Computer Problem: Create an input color image where the $R(x,y),G(x,y),B(x,y)$ bands are defined by scaling the triangle gray$-$level image using $R(x,y)=$ triangle $(x,y),G(x,y)={0\mathrm{.}5}^{**}$ triangle $(x,y),B(x,y)={0\mathrm{.}2}^{**}$ triangle $(x,y).$ Round non$-$integer values to the nearest integer so that each band is represented by an $8-$bit non$-$negative integer. Filter each band of the input color image separately using the Gaussian lowpass filter from Homework $6$ to obtain $R^{\text{'}}(x,y),G^{\text{'}}(x,y),B^{\text{'}}(x,y).$ Create a filtered color image where the bands are defined by $R^{\text{'}}(x,y),G^{\text{'}}(x,y),B^{\text{'}}(x,y).$ Submit the displayable input color image and the displayable filtered color image.