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An overview of morphological filtering

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Abstract

This paper consists of a tutorial overview of morphological filtering, a theory introduced in 1988 in the context of mathematical morphology. Its first section is devoted to the presentation of the lattice framework. Emphasis is put on the lattices of numerical functions in digital and continuous spaces. The basic filters, namely the openings and the closings, are then described and their various versions are listed. In the third section morphological filters are defined as increasing idempotent operators, and their laws of composition are proved. The last sections are concerned with two special classes of filters and their derivations: first, the alternating sequential filters allow us to bring into play families of operators depending on a positive scale parameter. Finally, the center and the toggle mappings modify the function under study by comparing it, at each point, with a few reference transforms.

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Author notes

  1. Luc Vincent

    Present address: Division of Applied Sciences, Pierce Hall, Harvard University, 29 Oxford Street, 02138, Cambridge, Massachusetts, USA

Authors and Affiliations

  1. Centre de Morphologie Mathématique, École Nationale Supérieure des Mines de Paris, 35 rue Saint-Honoré, 77305, Fontainebleau Cedex, France

    Jean Serra & Luc Vincent

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  1. Jean Serra
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  2. Luc Vincent
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Serra, J., Vincent, L. An overview of morphological filtering. Circuits Systems and Signal Process 11, 47–108 (1992). https://doi.org/10.1007/BF01189221

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  • DOI: https://doi.org/10.1007/BF01189221

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