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Communication Dans Un Congrès Année : 2013

Inf-structuring functions and self-dual marked flattenings in bi-Heyting algebra

Résumé

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 \textit{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.
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Dates et versions

hal-00803422 , version 1 (21-03-2013)

Identifiants

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Benjamin Perret. Inf-structuring functions and self-dual marked flattenings in bi-Heyting algebra. ISMM 2013, May 2013, Uppsala, Sweden. pp.365-376, ⟨10.1007/978-3-642-38294-9_31⟩. ⟨hal-00803422⟩
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