Processor-time optimal parallel algorithms for digitized images on mesh-connected processor arrays

We present processor-time optimal parallel algorithms for several problems onn ×n digitized image arrays, on a mesh-connected array havingp processors and a memory of sizeO(n2) words. The number of processorsp can vary over the range [1,n3/2] while providing optimal speedup for these problems. The class of image problems considered here includes labeling the connected components of an image; computing the convex hull, the diameter, and a smallest enclosing box of each component; and computing all closest neighbors. Such problems arise in medium-level vision and require global operations on image pixels. To achieve optimal performance, several efficient data-movement and reduction techniques are developed for the proposed organization.

[1]  Michael Ian Shamos,et al.  Geometric complexity , 1975, STOC.

[2]  H. M. Alnuweiri,et al.  Optimal image computations on reduced VLSI architectures , 1989 .

[3]  Terry J. Fountain,et al.  Cellular logic image processing , 1986 .

[4]  Sartaj Sahni,et al.  Finding Connected Components and Connected Ones on a Mesh-Connected Parallel Computer , 1980, SIAM J. Comput..

[5]  Viktor K. Prasanna,et al.  A VLSI-Based Multiprocessor Architecture for Implementing Parallel Algorithms , 1985, International Conference on Parallel Processing.

[6]  Kang G. Shin,et al.  Implementation of Decentralized Load Sharing in Networked Workstations Using the Condor Package , 1997, J. Parallel Distributed Comput..

[7]  Russ Miller,et al.  Data Movement Techniques for the Pyramid Computer , 1987, SIAM J. Comput..

[8]  Sartaj Sahni,et al.  Data broadcasting in SIMD computers , 1981, IEEE Transactions on Computers.

[9]  Russ Miller,et al.  Varying Diameter and Problem Size in Mesh-Connected Computers , 1985, ICPP.

[10]  S. N. Maheshwari,et al.  Efficient VLSI Networks for Parallel Processing Based on Orthogonal Trees , 1983, IEEE Transactions on Computers.

[11]  Viktor K. Prasanna,et al.  Parallel Geometric Algorithms for Digitized Pictures on Mesh of Trees , 1986, ICPP.

[12]  F. P. Preparata,et al.  Convex hulls of finite sets of points in two and three dimensions , 1977, CACM.

[13]  Ming-Deh A. Huang.  Solving some graph problems with optimal or near-optimal speedup on mesh-of-trees networks , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[14]  Russ Miller,et al.  Meshes with reconfigurable buses , 1988 .

[15]  Jorge L. C. Sanz,et al.  Hypercube and Shuffle-Exchange Algorithms for Image Component Labeling , 1987, J. Algorithms.

[16]  Dionysios I. Reisis,et al.  Image Computations on Meshes with Multiple Broadcast , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  S. H. Unger,et al.  A Computer Oriented toward Spatial Problems , 1958 .

[18]  Kai Hwang,et al.  An Orthogonal Multiprocessor for Parallel Scientific Computations , 1989, IEEE Trans. Computers.

[19]  Viktor K. Prasanna,et al.  Optimal geometric algorithms on fixed-size linear arrays and scan line arrays , 1988, Proceedings CVPR '88: The Computer Society Conference on Computer Vision and Pattern Recognition.

[20]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[21]  Kenneth E. Batcher,et al.  Design of a Massively Parallel Processor , 1980, IEEE Transactions on Computers.

[22]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[23]  Ronald L. Graham,et al.  An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1972, Inf. Process. Lett..

[24]  Viktor K. Prasanna,et al.  Optimal VLSI Sorting with Reduced Number of Processors , 1991, IEEE Trans. Computers.

[25]  S. H. Unger,et al.  A Computer Oriented toward Spatial Problems , 1899, Proceedings of the IRE.

[26]  Kai Hwang,et al.  Computer architecture and parallel processing , 1984, McGraw-Hill Series in computer organization and architecture.

[27]  Uzi Vishkin,et al.  An O(log n) Parallel Connectivity Algorithm , 1982, J. Algorithms.

[28]  Isaac D. Scherson,et al.  Parallel Sorting in Two-Dimensional VLSI Models of Computation , 1989, IEEE Trans. Computers.

[29]  Chul E. Kim.  On the Cellular Convexity of Complexes , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[30]  Robert Michael Owens,et al.  An architecture for a VLSI FFT processor , 1983, Integr..

[31]  Steven L. Tanimoto,et al.  A pyramidal approach to parallel processing , 1983, ISCA '83.

[32]  Viktor K. Prasanna,et al.  Fast Image Labeling Using Local Operators on Mesh-Connected Computers , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  Azriel Rosenfeld,et al.  Digital Picture Processing , 1976 .

[34]  H. T. Kung,et al.  Warp architecture and implementation , 1998, ISCA '98.

[35]  Azriel Rosenfeld,et al.  Parallel Image Processing by Memory-Augmented Cellular Automata , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[36]  Herbert Freeman,et al.  Determining the minimum-area encasing rectangle for an arbitrary closed curve , 1975, CACM.

[37]  Russ Miller,et al.  Geometric Algorithms for Digitized Pictures on a Mesh-Connected Computer , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[38]  Jeffrey D Ullma.  Computational Aspects of VLSI , 1984 .

[39]  Mikhail J. Atallah,et al.  Efficient Parallel Solutions to Some Geometric Problems , 1986, J. Parallel Distributed Comput..

[40]  Massimo Maresca,et al.  Polymorphic-Torus Architecture for Computer Vision , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[41]  Harold S. Stone,et al.  Parallel Processing with the Perfect Shuffle , 1971, IEEE Transactions on Computers.

[42]  Jan van Leeuwen,et al.  Dynamically maintaining configurations in the plane (Detailed Abstract) , 1980, STOC '80.

[43]  Lynn Conway,et al.  Introduction to VLSI systems , 1978 .

[44]  Leonidas J. Guibas,et al.  Parallel computational geometry , 1988, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).