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Chris_F

CIE Color Space Conundrum

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I have some questions regarding some confusion about color spaces, and since it is fairly graphics related, I was hopping somebody here could help me understand.

The first thing that I'm confused with is how ambiguous some of the terms for various color spaces are. It's hard to get an idea of how they relate to each other when it seems like they are the same but different. E.g. what is the difference between UV (as in YUV), U'V' (as in YU'V'), u*v* (as in L*u*v*) and U*V* (as in U*V*W*)? It seems like the CIE has defined U and V enough times to drive me bonkers.

Another thing that bothers me is that I've [url="http://wiki.patapom.com/index.php/Colorimetry#Color_Spaces"]seen[/url] YUV referred to as being device dependent, while XYZ and xyY are device independent. That makes no sense to me because [url="http://www5.informatik.tu-muenchen.de/lehre/vorlesungen/graphik/info/csc/COL_14.htm#topic13"]here[/url] it states that YUV is just a linear transformation of xyY which in turn is just a linear transformation of XYZ.

Lastly (I think), I have seen the Y in XYZ referred to as both luminance and lightness. This is extremely confusing because the Y in YUV stands for luminance while the L in LUV stands for lightness. YUV != LUV see my confusion?

This is probably just the start of my confusion. Any help in making heads or tales of this would be appreciated.
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Hi!

I can’t answer all your questions, since I simply don’t know how the U’V’, u*v* and so on are defined in particular. But, I can probably tell you what Y has to do with luminance.

Let’s start at the very beginning.
As you know, each color is a combination of red, green and blue. For each, there are special receptors in the eye. Decades ago some guys conducted experiments to figure out the three corresponding basis functions for the receptors. Those three are functions of the wavelength: [formula]r(\lambda), g(\lambda), b(\lambda)[/formula]. They basically allow you tell you how much you need of R, G and B to assemble a certain color. Problem was, they needed negative red in order to produce cyan, which is why a normalization of the curves was necessary, eventually yielding the norm spectral curves [formula]\bar{x}(\lambda), \bar{y} (\lambda), \bar{z} (\lambda)[/formula] (aka. color-matching functions).

The receptors are not equally sensitive. Green for instance is much better perceived than the others (since it is in the middle of the visible spectrum). Generally speaking there is also a curve describing how responsive the human eye is to certain wavelengths or let’s say how bright something is perceived. This curve is called V-Lambda curve (or in general spectral power distribution). This curve was also experimentally conducted and is averaged over many people. The curve changes a little depending on whether you look in daylight, the dawn or at night (photopic, mesopic and scotopic vision).

Anyway, when you start calculating with light you have to decide on one thing beforehand: Consider everything radiometric (luminance is the integral over the complete spectrum, more used in physics) or photometric (luminance is the integral over the visible spectrum weighted by the V-Lambda curve, more what we need). Though, you can convert between both if you wish.

To get rid of the wave length, we simply sum up over the whole visible spectrum.
In the CIE XYZ, we have:
[formula]X = \int_{380nm}^{780nm}L(\lambda)\bar{x}(\lambda) \partial \lambda[/formula]
[formula]Y = \int_{380nm}^{780nm}L(\lambda)\bar{y}(\lambda) \partial \lambda[/formula]
[formula]Z = \int_{380nm}^{780nm}L(\lambda)\bar{z}(\lambda) \partial \lambda[/formula]
Whereas [formula] L(\lambda)[/formula] is the luminance of a light source for a given wavelength. Each light source has some sort of own luminance profile (the mix of wavelengths it emits).

Now, let’s close the circle.
The norm spectral curve [formula] \bar{y} (\lambda)[/formula] is surprisingly, roughly equal to the V-Lambda curve. Y is the integral over the visible spectrum of the norm spectral curve [formula] \bar{y} (\lambda)[/formula]. The V-Lambda curve is the weight in the photometric luminance. Thus, since [formula] \bar{y} (\lambda)[/formula] and V-Lambda look equal, their integrals (Y and the photometric luminance) are quite similar as well. Which is why Y is sometimes called luminance (though, more precisely it’s photometric luminance…).

Over the years, the light spaces were rescaled to fit better particular needs: allow distance measurements between colors, be coherent with the human perception and so on. This is the point, where I got lost, too since there are simply too much. [img]http://public.gamedev.net//public/style_emoticons/default/smile.png[/img]

I hope that answered at least one of your questions. [img]http://public.gamedev.net//public/style_emoticons/default/smile.png[/img]
Best regards!
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