$4\mathrm{.}4$ The $33$ Convolution Filter below, when passed over an image while performing the

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

convolution operation, will generate an output Image in which each interior pixel represents:

J$)$ the local gradient in the vertical direction in the original image

b$)$ components of an image where the brightness steadily increases from left to right

c$)$ addition of white noise in the original image

d$)$ the local gradient in the horizontal direction in the original image.