We prove that the 2n-neighbourhood in an n-dimensional digital space is decomposed into the $2(n-1)$-neighbourhoods in the mutually orthogonal $(n-1)$-dimensional digital spaces. This decomposition and construction relation of the neighbourhoods and objects implies that morphological operations in an n-dimensional digital space can be computed as the union of one- and two-dimensional morphological operations on isothetic digital lines and planes intersecting with the digital object in the digital space.

中文翻译：

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高维邻域分解与构造

我们证明n维数字空间中的2 n个邻域被分解为$2（ñ-\mathrm{1个}）$-在相互正交的街区 $（ñ-\mathrm{1个}）$维数字空间。邻域和对象的这种分解和构造关系意味着，可以将n维数字空间中的形态运算计算为与数字中的数字对象相交的等轴数字线和平面上的一维和二维形态运算的并集。空间。