Abstract
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.
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References
S. L. Tanimoto, A. Klinger (eds.): Structured Computer Vision: Machine Perception Through Hierarchical Computation Structures (Academic Press. New York, 1980)
J. L. Bentley, H. T. Kung: “A Tree Machine for Searching Problems”, Department of Computer Science Technical Report 79–142, Carnegie-Mellon University (1979)
A. Kltnger, C. R. Dyer: Experiments on picture representation using regular decomposition, Computer Graphics Image Processing 5, 68–105 (1976)
G. M. Hunter, K. Steiglitz: Operations on images using quad trees, IEEE Trans. Pattern Analysis Machine Intelligence PAMI-1, 145–153 (1979)
C. R. Dyer, A. Rosenfeld, H. Samet: Region representation: boundary codes from quadtrees, Comm. ACM 23 171–179 (1980)
H. Samet: Region representation: quadtrees from boundary codes, Comm. ACM 23 163–170 (1980)
A. R. Hanson, E. M. Riseman: “Design of a Semantically-Directed Vision Processor”, Computer and Information Sciences Technical Report 74–1, University of Massachusetts (1974)
A. 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. 101–131
C. R. Dyer: “A Quadtree Machine for Parallel Image Processing”, Knowledge Systems Laboratory Technical Report KSL 51, University of Illinois at Chicago Circle (1981)
C. R. Dyer: “Augmented Cellular Automata for Image Analysis”, Ph.D. dissertation, Department of Computer Science, University of Maryland (1979)
S. L. Tanimoto, T. Pavlidis: A hierarchical data structure for picture processing. Computer Graphics Image Processing 14, 104–119 (1975)
A. Klinger: “Patterns and search statistics”, in Optimizing Methods in Statistics, ed. by J. S. Rustagi (Academic Press New York, 1972), pp. 303–339
M. 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. 728–733
K. Preston Jr., M. J. B. Duff, S. Levialdi, P. Norgren, J. I. Toriwaki: Basics of cellular logic with some applications in medical image processing, Proc. IEEE 51, 826–856 (1979)
S. 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. 421–429
A. Reeves: Personal communication (1981) 144
C. R. Dyer: Computing the Euler number of an image from its quadtree, Computer Graphics Image Processing 18, 270–276 (1980)
T. Dubitzki, A. Y. Wu, A. Rosenfeld: Parallel region property computation by active quadtree networks, IEEE Trans. Pattern Analysis Machine Intelligence PAMI-3, 626–633 (1981)
D. E. Knuth: The Art of Computer Programming, Vol. 3: Sorting and Searching (Addison-Wesley, Reading, MA, 1973)
P. E. Danielsson: Getting the median faster, Computer Graphics Image Processing 17, 71–78 (1981)
C. D. Thompson, H. T. Kung: Sorting on a mesh-connected parallel computer, Comm. ACM 20 263–270 (1982)
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© 1984 Springer-Verlag Berlin Heidelberg
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Tanimoto, S.L. (1984). Sorting, Histogramming, and Other Statistical Operations on a Pyramid Machine. In: Rosenfeld, A. (eds) Multiresolution Image Processing and Analysis. Springer Series in Information Sciences, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51590-3_10
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DOI: https://doi.org/10.1007/978-3-642-51590-3_10
Publisher Name: Springer, Berlin, Heidelberg
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