$($c$)($i$)$ Sampling a continuous Gaussian yields mask entries of floating$-$point

numbers. Because of the greater computational burden of convolving

floating$-$point numbers, the process can be made more efficient by

approximating the mask values with integers. However, the weights in the

mask tend to change the overall intensity values of the smoothed image. That

is why scale factor is introduced to "normalize" the weights. Scale factor

should only be introduced after convolving the integer mask with the image,

and not before. Why?

$(5$ Marks$)$

te: Question No$.2$ continues on page $3.$

$($ii$)$ In Gaussian smoothing, what are the considerations for determining the

standard deviation of Gaussian function?

$(5$ Marks$)$

$($d$)$ Assume that a $33$ gradient mask is represented by

and the variances of image pixel values in a $33$ neighborhood are given by the

following table.

$($i$)$ If $a=c$ and ${}_a^2={}_c^2=3{}_b^2,$ design a mask or operator with optimal weights

and explain why the proposed mask or operator is optimal.

$(5$ Marks$)$

$($ii$)$ If $b=2c$ and ${}_a^2=2{}_b^2={}_c^2,$ design a mask or operator with optimal

weights and explain why the proposed mask or operator is optimal.

$(10$ Marks$)$

SHOW ALL WORKING CLEARLY