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Decomposition of Convex Polygonal Morphological Structuring Elements into Neighborhood Subsets
February 1991 (vol. 13 no. 2)
pp. 153-162

A discussion is presented of the decomposition of convex polygon-shaped structuring elements into neighborhood subsets. Such decompositions will lead to efficient implementation of corresponding morphological operations on neighborhood-processing-based parallel image computers. It is proved that all convex polygons are decomposable. Efficient decomposition algorithms are developed for different machine structures. An O(1) time algorithm, with respect to the image size, is developed for the four-neighbor-connected mesh machines; a linear time algorithm for determining the optimal decomposition is provided for the machines that can quickly perform 3*3 morphological operations.

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Index Terms:
computerised picture processing; parallel architectures; convex polygonal morphological structuring elements; neighborhood subsets; neighborhood-processing-based parallel image computers; O(1) time algorithm; four-neighbor-connected mesh machines; linear time algorithm; optimal decomposition; 3*3 morphological operations; computerised picture processing; parallel architectures; set theory
J. Xu, "Decomposition of Convex Polygonal Morphological Structuring Elements into Neighborhood Subsets," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 153-162, Feb. 1991, doi:10.1109/34.67644
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