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<p>A theoretical lower bound on the number of points required in the decomposition of morphological structuring elements is described. It is shown that the decomposition of an arbitrary N-point structuring element will require at least (3 ln N/ln 3)points. Using this lower bound it is possible to find the optimal decompositions (in terms of the minimum number of unions or the minimum number of points) for all one-dimensional connected line segments. L-dimensional rectangles may be decomposed by optimally decomposing the L one-dimensional line segments that describe the rectangle.</p>
picture processing; lower bound; decomposition; morphological structuring elements; optimisation; picture processing

C. Richardson and R. Schafer, "A Lower Bound for Structuring Element Decompositions," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 13, no. , pp. 365-369, 1991.
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