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A Lower Bound for Structuring Element Decompositions
April 1991 (vol. 13 no. 4)
pp. 365-369

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.

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Index Terms:
picture processing; lower bound; decomposition; morphological structuring elements; optimisation; picture processing
C.H. Richardson, R.W. Schafer, "A Lower Bound for Structuring Element Decompositions," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 4, pp. 365-369, April 1991, doi:10.1109/34.88571
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