Image Sharpening

a$)$ Consider the following three Laplacian filters $A,B,$ and $C$ :

$A=\left[\begin{array}{ccc}1& 0& 1\\ 0& -4& 0\\ 1& 0& 1\end{array}\right],B=\left[\begin{array}{ccc}0& 1& 0\\ 1& -4& 1\\ 0& 1& 0\end{array}\right],C=\left[\begin{array}{ccc}1& 1& 1\\ 1& -8& 1\\ 1& 1& 1\end{array}\right]$

If we filter a given image I by using filters $A,B,$ and $C$ respectively to obtain the sharpened images I$\_$A$,$ I$\_$B$,$ and I$\_$C$.$

What can you say about these filtered images? $($Hint: compare the sharpness of the images$).$

b$)$ Write down a $5$ by $5$ Laplacian like filter with the centre element equal to $-24.$ Apply this Laplacian like filter to an image

I, do we get a sharper image compared to the images in part a$)?$ Explain your answer.

c$)$ How does this type of filter behave as a function of mask size, for example: $33,$

$55,99,$ and $1515?$