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Communication Dans Un Congrès Année : 2014

Facet Connectedness of Discrete Hyperplanes with Zero Intercept: The General Case

Résumé

A digital discrete hyperplane in Zd is defined by a normalvector v, a shift µ, and a thickness θ. The set of thicknesses θ for whichthe hyperplane is connected is a right unbounded interval of R+ . Itslower bound, called the connecting thickness of v with shift µ, may becomputed by means of the fully subtractive algorithm. A careful study ofthe behaviour of this algorithm allows us to give exhaustive results aboutthe connectedness of the hyperplane at the connecting thickness in thecase µ = 0. We show that it is connected if and only if the sequence ofvectors computed by the algorithm reaches in finite time a specific set ofvectors which has been shown to be Lebesgue negligible by Kraaikamp& Meester.

Dates et versions

hal-01083101 , version 1 (15-11-2014)

Identifiants

Citer

Eric Domenjoud, Xavier Provençal, Laurent Vuillon. Facet Connectedness of Discrete Hyperplanes with Zero Intercept: The General Case. 18th IAPR International Conference, DGCI 2014, Sep 2014, Siena, Italy. pp.1-12, ⟨10.1007/978-3-319-09955-2_1⟩. ⟨hal-01083101⟩
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