Greyscale

The Greyscale function converts the supplied RGB colour image to a greyscale version by apply$-$

ing a ratio of colours for each pixel.

Input:

An $m-$by$-$n$-$by$-3$ uint $8$ array representing an RGB colour image.

Output:

An $m-$by$-n-$by$-1$ uint $8$ array representing a greyscale image.

Suppose we have a colour image stored in the $3$D uint $8$ array named picture. Layers $1,2,$ and

$3$ represent the red $r,$ green $g,$ and blue $b$ pixel intensities, respectively.

To convert the image from colour to greyscale, we would use the Greyscale function to return a

greyscale image $($as the $2$D uint $8$ array greyscale$\_$picture$)$ as follows:The Greyscale function will need to calculate a grey pixel value p$\_($g$)$ for each pixel in the colour

image, using the corresponding $(r,g,b)$ value of each pixel and applying the following ratio ${?}^1$ :

$r$:$g$:$b=3$:$5$:$1$

For example, at pixel position $(1,1),$ we might have $(r,g,b)=(200,55,80).$ Applying our ratio

would result in the value:

$p_g^{(1,1)}=\frac{3}{9}200+\frac{5}{9}55+\frac{1}{9}80$

$=106\mathrm{.}111$dots

So pixel $(1,1)$ has the value $106$ in the output greyscale image.

Note: We must round the pixel value to the nearest integer. Make sure you don't round individual

weighted colours prematurely!

Need Matlab code