Abstract
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.