Q$3$ Figure Q$3\mathrm{.}1$ show a $3-$bit image of size $5-$by$-5$ image in the square, with $x$ and $y$ coordinates specified, Figure Q$3\mathrm{.}2$ show a Laplacian filter and Figure Q$3\mathrm{.}3$ show a lowpass filter.

$\backslash$table$[[\frac{Y}{x},$Image$],[1,2,3,4,5],[1,4,5,6,2,0],[2,4,4,6,1,0],[3,4,7,2,5,4],[4,3,0,6,2,6],[5,5,5,5,1,2]]$

$(3\mathrm{.}1)$

$\backslash$table$[[$Laplacian mask$],[0,1,0],[1,-4,1],[0,1,0]]$

$(3\mathrm{.}2)$

$\backslash$table$[[$Low pass filter$],[0\mathrm{.}01,0\mathrm{.}1,0\mathrm{.}01],[0\mathrm{.}1,0\mathrm{.}56,0\mathrm{.}1],[0\mathrm{.}01,0\mathrm{.}1,0\mathrm{.}01]]$

$(3\mathrm{.}3)$

Figure $23$

Compute the following:

$($a$)$ The output of a $33$ mean $($average$)$ filter at $(3,3).$

$5$

$($b$)$ The output of the $33$ Laplacian filter shown above at $(3,3).$

$5$

$($c$)$ The output of the $33$ low$-$pass filter shown above at $(3,3).$

$5$

$($d$)$ The histogram of the whole image.

$5$

$($e$)$ Enhance the image shown in Figure Q$3\mathrm{.}1$ using histogram equalization.

$5$

$($use the following table if necessary$).$

$\backslash$table$[[r_k,1,2,3,4,5,6,7,8],[P(r_k),,,,,,,,],[CDF{P}^{\text{'}}k,,,,,,,,],[s_k,,,,,,,,],[\backslash$table$[[$Mapping$],[$relationship$],[(r_k{s}_k)$