A region of $8-$bit quantized $128128$ image is shown below:

$($a$)$ Consider $V=\{4,5,12,13\}.$ Are the regions $R1$ and $R2,4-,8-,$ and$/$or $m-$connected?

Show your work and explain.

$($b$)$ A special type of neighborhood averaging filter is to be applied to this image. It is

computed by replacing the pixel value, $p(x,y),$ by the average value of the pixels that

are $D_8$ distance from pixel $p(x,y).$ Using D$82,$ apply this method to the pixel

$p(x,y)$ indicated in the image, and compute its new modified value.

$($c$)$ A special type of median filter is to be applied to this image. It is computed by

replacing the pixel value, $p(x,y),$ by the median value of the pixels that are $D4$ distance from

pixel $p(x,y).$ Using D$48,2,$ Apply this method to the pixel $p(x,y)$ indicated in the image,

and compute its new modified value.