Among the different flavors of well-composednesses on cubical grids, two of them, called, respectively, digital well-composedness (DWCness) and well-composedness in the sense of Alexandrov (AWCness), are known to be equivalent in 2D and in 3D. The former means that a cubical set does not contain critical configurations, while the latter means that the boundary of a cubical set is made of a disjoint union of discrete surfaces. In this paper, we prove that this equivalence holds in n-D, which is of interest because today images are not only 2D or 3D but also 4D and beyond. The main benefit of this proof is that the topological properties available for AWC sets, mainly their separation properties, are also true for DWC sets, and the properties of DWC sets are also true for AWC sets: an Euler number locally computable, equivalent connectivities from a local or global point of view. This result is also true for gray-level images thanks to cross section topology, which means that the sets of shapes of DWC gray-level images make a tree like the ones of AWC gray-level images.

之间的不同口味良好composednesses上立方体网格，其中两个，称为分别数字公镇定（DWCness）和在亚历山德罗感良好镇定（AWCness），已知在2D和3D是等同。前者表示三次方集不包含关键配置，而后者表示三次方集的边界由不连续的曲面的不交集组成。在本文中，我们证明了这等价于持有ñ-D，这很有趣，因为今天的图像不仅是2D或3D，而且还包括4D及以后。该证明的主要好处是，AWC集可用的拓扑属性（主要是它们的分离属性）对于DWC集也适用，而DWC集的属性也适用于AWC集：欧拉数局部可计算，等效连通性来自局部或全局的观点。由于具有横截面拓扑结构，因此该结果对于灰度图像也适用，这意味着DWC灰度图像的形状集像AWC灰度图像一样构成一棵树。