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.

[1]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[2]  Allen Klinger,et al.  PATTERNS AND SEARCH STATISTICS , 1971 .

[3]  Donald E. Knuth,et al.  Sorting and Searching , 1973 .

[4]  Theodosios Pavlidis,et al.  A hierarchical data structure for picture processing , 1975 .

[5]  Charles R. Dyer,et al.  Experiments on Picture Representation Using Regular Decomposition , 1976 .

[6]  H. T. Kung,et al.  Sorting on a mesh-connected parallel computer , 1977, CACM.

[7]  S. Levialdi,et al.  Basics of cellular logic with some applications in medical image processing , 1979, Proceedings of the IEEE.

[8]  Kenneth Steiglitz,et al.  Operations on Images Using Quad Trees , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  C. Dyer.  Computing the Euler number of an image from its quadtree , 1980 .

[10]  S. Tanimoto,et al.  Structured computer vision: Machine perception through hierarchical computation structures , 1980 .

[11]  Azriel Rosenfeld,et al.  Region representation: boundary codes from quadtrees , 1980, CACM.

[12]  Hanan Samet,et al.  Region representation: quadtrees from boundary codes , 1980, CACM.

[13]  T. M. Williams,et al.  Optimizing Methods in Statistics , 1981 .

[14]  P. Danielsson.  Getting the Median Faster , 1981 .

[15]  Allen R. Hanson,et al.  Processing Cones: A Computational Structure for Image Analysis. , 1981 .

[16]  Azriel Rosenfeld,et al.  Parallel Region Property Computation by Active Quadtree Networks , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.