Decomposition of convex polygonal morphological structuring elements into neighborhood subsets

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