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Optimal geometric algorithms for digitized images on fixed-size linear arrays and scan-line arrays

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Summary

Linear arrays are characterized by a small communication bandwidth and a large communication diameter rendering them unsuited to the implementation of global computations. This paper presents efficient data movement and partitioning techniques to overcome several shortcomings of linear arrays. These techniques are used to derive optimal parallel algorithms for several geometric problems onn×n images using a fixed-size linear array withp processors, where 1≤p≤n.O(n 2/p) time solutions are presented for labeling connected image regions, computing the convex hull of each region, and computing nearest neighbors. Consequently, a linear array withn processors can solve several image problems inO(n) time which is the same time taken by a two dimensional mesh-connected computer withn 2 processors. Limitations of linear arrays are analyzed by presenting a class of image problems which can be solved sequentially inO(n) 2) time, but require Ω(n 2) time on a linear array, irrespective of the number of processors used and the partitioning of the input image among the processors. An alternate communication-efficient fixed-size organization withp processors is proposed to solve such problems inO(n 2/p) time, for 1≤p≤n.

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References

  1. Aho A, Hopcroft J, Ullman J: Design and analysis of computer algorithms. Addison Wesley, 1974.

  2. Alnuweiri HM, Prasanna Kumar VK: Optimal image computations on reduced VLSI architectures. IEEE Trans Circuits Syst 36(10):1365–1375 (1989)

    Article  Google Scholar 

  3. Alnuweiri HM, Prasanna Kumar VK: Fast image labeling using local operators on mesh connected arrays. Proc Int Conf on Parallel Processing, 1989

  4. Alnuweiri HM, Prasanna Kumar VK: Processor-time optimal parallel algorithms for digitized images on mesh-connected arrays. Algorithmica (to appear)

  5. Annaratone M, Arnould E, Gross T, Kung HT, Lam M, Menzilcioglu O, Sarocky K, Webb JA: Warp architecture and implementation. Proc 13th Annu Int Symp on Computer Architecture, June 1986

  6. Baudet G, Stevenson D: Optimal sorting algorithms for parallel computers. IEEE Trans Comput (C-27) (1978)

  7. Doshi KA, Varman PJ: Optimal graph algorithms on a fixed-size linear array. IEEE Trans Comput (C-36) (1987)

  8. Dyer C: A VLSI pyramid machine for hierarchical parallel image processing. Proc of IEEE Conf on Pattern Recognition and Image Processing, 1981

  9. Fisher AI: Scan line array processors for image computations. Int Conf on Computer Architecture, 1986

  10. Graham RL: An efficient algorithm for determining the convex hull of a finite planar set. Inf Process Lett 1:132–133 (1972)

    Article  Google Scholar 

  11. Hinkle EB, Sanz JLC, Jain AK, Petkovic D:P 3 E new life for projection-based image processing. J Parallel Distrib Comput 4:45–87 (1987)

    Article  Google Scholar 

  12. Ja'Ja' J, Prasanna Kumar VK: Information transfer in distributed computing with applications to VLSI. J ACM 31:150–162 (1984)

    Article  Google Scholar 

  13. Kim CE: On the celluar convexity of complexes. IEEE Trans Pattern Anal Mach Intell, pp 617–625 (1981)

  14. Kung HT: Memory requriements for balanced computer architectures. Proc 13th Annu Int Symp on Computer Architecture, June 1986

  15. Kung HT, Webb JA: Mapping image processing operations onto a linear systolic machine. Distrib Comput 1 (1986)

  16. Marberg JM, Gafni e: Sorting in constant number of row and column phases on a mesh. Algorithmica 3 (1988)

  17. Miller R, Stout QF: Geometric algorithms for digitzed pictures on a mesh-connected computer. IEEE Trans Pattern Anal Mach Intell, March 1985

  18. Miller R, Stout QF: Data movement techniques for the pyramid computer. SIAM J Comput 2 (1987)

  19. Nassimi D, Sahni S: Finding connected components and connected ones on a mesh-connected parallel computer. SIAM J Comput 9 (4), 1980

  20. Nassimi D, Sahni S: Data broadcating in SIMD computers. IEEE Trans Comput C-30, 2, February 1981

  21. Prasanna Kumar VK, Eshaghian M: Geometric algorithms for digitized pictures on the mesh of trees organization. Proc IEEE International Conference on Parallel Processing, 1986

  22. Preparata F, Shamos MI: Computational Geometry: an Introduction. Springer, Berlin Heidelberg New York, 1985

    Google Scholar 

  23. Ramakrishnan IV, Varman PJ: Modular matrix multiplication on a linear array. IEEE Trans Comput C-33, November 1984

  24. Rosenfeld A: Parallel image processing using cellular arrays. IEEE Computer v. 16, 1983

  25. Ullman J: Computational Aspects of VLSI. Computer Science Press, 1984

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Authors and Affiliations

  1. Department of Electrical Engineering, University of British Columbia, B.C., Vancouver, Canada, V6T 1W5

    Hussein M. Alnuweiri

  2. Department of EE-Systems, EEB-244, University of Southern California, 90089-2562, Los Angeles, CA, USA

    Viktor K. Prasanna

Authors
  1. Hussein M. Alnuweiri
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  2. Viktor K. Prasanna
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Additional information

Hussein M. Alnuweiri received the B.S. and M.S. degrees in 1983 and 1984, respectively, both in electrical engineering from King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, and received the Ph.D. degree also in electrical engineering in 1989 from the University of Southern California, Los Angeles. Currently he is an assistant professor in the electrical engineering department at University of British Columbia. His research interests include parallel architectures and algorithms, computational aspects of VLSI networks, complexity of parallel computations, and algorithmic aspects of image analysis, vision, and robot motion planning.

Viktor K. Prasanna (V. K. Prasanna Kumar) received his BS in Electronics Engineering from the Bangalore University, his MS from the School of Automation, Indian Institute of Science. He obtained his Ph.D. in Computer Science from Pennsylvania State University in 1983. Currently, he is an Associate Professor in the department of Electrical Engineering-Systems, University of Southern California, Los Angeles. His current research interests include Parallel Computation, Computer Architecture, VLSI Computations and Computational aspects of Image Processing and Vision. He is the editor of the book “Parallel Architectures and Algorithms for Image understanding” published by Academic Press. Professor Prasanna serves on number of international committees and panels and is a consultant for several industries. He is the program chair of the 1992 International Parallel Processing Symposium sponsored by IEEE Computer Society and is a subject area editor of Journal of Parallel and Distributed Computing.

This research was supported in part by the National Science Foundation under grant IRI-8710836 and in part by DARPA under contract F 33615-87-C-1436 monitored by Wright Patterson Airforce Base. A preliminary version of this paper appears in the IEEE Conference on Computer Vision and Pattern Recognition, 1988.

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Alnuweiri, H.M., Prasanna, V.K. Optimal geometric algorithms for digitized images on fixed-size linear arrays and scan-line arrays. Distrib Comput 5, 55–65 (1991). https://doi.org/10.1007/BF02259747

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  • DOI: https://doi.org/10.1007/BF02259747

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