A simple (image independent) way of converting a full-color (24-bit color) RGB image into an 8-bit color (GIF) image is to allocate, e.g., 3 bits each to $R$ and $G$, and 2 bits to $B$. This results in poor quality of color, since you'll always only have 8 levels for R, G, and 4 levels for B, respectively.
Describe in sufficient detail an image dependent color conversion algorithm that will take into account of color content of the image so as to yield better 8-bit color (GIF) images.

Question

A simple (image independent) way of converting a full-color (24-bit color) RGB image into an 8-bit color (GIF) image is to allocate, e.g., 3 bits each to $R$ and $G$, and 2 bits to $B$. This results in poor quality of color, since you'll always only have 8 levels for R, G, and 4 levels for B, respectively. 
Describe in sufficient detail an image dependent color conversion algorithm that will take into account of color content of the image so as to yield better 8-bit color (GIF) images.

Quizplus · Accepted Answer

The Answer is Median-cut is the simplest approach. A better way would be to carry out a Karhunen-Loève analysis - could simply use a Singular Value Decomposition to optimally decorrelate the color channels.
(Very good students could be directed towards thinking about Independent Component Analysis.)

A Simple (Image Independent) Way of Converting a Full-Color (24-Bit RRR

A Simple (Image Independent) Way of Converting a Full-Color (24-Bit $R$