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 publish 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.

在离散拓扑中，我们喜欢数字组合良好（简称DWC）的插值，因为它们消除了立方图像中的夹点。通常，精心组合的插值是局部的，有时是自对插的（它们以相同的方式处理图像中的暗和亮成分）。在我们的案例中，我们对n -D自对偶DWC插值以获得纯自对树形状特别感兴趣。但是，已经证明，我们不能同时具有局部，自对偶和良好组成的n -D插值。通过消除局部性约束，我们获得了n-D插值在实践中具有许多属性：它是自对偶，DWC，且介于两者之间（最后一个属性表示保留轮廓）。由于我们之前没有发布过这些结果的证明，因此我们建议在第一时间提供此处最后两个属性（DWCness和inbetweeness）的证明以及自我二重性证明的草图（自我对偶需要更多的物质，并且会在以后出现）。给出了一些理论和实践结果。