Sorting, Histogramming, and Other Statistical Operations on a Pyramid Machine
We define a pyramid machine to consist of an SIMD cellular array having pyramid interconnections, together with a controller consisting of a conventional microcomputer augmented with hardware to communicate with the cellular array. Primarily intended for graphics and image analysis applications, pyramid machines may also be used for more general data processing. Many operations can be performed in 0(log N) time with this architecture; finding maxima, areas, and centroids are typical of such operations. Here algorithms are given for sorting, for finding the kth largest element, for local order statistics, for median filtering of image data, for computing the histogram of a set of numbers, and for computing the mean and standard deviation. Most of these algorithms run as fast as or faster than the best known algorithms for any SISD or flat array SIMD computer. Others offer simpler programs than those for the optimal algorithms.
KeywordsEdge Image Euler Number Elementary Operation Tree Machine Cellular Array
Unable to display preview. Download preview PDF.
- 10.1S. L. Tanimoto, A. Klinger (eds.): Structured Computer Vision: Machine Perception Through Hierarchical Computation Structures (Academic Press. New York, 1980)Google Scholar
- 10.2J. L. Bentley, H. T. Kung: “A Tree Machine for Searching Problems”, Department of Computer Science Technical Report 79–142, Carnegie-Mellon University (1979)Google Scholar
- 10.7A. R. Hanson, E. M. Riseman: “Design of a Semantically-Directed Vision Processor”, Computer and Information Sciences Technical Report 74–1, University of Massachusetts (1974)Google Scholar
- 10.8A. R. Hanson, E. M. Riseman: “Processing cones: a computational structure for image analysis”, in Structured Computer Vision: Machine Perception Through Hierarchical Computation Structures, ed. by S. L. Tanimoto, A. Klinger (Academic Press, New York, 1980), pp. 101–131Google Scholar
- 10.9C. R. Dyer: “A Quadtree Machine for Parallel Image Processing”, Knowledge Systems Laboratory Technical Report KSL 51, University of Illinois at Chicago Circle (1981)Google Scholar
- 10.10C. R. Dyer: “Augmented Cellular Automata for Image Analysis”, Ph.D. dissertation, Department of Computer Science, University of Maryland (1979)Google Scholar
- 10.12A. Klinger: “Patterns and search statistics”, in Optimizing Methods in Statistics, ed. by J. S. Rustagi (Academic Press New York, 1972), pp. 303–339Google Scholar
- 10.13M. J. B. Duff: “CLIP 4: a large scale integrated circuit array parallel processor”, in Proc. 3rd Int’l. Joint Conf. on Pattern Recognition, Coronado, CA, 1976, pp. 728–733Google Scholar
- 10.15S. L. Tanimoto: “Programming techniques for hierarchical parellel image processors”, in Multicomputers and Image Processing: Algorithms and Programs, ed. by K. Preston Jr., Lo Uhr (Academic Press, New York, 1982) pp. 421–429Google Scholar
- 10.16A. Reeves: Personal communication (1981) 144Google Scholar
- 10.19D. E. Knuth: The Art of Computer Programming, Vol. 3: Sorting and Searching (Addison-Wesley, Reading, MA, 1973)Google Scholar