This paper introduces a generalization of self-dual marked flattenings defined in the lattice of mappings. This definition provides a way to associate a self-dual operator to every mapping that decomposes an element into sub-elements (i.e. gives a cover). Contrary to classical flattenings whose definition relies on the complemented structure of the powerset lattices, our approach uses the pseudo relative complement and supplement of the bi-Heyting algebra and a new notion of inf-structuring functions that provides a very general way to structure the space. We show that using an inf-structuring function based on connections allows to recover the original definition of marked flattenings and we provide, as an example, a simple inf-structuring function whose derived self-dual operator better preserves contrasts and does not introduce new pixel values.


inf-structuring function self-dual operator flattening Heyting algebra connection hyper-connection image processing mathematical morphology 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Benjamin Perret
    • 1
  1. 1.Laboratoire d’Informatique Gaspard-Monge, Equipe A3SI, ESIEE ParisUniversité Paris-EstNoisy le Grand CEDEXFrance

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