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The digital morphological sampling theorem

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4 Author(s)
Haralick, R.M. ; Dept. of Electr. Eng., Washington Univ., Seattle, WA, USA ; Zhuang, S. ; Lin, C. ; Lee, J.

Morphological sampling reduces processing time and cost and yet produces results sufficiently close to the result of full processing. A morphological sampling theorem is described which states: (1) how a digital image must be morphologically filtered before sampling in order to preserve the relevant information after sampling; (2) to what precision an appropriate morphologically filtered image can be reconstructed after sampling; and (3) the relationship between morphologically operating before sampling and the more computationally efficient scheme of morphologically operating on the sampled image with a sampled structuring element. The digital sampling theorem is developed first for the case of binary morphology, and then it is extended to gray-scale morphology through the use of the umbra homomorphism theorems

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Acoustics, Speech and Signal Processing, IEEE Transactions on  (Volume:37 ,  Issue: 12 )