Volume 401 of the series Lecture Notes in Computer Science pp 1424
Computing digitized voronoi diagrams on a systolic screen and applications to clustering
 Frank DehneAffiliated withCenter for Parallel and Distributed Computing School of Computer Science, Carleton University
Abstract
A systolic screen of size M is a √M × √M meshofprocessors where each processing element P_{ij} represents the pixel (i,j) of a digitized plane П of √M × √M pixels. In this paper we study the computation of the Voronoi diagram of a set of n planar objects represented by disjoint images contained in П. We present O(√M) time algorithms to compute the Voronoi diagram for a large class of object types (e.g., points, line segments, circles, ellipses, and polygons of constant size) and distance functions (e.g., all L_{p} metrices).
Since the Voronoi diagram is used in many geometric applications, the above result has numerous consequences for the design of efficient image processing algorithms on a systolic screen. We obtain, e.g., an O(√M) time systolic screen algorithm for "optical clustering"; i.e., identifying those groups of objects in a digitized picture that are "close" in the sense of human perception.
 Title
 Computing digitized voronoi diagrams on a systolic screen and applications to clustering
 Book Title
 Optimal Algorithms
 Book Subtitle
 International Symposium Varna, Bulgaria, May 29–June 2, 1989 Proceedings
 Pages
 pp 1424
 Copyright
 1989
 DOI
 10.1007/3540518592_3
 Print ISBN
 9783540518594
 Online ISBN
 9783540468318
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 401
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Frank Dehne ^{(1)}
 Author Affiliations

 1. Center for Parallel and Distributed Computing School of Computer Science, Carleton University, K1S 5B6, Ottawa, Canada
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