Beta RGB

There are many RGB working spaces in existence. Some have derived from color television and video standards. Others have come about by tedious trial-and-error efforts or even by accident. It can be difficult choosing the "best" working space for any given application. In fact, it is not at all obvious what working space attributes are even desirable.

One important characteristic would be that the working space is suffiently large that it can properly encode (or contain) all colors that are important to an application. This implies "larger is better."

Another attribute, which conflicts with the above, is that the working space should be as small as possible, so that quantization errors may be minimized. This implies "smaller is better."

Since working space definitions are normally derived from theoretical monitor mathematical models, there is a small set of numbers that fully defines them. However, because of this, the gamut has a characteristic "shape" which cannot be arbitrarily formed. Therefore, a good working space would have a gamut shape that minimizes wasted space. This has to do with shape, not size.

In an effort to quantify and evaluate the various existing working spaces, I performed many types of calculations and gamut comparisons, summarized on the RGB Working Space Information page. As part of this exercise, I chose various color sets of possibly important colors, such as different film types, color charts and printing gamuts. After doing this, it was a natural progression to turn this problem around and define the optimal working space for the combined sets of colors. Thus, Beta RGB was born.

Choice of a Reference White

Since Adobe Photoshop and the ICC profile specifications both use D50 as a reference white, this was the logical choice. If instead, a non-D50 white was chosen, then both the creation of, and the use of the working space would require adaptation, which opens the door just a crack for mistakes to be made. Specifying the working space directly in D50 avoids this possibility for error.

The reference white of Beta RGB is:

 Reference White = D50

Choice of Reference Primaries

For this part, I mathematically found the optimally sized and shaped working space that contained all of the colors in my reference set. So the gamut is large enough to encode the colors, but no larger. Here is a chromaticity diagram showing the color set along with the working space:

I have intentionally excluded the FOGRA colors from this illustration because none is a defining color, and there are so many of them (1856) that they would obscure many of the more interesting colors.

The chromaticity coordinates of the Beta RGB primaries are:

 Red = (0.6888, 0.3112) Green = (0.1986, 0.7551) Blue = (0.1265, 0.0352)

Choice of Gamma

Gamma does not affect the size or shape of the gamut. It does affect the distribution of RGB points within the gamut. Therefore, it is an important consideration for controlling quantization. I have previously analyzed the optimal gamma for the grayscale only (you can see this analysis here). This result was about 2.2 (actually either 2.1723 or 2.3243 depending upon the error metric used).

For Beta RGB, I additionally performed a three-dimensional analysis, where I looked at the ΔE produced by tiny perturbations in RGB space, measured at each of the locations in the color set. For each color, the RGB value was perturbed a distance of one-percent in each of 20 different directions (I used the centers of the 20 faces of an icosahedron to evenly distribute the directions in three-space). Minimizing the RMS ΔE resulted in a gamma of 2.12. This was sufficiently close to 2.2 that I did not feel a deviation from a "standard" 2.2 value was warranted.

The gamma of Beta RGB is:

 Gamma = 2.2