We develop a method to construct morphological operations in higher-dimensional digital space from collection of one-dimensional set operations along digital isothetic lines in the space.

First, we prove that the 2n-neighbourhood in the n-dimensional digital space is decomposed into the 2(n-1)-neighbourhoods in the n (n-1)-dimensional digital spaces.

Second, we derive a method to construct the object boundary in the n-dimensional digital space form the mutually orthogonal n digital boundaries in (n-1)-dimensional digital spaces.

This decomposition and construction relation between fine and coarse dimensions implies that the object boundary in the n-dimensional digital space can be computed as the union of the endpoints of isothetic digital lines intersecting with the digital object in the digital space.