Classification of Fuzzy Mathematical Morphologies Based on Concepts of Inclusion Measure and Duality

  • Authors:

  • Peter Sussner;Marcos Eduardo Valle

  • Affiliations:

  • Institute of Mathematics, Statistics, and Scientific Computation, State University of Campinas, Campinas, Brazil CEP13081-970;Center for Exact Sciences, State University of Londrina, Londrina, Brazil CEP86051-990

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2008

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Abstract

Mathematical morphology was originally conceived as a set theoretic approach for the processing of binary images. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory. This paper discusses and compares several well-known and new approaches towards gray-scale and fuzzy mathematical morphology. We show in particular that a certain approach to fuzzy mathematical morphology ultimately depends on the choice of a fuzzy inclusion measure and on a notion of duality. This fact gives rise to a clearly defined scheme for classifying fuzzy mathematical morphologies. The umbra and the level set approach, an extension of the threshold approach to gray-scale mathematical morphology, can also be embedded in this scheme since they can be identified with certain fuzzy approaches.