Show that convolving an image with a discrete, separable $2$D filter kernel is equivalent to

convolving with two $1$D filter kernels. Estimate the number of operations saved for an NxN image

and a $2$k $+1\backslash$times $2$k $+1$ kernel.The two images shown in the following figure are quite different, but their histograms are the

same. Suppose that each image is blurred using a $33$ box kernel.

$($a$)$ Would the histograms of the blurred images still be equal? Explain.

Computer Vision Questions Set

$($b$)$ If your answer is no$,$ either sketch the two histograms or give two tables detailing the

histogram components.