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Sorting a list of colors in one dimension?

Asked 2010-06-10T12:44:16.707
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I would like to sort a one-dimensional list of colors so that colors that a typical human would perceive as "like" each other are near each other.

Obviously this is a difficult or perhaps impossible problem to get "perfectly", since colors are typically described with three dimensions, but that doesn't mean that there aren't some sorting methods that look obviously more natural than others.

For example, sorting by RGB doesn't work very well, as it will sort in the following order, for example:

(1) R=254 G=0 B=0 (2) R=254 G=255 B=0 (3) R=255 G=0 B=0 (4) R=255 G=255 B=0

That is, it will alternate those colors red, yellow, red, yellow, with the two "reds" being essentially imperceivably different than each other, and the two yellows also being imperceivably different from each other.

But sorting by HLS works much better, generally speaking, and I think HSL even better than that; with either, the reds will be next to each other, and the yellows will be next to each other.

But HLS/HSL has some problems, too; things that people would perceive as "black" could be split far apart from each other, as could things that people would perceive as "white".

Again, I understand that I pretty much have to accept that there will be some splits like this; I'm just wondering if anyone has found a better way than HLS/HSL. And I'm aware that "better" is somewhat arbitrary; I mean "more natural to a typical human".

For example, a vague thought I've had, but have not yet tried, is perhaps "L is the most important thing if it is very high or very low", but otherwise it is the least important. Has anyone tried this? Has it worked well? What specifically did you decide "very low" and "very high" meant? And so on. Or has anyone found anything else that would improve upon HSL?

I should also note that I am aware that I can define a space-filling curve through the cube of colors, and order them one-dimensionally as they

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Here's an idea I came up with after a couple of minutes' thought. It might be crap, or it might not even work at all, but I'll spit it out anyway.

Define a distance function on the space of colours, d(x, y) (where the inputs x and y are colours and the output is perhaps a floating-point number). The distance function you choose may not be terribly important. It might be the sum of the squares of the differences in R, G and B components, say, or it might be a polynomial in the differences in H, L and S components (with the components differently weighted according to how important you feel they are).

Then you calculate the "distance" of each colour in your list from each other, which effectively gives you a graph. Next you calculate the minimum spanning tree of your graph. Then you identify the longest path (with no backtracking) that exists in your MST. The endpoints of this path will be the endpoints of the final list. Next you try to "flatten" the tree into a line by bringing points in the "branches" off your path into the path itself.

Hmm. This might not work all that well if your MST ends up in the shape of a near-loop in colour space. But maybe any approach would have that problem.

answered 2010-06-10T12:56:43.077

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