# Is the low statistical correlation between the HSV channels, conditional upon the color name, a well known property of the color space?

I have been investigating color as part of a academic project. One of the assumptions I make as part of a larger project, is the conditional independence of the 3 channels of HSV, given the color name people tend to ascribe it.

Or to put it another way: If you (an ideal color knower) are trying to guess the Hue of a color patch that I am holding. And if I had already told you what I would call it. Then your chance of guessing correctly does not improve much, if I also told you the measured Saturation or Value of the color patch. and similar for the other channels.

I did a bit of an investigation of this using the results of XKCD color survey. I looked at the Spearman's correlations between each channel, after grouping the responses by ascribed name. And I found that for over three-quarters of all color-names, the correlation between channels was at most weak (|ρ|<0.20).

I repeated this test for 15 other color spaces: RGB, HSI, HSL, xyY, XYZ, Lab, Luv, LCHab, LCHuv, DIN99, DIN99d, DIN99o, LMS, YIQ, and YCbCr. HSV was the lowest -- many had rather strong collectations.

There are a few problems with the test. It underestimates the correlation for non-monotonic variables. In particular since Hue is in a circle, that causes it to underestimate. My gut is telling me though, that that underestimation shouldn't be by more than a 100%, which would still leave the correlation of HSV lower than any other color-space, except HSI, and HSL which have the same wrap-around problem. Anyway, because of limitations like this, my test is more suggestive of this conditional independence, than it is proof of.

I am wondering if in-fact it is already a well established fact about color spaces, that HSV has this property. Reference to books, or papers would be appreciated.

It does make a certain amount of sense: When someone tells us the name of a color, they are primarily informing us of one aspect of H, S, or V. If I say "Green", I am suggesting a range of Hues -- I'm not saying much about the Saturation or Value, except that neither the saturation nor the value are very small. Similar for things like Black, Grey and White, for other channels. And further if I say "Pale Green", you know about the Hue -- it will be greenish, and the Saturation -- it will be low. And I know these things just from the name. It is not like "Pale Green"s with 1 particular hue, will always have 1 particular saturation etc.

I feel like this should perhaps fall out of the fact that Hue, Saturation, and Value are well distinct properties, as far as humans perceive -- and thus name -- colors.

Having low correlation like this makes HSV a more expressive space

• This makes sense, HSV isnt particularily good at describing how eyes work but rather it is a model developed for artists to mimic the model of color they are used to think it all worked before the inner working of the eye was known. So it is an artist tool Not a scientific one. Humans do not see hue! – joojaa Jun 17 '17 at 6:59
• A (very) brief search of Google Scholar isn't turning up much re: this being a well-investigated property. Perhaps your realization/research is more novel than you thought? – Sebastian Lenartowicz Jun 18 '17 at 21:19
• It would be great if you could post your data plus any plots you made - is that possible? Would love to investigate further. – jtlz2 Apr 25 '19 at 19:37
• @jtlz2 here is the experimental code. nbviewer.jupyter.org/github/oxinabox/ColoringNames.jl/blob/… This suggestive result is currently in an appendix for a paper I have under-review (For a paper I worked on and off on for apparently 2 years...) – Lyndon White Apr 25 '19 at 22:19