Decomposition and construction of higher-dimensional neighbourhood operations.

• The neighbourhood in an n -space is decomposed into neighbourhoods in (n − 1) -space. • Morphological operations in an n -space is the union of those on lines. • The object boundary is constructed from those in lower dimensional space. • The distance transform is computed from those in lower-dimensional space. We prove that the 2 n -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. [ABSTRACT FROM AUTHOR]