Problem II$,30$ Points. Consider the following $6464$ RGB image, which is divided into $4$ non$-$overlapping blocks $($with same size$).$ Each block contains exactly $1$ color, which the corresponding RGB value is shown below.

$(1).$ Please convert this image into the HSI color space. Please describe the appearances of the hue channel, the saturation channel and the intensity channel, respectively. Please Compute H$,$ S$,$ I value for $4$ blocks, respectively. $(20Pts)$

$(2).$ Suppose we blur the saturation channel by a $1616$ arithmetic mean filter, and then convert the HSI image back to the RGB color space. What does the output image look like? Any changes compared with the original RGB image? Describe the appearance of the result

$($Notice: we ignore image border effects due to filtering$).(10$ Pts$)$