A gray$-$scale image, f$($x$,$ y$),$ is corrupted by nonoverlapping noise spikes that can be modeled

as small, cylindrical artifacts of radii min

R r $$ max

$$

R

and amplitude min

A a $$ max

$$

A

$.$

$($a$)$ Develop a morphological filtering approach for cleaning up the image.

$($b$)$ Repeat $($a$),$ but now assume that there is overlapping of$,$ at most, four noise spikes.