Algorithms for Image Component Labeling on SIMD Mesh-Connected Computers
IEEE Transactions on Computers
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In this paper we design and analyse parallel algorithms with the goal to get exact bounds on their speed-ups on real machines. For this purpose we employ the BSP* model which is an extension of Valiant's BSP model and rewards blockwise communication. Further we use Valiant's notion of c-optimality. Intuitively a c-optimal parallel algorithm for p processors tends to speed-up p/c, where the communication time is asymptotically smaller than the computation time. We consider a basic problem in Image Processing, Connected Component Labeling for two and three dimensional images. Our algorithms are randomized and 2-optimal with high probability for a wide range of BSP* parameters where the range becomes larger with growing input sizes. Our algorithms improve on previous results as they either need an asymptotically smaller amount of data to be communicated or fewer communication rounds. We further report on implementation work and experiments.