Mathematical Morphology Operators over Concept Lattices

  • Jamal Atif
  • Isabelle Bloch
  • Felix Distel
  • Céline Hudelot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7880)


Although mathematical morphology and formal concept analysis are two lattice-based data analysis theories, they are still developed in two disconnected research communities. The aim of this paper is to contribute to fill this gap, beyond the classical relationship between the Galois connections defined by the derivation operators and the adjunctions underlying the algebraic mathematical morphology framework. In particular we define mathematical morphology operators over concept lattices, based on distances, valuations, or neighborhood relations in concept lattices. Their properties are also discussed. These operators provide new tools for reasoning over concept lattices.


Complete Lattice Concept Lattice Mathematical Morphology Formal Context Neighborhood Relation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jamal Atif
    • 1
  • Isabelle Bloch
    • 2
  • Felix Distel
    • 3
  • Céline Hudelot
    • 4
  1. 1.LRI - TAOUniversité Paris SudOrsayFrance
  2. 2.Telecom ParisTech - CNRS LTCIInstitut Mines TelecomParisFrance
  3. 3.Fakultät Informatik - Institut für theoretische InformatikTechnische Universität DresdenDresdenGermany
  4. 4.MAS LaboratoryEcole Centrale de ParisFrance

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