a$)$ The matrix I below represents a $77$ image patch and $S$ is a $33$ structuring element.

$I=\left[\begin{array}{ccccccc}0& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 1& 1& 1& 0\\ 0& 0& 1& 1& 1& 1& 0\\ 0& 0& 0& 1& 1& 1& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\end{array}\right]$

$S=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

i$)$ Using the given structuring element $S,$ erode image patch I.

$5$

ii$)$ Using the given structuring element $S,$ dilate image patch I.

$5$

iii$)$ Using the given structuring element $S,$ apply morphological opening on

$5$

image patch I.