Abstract
In this paper, we present optimal parallel algorithms for optical clustering on a mesh-connected computer.Optical clustering is a clustering technique based on the principal of optical resolution, and is of particular interest in picture analysis. The algorithms we present are based on the application of parallel algorithms in computational geometry and graph theory. In particular, we show that given a setS ofN points in the Euclidean plane, the following problems can be solved in optimal\(O\left( {\sqrt N } \right)\) time on a mesh-connected computer of sizeN.
-
1.
Determine the optical clusters ofS with respect to a given separation parameter.
-
2.
Given an interval [a, b] representing the number of optical clusters desired in the clustering ofS, determine the range of the separation parameter that will result in such an optical clustering.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. Dehne, Optical clustering,The Visual Computer,2:39–43 (1986).
P. W. Palumbo, S. N. Srihari, and J. Soh, Real-Time Address Block Location Using Pipelining and Multiprocessing,IEEE computer, special issue on Document Image Analysis Systems, accepted for publication, to appear (June 1992).
F. T. Leighton,Introduction to Parallel Algorithms and Architecturis: Arrays, Trees, Hypercubes, Morgan Kaufmann Publishers, California (1992).
R. Miller and Q. F. Stout,Parallel Algorithms for Regular Architectures, manuscript to be published by MIT press.
D. Nassimi and S. Sahni, Bitonic Sort on a Mesh-Connected Parallel Computer,IEEE Transactions on Computers,C-27(1):2–7 (January 1979).
D. Nassimi and S. Sahni, Data Broadcasting in SIMD Computers,IEEE Transactions on Computers,C-30(2):101–107 (February 1981).
C. D. Thompson and H. T. Kung, Sorting on a Mesh-Connected Parallel Computer,Communications of the ACM,20(4):263–271 (April 1977).
M. I. Shamos and D. Hoey, Closest Point Problems,SIAM J. on Comp., pp. 744–757 (1980).
P. Chew and R. L. Drysdale, Voronoi Diagrams Based on Convex Distance Functions,Proc. of First Symposium on Computational Geometry (1985).
C. Jeong and D. T. Lee, Parallel Geometric Algorithms on Mesh-Connected Computers,Proc. of Fall Joint Computer Conference (1987).
S. E. Hambrusch and F. Dehne, Determining Maximumk-Width Connectivity on Meshes,Proc. Int. Parallel Proc. Symposium, pp. 234–241 (1992).
J. Reif and Q. F. Stout, Optimal Component Labeling Algorithms for Mesh-Computers and VLSI (to appear).
D. Nassimi and S. Sahni, Finding Connected Components and Connected Ones on a Mesh-Connected Parallel Computer,SIAM J. on Comp., pp. 744–757 (1980).
T. Dubitzki, A. Wu, and A. Rosenfeld, “Parallel Computation of Contour Properties,IEEE Transactions on Pattern Analysis and Machine Intelligence,3:331–337 (1981).
H. Freeman, Computer Processing of Line-Drawing Images,Computing Surveys,6:57–97 (1974).
R. Miller and Q. F. Stout, Mesh Computer Algorithms for Computational Geometry,IEEE Transactions on Computers,38(3):321–340 (March 1989).
Author information
Authors and Affiliations
Additional information
Research partially supported by the Natural Sciences and Engineering Research Council of Canada and the National Science Foundation under Grant IRI-9108288.
Rights and permissions
About this article
Cite this article
Dehne, F., Miller, R. & Rau-Chaplin, A. Optical clustering on a mesh-connected computer. Int J Parallel Prog 20, 475–486 (1991). https://doi.org/10.1007/BF01547896
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01547896