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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

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    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 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 at 22:19
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You may have stumbled upon an empirical observation that HSV is a colour/color space in which the variance is greatest between the channels / the channels are the least correlated. I would be interested to see your plots/data.

In maths and physics, these 3 axes - the ones of maximum variance - are called eigenvectors. Any color can be expressed as a linear combination of the eigenvectors, with one coefficient describing the relative amplitude of each. This is also how you can transform from one color space to another.

You could calculate the eigenvectors from your data points and see how well they align with HSV (as opposed to any other color space). Quite well I suspect given your interesting observation.

Eigenvectors have a special place in physics. One application - among very many - is to compression.

Hope that helps.

  • The reason why HSV type spaces score badly is that while they align very well with art history (in other words color theoy, artists), they dont align well with how human sensory apparatus work (which is studied by color science). There is a implied reason why the scientific approach produced better results, they are based on measurements of real data and human input and knowledge of bilogy, technical spaces like RGB build on this kind of knowledge. In fact HSV does not even attempt in any way spread the colors out as they are perceptually spread or even what the color are. – joojaa Apr 25 at 20:42

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