I am very interested in the "best-fit reduced palette of colors" approach, but then to create mosaics. Say you have lots tiles/beads/bricks/marbles whatever in a handful of colors (and not covering the entire color space, but say three shades of blue, brown and bright pink) how can you represent a full color image as accurately as possible using only that very limited palette (and in a fairly limited resolution, as placing 10k tiles is not fun).

I have had some success manually using Photoshop to generate a reduced color space image to only 5 distinct colors (probably optimally chosen by the algorithm) and then remapping those 5 colors to 5 the 5 colors I actually have. There must be better ways