Issue No. 06 - June (1991 vol. 13)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/34.87343
<p>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.</p>
picture processing; gray-level morphology; lattices; threshold set; flat operators; dilations; erosions; picture processing; set theory
H. Heijmans, "Theoretical Aspects of Gray-Level Morphology," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 13, no. , pp. 568-582, 1991.