Morphological erosion ($A\ominus B$)

For foreground set $A$ and structuring element $B$, morphological erosion isThus 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.^[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.