This paper presents the main results of our research on mathematical morphology for three-dimensional images. The first issue is to decide which grid must be used. The face-centred cubic grid and the centred cubic grid seem to be more suitable than the cubic grid in terms of possible rotations. For these two grids we derive the formulae for the basic Minkovski measures. Then we show through several examples that extension from 2D to 3D is straightforward for most transformations. The efficiency of direct 3D processing is illustrated by applications to filtering, overlapping particle separation and grey-scale image segmentation.
Gratin, C. and Meyer, F.
"Morphological Three-Dimensional Analysis,"
Scanning Microscopy: Vol. 1992
, Article 12.
Available at: https://digitalcommons.usu.edu/microscopy/vol1992/iss6/12