proceedings of the 8th international conference on Algorithms and Architectures for Parallel Processing
3D block-based medial axis transform and chessboard distance transform based on dominance
Image and Vision Computing
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In this paper, we present algorithms for computing the Euclidean distance transform (EDT) of a binary image on the array with reconfigurable optical buses (AROB). First, we develop a parallel algorithm termed as Algorithm Expander which can be implemented in O(1) time on an AROB with N×Nδ processors, where δ=1/k, k is a constant and a positive integer. Algorithm Expander is designed to compute a higher dimensional EDT based on the computed lower dimensional EDT. It functions as a general EDT expander for us to expand EDT from a lower dimension to a higher dimension. We then develop parallel algorithms for the two-dimensional (2-D)_EDT of a binary image array of size N×N in O(1) time on an AROB with N×N×Nδ processors and for the three-dimensional (3-D)_EDT of a binary image of size N×N×N in O(1) time on an AROB with N×N×N×Nδ processors. To the best of our knowledge, all results derived above are the best O(1) time algorithms known. We then extend it to compute the nD_EDT of a binary image of size Nn in O(n) time on an AROB with Nn+δ processors. We also apply our parallel EDT algorithms to build Voronoi diagram and Voronoi polyhetra (polygons), to find all maximal empty spheres and the largest empty sphere, and to compute the medial axis transform. All of these applications can be solved in the same time complexity on an AROB with the same number of processors as needed for solving the EDT problems in the same dimensions.