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Article Dans Une Revue Journal of Mathematical Imaging and Vision Année : 2020

Topological Properties of the First Non-Local Digitally Well-Composed Interpolation on n-D Cubical Grids

Résumé

In discrete topology, we like digitally well-composed (shortly DWC) interpolations because they remove pinches in cubical images. Usual well-composed interpolations are local and sometimes self-dual (they treat in a same way dark and bright components in the image). In our case, we are particularly interested in n-D self-dual DWC interpolations to obtain a purely self-dual tree of shapes. However , it has been proved that we cannot have an n-D interpolation which is at the same time local, self-dual, and well-composed. By removing the locality constraint, we have obtained an n-D interpolation with many properties in practice: it is self-dual, DWC, and in-between (this last property means that it preserves the contours). Since we did not published the proofs of these results before, we propose to provide in a first time the proofs of the two last properties here (DWCness and in-betweeness) and a sketch of the proof of self-duality (the complete proof of self-duality requires more material and will come later). Some theoretical and practical results are given.
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Dates et versions

hal-02990810 , version 1 (05-11-2020)

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Nicolas Boutry, Laurent Najman, Thierry Géraud. Topological Properties of the First Non-Local Digitally Well-Composed Interpolation on n-D Cubical Grids. Journal of Mathematical Imaging and Vision, 2020, 62 (9), pp.1256-1284. ⟨10.1007/s10851-020-00989-y⟩. ⟨hal-02990810⟩
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