= Morphological erosion
{title2=$A\ominus B$}
For foreground <set> $A$ and <structuring element> $B$, <morphological erosion> is
$$
A\ominus B=\{z:z+B\subseteq A\}.
$$
Thus an output position is retained only when every offset in the translated <structuring element> lands inside the foreground. This can shrink regions and remove features narrower than the neighborhood.<Morphological Filtering in the scikit-image documentation>[Erosion, local-neighborhood minimum and disk example]{ref}
For $A=\{0,1,2,5\}$ and $B=\{0,1\}$, only starts zero and one have their successor in $A$, giving $A\ominus B=\{0,1\}$. The point five disappears. For grayscale data with a flat footprint, the analogous operation takes a local minimum. An image implementation additionally chooses border rules; the <set> formula assumes the ambient space outside $A$ is background.
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