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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

J. Jonker, A. Meijster, W. H. Hesselink, M. H. Wilkinson and H. Gao, "Concurrent Computation of Attribute Filters on Shared Memory Parallel Machines," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 30, no. , pp. 1800-1813, 2007.
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