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Morphological attribute filters have not previously been parallelized, mainly because they are both global and non-separable. We propose a parallel algorithm which achieves efficient parallelism for a large class of attribute filters, including attribute openings, closings, thinnings and thickenings, based on Salembier's Max-Trees and Min-trees. The image or volume is first partitioned in multiple slices. We then compute the Max-trees of each slice using any sequential Max-Tree algorithm. Subsequently, the Max-trees of the slices can be merged to obtain the Max-tree of the image. A C-implementation yielded good speed-ups on both a 16-processor MIPS 14000 parallel machine, and a dual-core Opteron-based machine. It is shown that the speed-up of the parallel algorithm is a direct measure of the gain with respect to the sequential algorithm used. Furthermore, the concurrent algorithm shows a speed gain of up to 72% on a single-core processor, due to reduced cache thrashing.
Filtering, Enhancement Parallel algorithms, mathematical morphology, connected filters
Jan-Eppo Jonker, Arnold Meijster, Wim H. Hesselink, Michael H.F. Wilkinson, Hui Gao, "Concurrent Computation of Attribute Filters on Shared Memory Parallel Machines", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 30, no. , pp. 1800-1813, October 2008, doi:10.1109/TPAMI.2007.70836
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