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Theoretical Aspects of Gray-Level Morphology
June 1991 (vol. 13 no. 6)
pp. 568-582

After a brief discussion of the extension of mathematical morphology to complete lattices, the space of gray-level functions is considered and the concept of a threshold set is introduced. It is shown how one can use binary morphological operators and thresholding techniques to build a large class of gray-level morphological operators. Particular attention is given to the class of so-called flat operators, i.e. operators which commute with thresholding. It is also shown how to define dilations and erosions with nonflat structuring elements if the gray-level set is finite. It is reported that mere truncation yields wrong results.

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Index Terms:
picture processing; gray-level morphology; lattices; threshold set; flat operators; dilations; erosions; picture processing; set theory
Citation:
H.J.A.M. Heijmans, "Theoretical Aspects of Gray-Level Morphology," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 6, pp. 568-582, June 1991, doi:10.1109/34.87343
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