$($b$)$ Consider the $3$ bit image shown in Table Q$1($b$1),$ evaluate the matched histogram for the image given the specified histogram in Figure Q$1($b$2).$

$[15$ marks$]$

$($c$)$ Table Q$1($b$1)$

$\backslash$table$[[1,6,6,6,7,6],[7,1,7,7,7,7],[0,7,1,1,0,5],[3,0,6,7,7,1],[6,5,7,3,0,2],[3,3,3,7,6,6],[3,3,6,4,2,7],[6,1,6,3,7,6],[5,7,6,7,7,]]$