Circuits, Systems and Signal Processing

, Volume 11, Issue 1, pp 47–108

An overview of morphological filtering

  • Jean Serra
  • Luc Vincent

DOI: 10.1007/BF01189221

Cite this article as:
Serra, J. & Vincent, L. Circuits Systems and Signal Process (1992) 11: 47. doi:10.1007/BF01189221


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.

Copyright information

© Birkhäuser 1992

Authors and Affiliations

  • Jean Serra
    • 1
  • Luc Vincent
    • 1
  1. 1.Centre de Morphologie MathématiqueÉcole Nationale Supérieure des Mines de ParisFontainebleau CedexFrance
  2. 2.Division of Applied Sciences, Pierce HallHarvard UniversityCambridgeUSA

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