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A lower bound for structuring element decompositions

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2 Author(s)
C. H. Richardson ; Digital Signal Process. Lab., Georgia Inst. of Technol., Atlanta, GA, USA ; R. W. Schafer

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

Published in:

IEEE Transactions on Pattern Analysis and Machine Intelligence  (Volume:13 ,  Issue: 4 )