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Chromaticity and chrominance

Doug Kerr

Well-known member
In my discussions of various color spaces (notably of late those used for HDR work) I often make reference to (and draw the distinction between) chromaticity and chrominance.

I thought it might be used to give a brief review of this.

Luminance-chromaticity color models

One class of color model divides the three coordinates used to describe a color into two aspects:

Luminance. This is often thought of as describing the "brightness" of the light; actually there is a formal quantity "brightness" which is not quite the same thing, but to get a general ideal of the concept of luminance, it is reasonable to think of it as being "brightness".

Chromaticity. This is the property that, to speak colloquially, distinguishes red from blue, and also distinguishes red from pink.

Now, since there must be three coordinates altogether to describe a color, chromaticity must itself be described by two coordinates. There are several models under which that can be done. One formal way is with the CIE coordinates x and y.

An important point for us in this discussion is this:

If we start with light of a certain color, and attenuate is (as if with a neutral density filter), its luminance decreases, but its chromaticity is unchanged. Whatever two numbers describe the chromaticity do not change.​

Luminance-chrominance color models

These describe the color of light with what is best thought of as a recipe. We start with a certain "potency" of "white" light (where, yes, "white" means in terms of some arbitrary "white" illuminant).

Then in general, we add a "colorant dose". This makes the overall light be, for example. red, or blue, or pink.

Now, to describe the color under such a model, we state:

• The "potency" of the white ingredient, which we say is the luminance of the color.

• The nature of the colorant, which we say is the chrominance of the color.

As with chromaticity, there are different ways to state chrominance. One way is to state its hue and its "potency".

I must digress now to head off what may seem a paradox.

If the amount of the "white light ingredient" in a color is equal to the luminance of the color, and then we add more light (the "colorant"), that should increase the overall luminance of the "mixture", so the luminance of the color is no longer equal to the "potency" of the white ingredient.

But in fact the colorant does always has zero luminance. It has "colorfulness", but no luminance. What kind of light might that possibly be? Indeed, no physical kind of light.

But this "recipe" is not really a "recipe" for making light, just a virtual recipe for for describing it. So we can work with "fictional" ingredients that have a certain mathematical significance but do not correspond to anything we can make physically.

The paint metaphor

Now a homey metaphor for the workings of chrominance can be given. It involves mixing paint. We must be careful about what represents what. Here the amount of paint to be made corresponds to the luminance of the light (its overall potency). The "color" of the paint (as the paint dealer would describe it) corresponds to the chromaticity of the light.

Now to make a gallon of "dusky rose", we start with (about) one gallon of "white base". That amount corresponds to the luminance of the light. To that, per a recipe we have in a box of cards, or in the paint computer, we add a certain colorant dose (probably made of several ingredients). This colorant dose corresponds to the chrominance of the light.

The paradox now visits us again. For the metaphor to work perfectly, to make a gallon of finished paint (that is light of a certain luminance), we should be able to start with a gallon of white paint (the "white light" whose potency is the same as the desired luminance of the light to be described). But now how will the colorant dose fit in the can - how does it not increase the total amount of paint made (the luminance of the light)?

The answer is that this colorant is also fanciful. It is so concentrated that the amount needed for any recipe has infinitesimal volume.

Now suppose that instead of needing a gallon of paint (representing one unit of luminance for our light), we only want one quart (representing 1/4 unit of luminance). But we want the paint to be the same "color" (that is, for the light to have the same chromaticity).

So we start with one quart of the white base paint and add 1/4 as much of the "colorant dose" (of the same composition of individual colorant ingredients).

In our light model, that corresponds to a chrominance "of the same hue but 1/4 the potency".

Now lets get fully back to light. The metaphor about the paint shows us why this is so:

if we start with light of a certain color, and attenuate is (as if with a neutral density filter), its luminance decreases, and the "potency" aspect of its chrominance decreases. One or both of the two numbers that describe the chromaticity will change.​

This, compared to the corresponding statement for the luminance-chromaticity class of models, illuminates an important practical difference between the two basic schemes.

Actual color spaces

How does this apply to actual color spaces we encounter?

Well, the RGB family, and CIE XYZ, are tristimulus color spaces, and neither concept applies.

The CIE xyY color space is a luminance-chromaticity scheme. Y is the luminance, and x and y define the chromaticity.

The YIQ color space used for NTSC television is very nearly a luminance-chrominance scheme (and is in fact the godfather of those). Y is something like luminance and I and Q describe something that is conceptually much like chrominance.* There, if we "fade" an image, Y, I, and Q all decrease (proportionally).

* Y and I/Q are sometimes called "luma" and "chroma", in part to alert us to the fact that they are not luminance and chrominance.​

All that also applies to the YUV color space, and also to YCbCr.

L*a*b is also something like a luminance-chrominance scheme. Again, if we decrease the luminance of a color, keeping its chromaticity the same, L*, a*, and b* all decrease (they would actually do so proportionally over most of the range except that L* has an offset in it).

This is the reason, by the way, that when the maker of a neutral density filter says, "this is very chromatically neutral - a* and b* [presumably referring to its "transmissive color under the L*a*b color space"] are both less than 2", no specific degree of neutrality of chromaticity has really been asserted.

Best regards,

Doug
 
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