SUMMARYAfter a discussion of the best grid for the digitization of three‐dimensional (3‐D) images, two grids are retained for which the approximations of the elementary disc are respectively the cuboctahedron and the rhombododecahedron. These are used to derive the formulae for the basic Minkowski measures. The extension from 2‐D to 3‐D is demonstrated to be straightforward for most transformations of mathematical morphology, and covers almost all practical sit