 Morphological opening

Morphological opening applies morphological erosion and then morphological dilation with the same structuring element. For a foreground set $A$ and structuring element $B$,It keeps the union of all translated copies of $B$ contained in $A$. Consequently the result is contained in $A$, and repeating the operation changes nothing: morphological opening is idempotent.

For a one-dimensional example, take $A=\{0,1,2,5\}$ and $B=\{0,1\}$. Morphological erosion gives $\{0,1\}$ and the following morphological dilation restores $\{0,1,2\}$; the isolated point at five disappears. The surviving run is restored rather than shifted. In image processing, selecting the structuring element controls which bright features survive. Scikit-image demonstrates removal of bright regions too thin to contain the chosen footprint.^[ref]