$3$ In addition to spatial resolution, the engineering of image formation also

poses limits on the number of quantization $($colour or grey$-$scale$)$ levels in a given image.

Using the Matlab function imapprox$()$ we can approximate a given image represented in a

given colour space $($e$.$g$.$ RGB or grey scale, Section $1\mathrm{.}4\mathrm{.}1\mathrm{.}1)$ with fewer colours. This function

operates on an indexed image $($essentially an image with a reference look$-$up table for each of

its values known as a colour map$)$ see indexed images in Matlab Help. A conventional

image $($e$.$g$.$ Matlab example peppers.png$)$ can be converted to an indexed image and

associated look$-$up table colour map using the Matlab rgb$2$ind$()$function $($or gray$2$ind$()$ for

grey$-$scale images$).$ Investigate the use of imapprox$()$ and rgb$2$ind$()/$gray$2$ind$()$ to reduce

the number of colours in a colour image example and a greyscale image example.

Experiment with different levels of colour reduction. How do your findings tally with the

discussion of human colour perception in Section $2\mathrm{.}3\mathrm{.}2\mathrm{.}1)?$