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  #1  
Old July 11th, 2011, 06:49 PM
Doug Kerr Doug Kerr is online now
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Default The Unified Color Beyond RGB (GMWAS) color space

[GMWAS: gag me with a spoon]

Unified Color Technologies (UCT), in their line of HDR image processing software, uses a color space they call "Beyond RGB". Just what is that?

Well, it turns out that the native file format for BRGB is BEF, and I suspect that describes a color space as well (Bef, actually).

One chart that appears here and there in the UCT documentation, "illustrating" the BRGB color space, is labeled "Bef2" (maybe an editorial slip). So maybe "Beyond RGB" is also "(a little) beyond Bef".

It appears that this color space is either a luminance-chrominance color space or a pseudo-luminance, pseudo-chrominance color space (I actually suspect the former). For reference, the L*a*b* color space is a pseudo-luminance, pseudo-chrominance color space.

Evidently, the coordinates of the color space are B, e, and f (fancy that). B is apparently the luminance (or pseudo-luminance) coordinate; the symbol is doubtless evocative of "brightness".

The coordinates e and f are apparently broadly similar in concept to the coordinates a* and b* of the L*a*b* color space (often called just "a" and "b").

Apparently 32-bit floating point representations of the coordinates are used (probably per IEEE-754).

This figure appears here and there in the UCT stuff:


Copyright Unified Color Technologies (I guess). Fair use for review purposes.

It is apparently a section through the color space of the Bef2 color space at some value of B (a chrominance plane). Apparently it shows a section through the sRGB color space as plotted in the Bef2 color space. Its gamut boundary is apparently the boundary of the gamut of human visibility at that value of B.

In all their literature, they use the word "color" to mean either chromaticity or chrominance. (As I say in my papers on color models, "as lay people, unaware of the technical meaning of color, do".)

In one piece, they say:

Beyond RGB is similar in concept to the Lab color space, in that it is also a three dimensional space with brightness or luminance on one axis and color information on the other two. In practical application however they differ significantly. Brightness changes in Lab can often introduce changes in color too, where as Beyond RGB maintains the integrity of the color data as brightness is changed. [Color keying added.]

What does the red passage mean? It might mean this:
In the L*a*b* color space, if we change L* but leave a* and b* the same, the chromaticity of the represented color changes.
[True.]

or maybe this:
In the L*a*b* color space, if we change L* but leave a* and b* the same, the chrominance of the represented color changes.
[A little true.]

Or maybe something else.

What does the green passage mean? It might mean this:
In the BRGB color space, if we change B but leave e and f the same, the chromaticity of the represented color does not change.
[Hard to believe, if e and f define a chrominance plane.]

or maybe this:
In the BRGB color space, if we change B but leave e and f the same, the chrominance of the represented color does not change.
[Easy to believe, but so what.]

Or maybe something else (but no doubt very desirable).

It's also possible that e and f are chromaticity, rather than chrominance, coordinates. In that case, presumably, if we change B but not e or f, the chromaticity of the represented color does not change.

That's all I know so far.

Best regards,

Doug
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  #2  
Old July 12th, 2011, 07:46 AM
Andrew Rodney Andrew Rodney is offline
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Quote:
Originally Posted by Doug Kerr View Post
[GMWAS: gag me with a spoon]
In one piece, they say:

Beyond RGB is similar in concept to the Lab color space, in that it is also a three dimensional space with brightness or luminance on one axis and color information on the other two.
That they lump brightness (not Lightness) and luminance in the same sentence as if they are the same is enough to warrant suspicion here!

From what I understand, the L in Lab is Lightness (a property of color). Brightness is a human perception, not the same. Luminance is the properly of an emissive surface or reflection from a surface (cd/m2).
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  #3  
Old July 12th, 2011, 08:20 AM
Doug Kerr Doug Kerr is online now
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Hi, Andrew,

Quote:
Originally Posted by Andrew Rodney View Post
That they lump brightness (not Lightness) and luminance in the same sentence as if they are the same is enough to warrant suspicion here!

From what I understand, the L in Lab is Lightness (a property of color). Brightness is a human perception, not the same. Luminance is the properly of an emissive surface or reflection from a surface (cd/m2).
A distinction well taken.

The notion of lightness flows in part from the original orientation of the L*a*b* color space as a descriptor of "reflective color" (for paint finishes and the like).

But once we follow it to its later role for describing the color of light, the quantity L* tracks more closely with brightness (in the sense you mentioned) than luminance.

Just a small detail - the dimensionality of luminance is not luminous flux per unit area (as your unit suggests), but rather is luminous flux per unit solid angle per unit area, so its unit is:

cd•sr^-2•m^-2

(I have to use that form to avoid ambiguity when we have more than one "per".)

Another way to write it unambiguously (not considered editorially polite, because of the parentheses) is:

(cd/sr^2)/m^2

***********

Sparing no expense for our collective enlightenment, I have just sprung for the $18.00 cost of a paper in the SPIE journal by three Russian guys that discusses at some length the Bef color space and a later derivative, LinLogBef, comparing them with other color spaces of interest in the field of HDR imaging.

