Structuring element

A structuring element specifies the neighborhood shape and reference position used by an operation in mathematical morphology. In binary image processing, represent it as a finite set $B$ of offsets. Morphological erosion tests where a translated $B$ fits inside the foreground; morphological dilation adds its offsets to foreground positions.

A three-by-three square uses all nine offsets around its center, while a cross uses the center and its four horizontal or vertical neighbors. They treat diagonal features differently despite having the same width. Scikit-image's morphology demonstration uses a disk-shaped footprint whose radius controls the affected scale.^[ref] The reference position matters for asymmetric shapes, and finite-image border rules must specify how neighborhoods outside the image are treated.