Parallel algorithms for labeling image components

Abstract

We study the problem of labeling connected components of an N1/2×N1/2 image using parallel computers. The following new results are presented: 1). Based on the CRCW PRAM (Concurrent-Read Concurrent-Write Parallel Random Access Machine) N model, we show that (Formula Presented.) processors are necessary and sufficient to solve the image component problem in O(logN) time. The best known algorithm uses N processors to achieve the same time bound. 2). We show that (Formula Presented.) hypercube or shuffle processors are necessary and sufficient to solve the same problem in O(log2N) time. This new result improves the processor requirement of the best existing algorithm by a factor of O(log2N). 3). We present a new mesh computer algorithm aimed to improve the utilization of the processor resource while maintaining reasonable speedup over the sequential algorithm. The algorithm that is presented uses only O(N1/2) processors and executes in O(N1/2logN) time. This time complexity is a factor of O(logN) away from the optimal time complexity of O(N1/2); however, the number of processors is reduced by a factor of O(N1/2) from O(N). 4). We show that these algorithms can be extended to compute components in k-dimension and to compute components based on generalized connectivities.