DIPlib uses a different name for the various possible connectivites than you might be used to. This is to generalize this parameter to images of any dimensionality. It is defined as follows: if connectivity is 1 all pixels for which only one coordinate differs from the pixel's coordinates by maximally 1 are considered neighbours; if it is 2, all pixels for which one or two coordinates differ maximally 1 are considered neighbours. The connectivity can never be larger than the image dimensionality.
In terms of the obsolete connectivity definitions we have:
| In 2-D | this connectivity | corresponds to | and forms this structuring element |
| 1 | 4 connectivity | diamond | |
| 2 | 8 connectivity | square | |
| -1 | 4-8 connectivity | octagon | |
| -2 | 8-4 connectivity | octagon | |
| In 3-D | this connectivity | corresponds to | and forms this structuring element |
| 1 | 6 connectivity | octahedron | |
| 2 | 18 connectivity | cuboctahedron | |
| 3 | 26 connectivity | cube | |
| -1 | 6-26 connectivity | small rhombicuboctahedron | |
| -3 | 26-6 connectivity | small rhombicuboctahedron |
The negative connectivities are only defined for the functions in binary morphology such as BinaryDilation and BinaryErosion. These alternate steps with different connectivity to produce a better approximation to an isotropic structuring element.