Theoretical Aspects of Gray-Level Morphology

  • Authors:

  • Henk J. A. M Heijmans

  • Affiliations:

  • -

  • Venue:
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
  • Year:
  • 1991

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Abstract

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.