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

Essay

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.