= 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.<Morphological Filtering in the scikit-image documentation>[Structuring element and Erosion]{ref} The reference position matters for asymmetric shapes, and finite-image border rules must specify how neighborhoods outside the image are treated.
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