Interestingly, their paper shows the same figure I showed, and mentions that it is in fact a slice of the color space of the Bef color space for B= <black>. (I don't yet know how the coding works, so I cannot say what the numerical value of B is for <black>.)

We often run into this presentation when we show "chrominance" or "chromaticity" planes. The one shown is in fact most often for luminance=0 (although this is rarely mentioned). That of course seems paradoxical, since there is only one color with luminance=0 ("black"), for which chromaticity or chrominance is "undefined".

But in fact, an infinitesimal distance up the luminance axis, chromaticity or chrominance is meaningful. That is, a color with a very tiny, but not zero, luminance has a valid chromaticity or chrominance. Its range is the so-called "zero-luminance chromaticity [or chrominance] gamut". Formally (and less paradoxically), it is the limit of the chromaticity [chrominance] gamut as luminance approaches zero.

In fact, for the sRGB color space, the chromaticity gamut usually shown is that gamut (although it also applies through a finite range of luminance).

If you consider color in the CIE xyY system (the usual chromaticity presentation is an x-y plane of that three-dimensional space for some unmentioned value of Y), the sRGB gamut is of course a three-dimensional solid. If we look at its bottom (not the projection of the entire solid on that plane; just the "face" we would paste felt on so it did not scratch our coffee table), that is the sRGB gamut we usually see. And that face is in fact the "zero luminance chromaticity gamut" (indeed a mathematical fiction).

Now, to read some some Russian literature.

Best regards,

Doug
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Old July 12th, 2011, 11:15 AM
Doug Kerr Doug Kerr is online now
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Well, the $18.00 paper was not of too much help (although certainly interesting).

But some clues in it allowed me to find another paper by two of the same authors that has been most enlightening.

What follows is my quick interpretation of what I have read so far.

**********

The Bef color coordinate system is a transform of another color coordinate system, DEF.

That coordinate system may be grasped from this figure (which I think is considered to be "drawn" in the CIE XYZ color space):


It is a three axis system.

• Axis D is the axis along which lie the color representations of all colors whose chromaticity if that of standard illuminant D65. (Yes, "D" is evocative of "daylight".)

• Axis E is the axis along which lie the color representations of all colors whose chromaticity is that of monochromatic (spectral) light of wavelength 700 nm.

• Axis F is orthogonal to the first two (that is, at right angles to both).

Now, there is a transform of this color coordinate system into one whose coordinates relate to a certain meaning of brightness (B), hue (H), and chroma (C). (We can inexactly think of chroma as being like saturation.)

For a color at point S, then B is the length of the vector from the origin to S; H is the angle the projection of that vector onto the E-F plane makes with the E axis; and C is the angle that vector makes with the D axis.

When C=0, we have a color along the D axis, where chromaticity is always that of D65; that is, such a color would have zero saturation (assuming a white point of D65).

Neat!

Note that C and H together define the chromaticity of the color.

B is something like luminance, but not exactly.

Now, the Bef color coordinate system transforms the DEF coordinate system into a form slightly reminiscent of the L*a*b* color space.

B is the same B we just saw in the BHC color space. Algebraically, from the DEF model:

B=sqrt(D^2+E^2+F^2)

Also:

e= E/B

f=F/B

Note that in this model, if we start with a certain color (a certain B, e, f) and change B (to make the "brightness" of the color greater or less, but not to change its chromaticity), the values of e and f do not change.

Thus, the e-f plane becomes a plane of chromaticity.

Why do I not speak of this as the "Bef color space"? Two reasons:

• I prefer, in this kind of work, to use the term color space in its original technical meaning: the "realm" of possible values of the color coordinates in a color representation system.

• I have not so far given (nor seen, actually) definitions of how the numerical values of B, e, and f are to be determined (part of the definition of a color space in the modern meaning of the term).

A parallel is that "RGB" is a color coordinate system ("color model"); sRGB is a color space.

*********

Now how this exactly relates to the Beyond RGB color space (GMWAS), I'm not sure.

By the way, the "2" in "Bef2" reminds me of the "DEF2" color coordinate system described by the authors of the paper I have been discussing. It means a DEF color coordinate system that is specifically predicated on the "2° standard observer" visual response (the one on which the 1931 CIE XYZ color space is predicated). "Bef2" may have the same significance.

And perhaps "Beyond RGB" is just a new marketing name (or accolade) for the Bef color space. "Where's the Be(e)f?"

Well, that's all we know so far.

Best regards,

Doug
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  #5  
Old July 12th, 2011, 11:37 AM
Asher Kelman Asher Kelman is online now
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Doug,

I commend you for your engineering sleuth-work and myself for reading every word and following your logic.

I hope the company might add their comments.

Asher
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  #6  
Old July 12th, 2011, 12:03 PM
Doug Kerr Doug Kerr is online now
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Hi, Asher,

Quote:
Originally Posted by Asher Kelman View Post
I commend you for your engineering sleuth-work and myself for reading every word and following your logic.
Thank you, and I commend you for your diligence as well!

Best regards,

Doug
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