Q$3(20$ Marks$).$ We wish make a local threshold of an image $f(x,y)$ in order to find pixels which are significantly brighter than their surroundings.

We create an output $g(x,y)$ such that

$g(x,y)=\{\begin{array}{ccc}1,& f(x,y)>\text{m}\text{e}\text{a}\text{n}\{f(x,& y)\}+T\\ 0,& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

where mean $\{f(x,y)\}$ is the local mean averaged over a $55$ pixel region, and $T$ is an input parameter. Explain how you would implement the above process using standard linear convolution followed by thresholding. What is the convolution filter kernel that should be used?