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Constant time BSR solutions to L1 metric and digital geometry problems

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Abstract

In this paper we solve several geometric and image problems using the BSR (broadcasting with selective reduction) model of parallel computation. All of the solutions presented are constant time algorithms. The computational geometry problems are based on city block distance metrics: all nearest neighbors and furthest pairs ofm points in a plane are computed on a two criteria BSR withm processors, the all nearest foreign neighbors and the all furthest foreign pairs ofm points in the plane problems are solved on three criteria BSR withm processors while the area and perimeter ofm isooriented rectangles are found on a one criterion BSR withm 2 processors. The problems on ann ×n binary image which are solved here all use BSR withn 2 processors and include: histogramming (one criterion), distance transform (one criterion), medial axis transform (three criteria) and discrete Voronoi diagram of labeled images (two criteria).

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Authors and Affiliations

  1. Department of Mathematics, Long Island University, 11968, Southampton, NY, USA

    Robert A. Melter

  2. Computer Science Department, University of Ottawa, K1N 9B4, Ottawa, Ont, Canada

    Ivan Stojmenović

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  1. Robert A. Melter
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  2. Ivan Stojmenović
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Melter, R.A., Stojmenović, I. Constant time BSR solutions to L1 metric and digital geometry problems. J Math Imaging Vis 5, 119–127 (1995). https://doi.org/10.1007/BF01250524

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