Hypercube and Shuffle-Exchange Algorithms for Image Component Labeling

This paper presents algorithms for labeling the connected components of a binary image using a hypercube or shuffle-exchange computer. The algorithms label the components of an sq 1 + N x sq 1 + N pixel image in O(long sq of N) time using a hypercube or shuffle-exchange computer with N processors and a constant amount of memory per processor. The algorithms that are presented are the first to solve this problem in O(log sq of N) time. The algorithms are based on a divide-and-conquer approach and use as a subroutine an O(log N) time PRAM algorithm for labeling the connected components of a graph. The simulation of the PRAM by the hypercube and shuffle-exchange computers is particularly efficient because the PRAM that is being simulated has only O(N to the 3/4 power) processors and memory cells.

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

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

[3]  Quentin F. Stout,et al.  PROPERTIES OF DIVIDE-AND-CONQUER ALGORITMS FOR IMAGE PROCESSING. , 1985 .

[4]  Jorge L. C. Sanz,et al.  Algorithms for Image Component Labeling on SIMD Mesh-Connected Computers , 1987, IEEE Trans. Computers.

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

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

[7]  Sartaj Sahni,et al.  Parallel permutation and sorting algorithms and a new generalized connection network , 1982, JACM.

[8]  Azriel Rosenfeld,et al.  Parallel Processing of Linear Quadtrees on a Mesh-Connected Computer , 1989, J. Parallel Distributed Comput..

[9]  Azriel Rosenfeld,et al.  Parallel Image Processing Using Cellular Arrays , 1983, Computer.

[10]  Steven Fortune,et al.  Parallelism in random access machines , 1978, STOC.

[11]  Richard Cole,et al.  Approximate and exact parallel scheduling with applications to list, tree and graph problems , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

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

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