Mathematical Morphology Operators over Concept Lattices

Jamal AtifJamal Atif, Isabelle BlochIsabelle Bloch, Felix DistelFelix Distel, Céline HudelotCéline Hudelot

Download

Jamal Atif, Isabelle Bloch, Felix Distel, Céline Hudelot
Mathematical Morphology Operators over Concept Lattices
In Peggy Cellier and Felix Distel and Bernhard Ganter, eds., Proceedings of the 11th International Conference on Formal Concept Analysis (ICFCA'13), volume 7880 of Lecture Notes in Computer Science, 28-43, 2013. Springer

Details
Bibtex

KurzfassungAbstract
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.
Forschungsgruppe:Research Group: AutomatentheorieAutomata Theory

The final publication is available at Springer.

@inproceedings{ AtEtAl-ICFCA13,
  author = {Jamal {Atif} and Isabelle {Bloch} and Felix {Distel} and C\'{e}line {Hudelot}},
  booktitle = {Proceedings of the 11th International Conference on Formal Concept Analysis {(ICFCA'13)}},
  editor = {Peggy {Cellier} and Felix {Distel} and Bernhard {Ganter}},
  pages = {28--43},
  publisher = {Springer-Verlag},
  series = {Lecture Notes in Computer Science},
  title = {Mathematical Morphology Operators over Concept Lattices},
  volume = {7880},
  year = {2013},
}