If you are given N maximally distant colors (and some associated distance metric), can you come up with a way to sort those colors into some order such that the first M are also reasonably close to being a maximally distinct set?

In other words, given a bunch of distinct colors, come up with an ordering so I can use as many colors as I need starting at the beginning and be reasonably assured that they are all distinct and that nearby colors are also very distinct (e.g., bluish red isn't next to reddish blue).

Randomizing is OK but certainly not optimal.

*Clarification: Given some large and visually distinct set of colors (say 256, or 1024), I want to sort them such that when I use the first, say, 16 of them that I get a relatively visually distinct subset of colors. This is equivalent, roughly, to saying I want to sort this list of 1024 so that the closer individual colors are visually, the farther apart they are on the list.*

This also sounds to me like some kind of

resistance graphwhere you try to map out the path of least resistance. If you inverse the requirements, path of maximum resistance, it could perhaps be used to produce a set that from the start produces maximum difference as you go, and towards the end starts to go back to values closer to the others.For instance, here's one way to perhaps do what you want.

how far away this color is from all other colors in totalThis would, it seems, produce a list that starts with the color that is farthest away from all other colors, and then go down, colors towards the end of the list would be closer to other colors in general.

Edit: Reading your reply to my first post, about the spatial subdivision, would not exactly fit the above description, since colors close to other colors would fall to the bottom of the list, but let's say you have a cluster of colors somewhere, at least one of the colors from that cluster would be located near the start of the list, and it would be the one that generally was farthest away from all other colors in total. If that makes sense.

This problem is called color quantization, and has many well known algorithms: http://en.wikipedia.org/wiki/Color_quantization I know people who implemented the octree approach to good effect.

It seems perception is important to you, in that case you might want to consider working with a perceptual color space such as YUV, YCbCr or Lab. Everytime I've used those, they have given me much better results than sRGB alone.

Converting to and from sRGB can be a pain but in your case it could actually make the algorithm simpler and as a bonus it will mostly work for color blinds too!

N maximally distant colors can be considered a set of well-distributed points in a 3-dimensional (color) space. If you can generate them from a Halton sequence, then any prefix (the first M colors) also consists of well-distributed points.

If I'm understanding the question correctly, you wish to obtain the subset of

Mcolours with thehighest mean distancebetween colours, given some distance functiond.Put another way, considering the initial set of

Ncolours as a large, undirected graph in which all colours are connected, you want to find thelongest paththat visits anyMnodes.Solving NP-complete graph problems is way beyond me I'm afraid, but you could try running a simple physical simulation:

Mrandom points in colour spacedistance^ 2) as the magnitude of the vector)NIt's far from efficient, but for small

Mit may be efficient enough, and it will give near optimal results.If your colour distance function is simple, there may be a more deterministic way of generating the optimal subset.

This greedy algorithm should give you good results.

You could just sort the candidate colors based on the maximum-distanced of the minimum-distance to any of the index colors.

Using Euclidean color distance:

Though you can replace it with anything you want. It just needs a color distance routine.

Do you mean that from a set of N colors, you need to pick M colors, where M < N, such that M is the

bestrepresentation of the N colors in the M space?As a better example, reduce a true-color (24 bit color space) to a 8-bit mapped color space (GIF?).

There are quantization algorithms for this, like the Adaptive Spatial Subdivision algorithm used by ImageMagic.

These algorithms usually don't just pick existing colors from the source space but creates new colors in the target space that most closely resemble the source colors. As a simplified example, if you have 3 colors in the original image where two are red (with different intensity or bluish tints etc.) and the third is blue, and need to reduce to two colors, the target image could have a red color that is some kind of average of the original two red + the blue color from the original image.

If you need something else then I didn't understand your question :)

You can split them in to RGB HEX format so that you can compare the R with R's of a different color, same with the G and B.

Same format as HTML

So the only thing you would need to decide is how close you want the colors and what is an acceptable difference for the segments to be considered different.