I've been spending little time with various papers and presentations by Sergey Bezryadin, evidently the chief boffin at KEW/Unified Color. The papers are very technical, and involve some concepts in which I am not fluent, but they are well written and generally easy to follow. Although Sergey is Russian, his technical English is very good (if you don't always expect there to be definite articles in the expected place), and he has a good didactic approach.

Every time I read a statement in one of his PPS presentations, and thought, "Well, I think that would only be so if . . .", his next slide says, "Well, actually that is only so if . . .

The DEF color space (which is essentially the starting place for the Bef color space, which is what Beyond RGB is, or is derived from). It is based on what are called the

*Cohen metrics*, which we can think of as defining a color space. The name refers to work by Jozef Cohen, who points out that a certain color space (or class of color spaces) has fundamental properties that commend them for certain work. They are, in a sense, "our native color space".

Most prominently, the "Cohen metrics" color spaces have the property that, overall, distances between points in the color space (using that term in its original meaning) are consistent with perceived color difference.

(I believe it was Bart who commented earlier that he thought the color space here was somehow connected with color difference formulas. I think that was right on.)

Now the DEF color space is evidently a transform of the "Cohen metrics" color space such that it is

*orthonormal* with respect to the Cohen space.

That means that whatever is the distance between the points representing two colors in one color space, there will be the same distance between the point representing the colors in the other color space.

Sergey in fact in one of his presentations neatly shows that this is not true of a comparison between a linear version of sRGB (what I call srgb) and the CIE XYZ color space (the one used for "scientific" description of color.

In any case, it seems that the DEF color space is defined so as to meet that criterion of orthonormality with respect to the Cohen metrics plus these arbitrary (but certainly sensible) criteria:

• The D axis is the locus of all colors whose chromaticity is that of standard illuminant D65.

• The E axis is at right angles to that* and "heads toward" the chromaticity of monochromatic light of wavelength 700 nm.

• The F axis is at right angles to those two*.

*In the context of orthonormality with respect to Cohen metrics.

I've ordered Cohen's book.

All very interesting.

Next I will be attacking 32- and 16-but floating point numbers, and denormalization, and all that. Many with serious computer science experiences will already know about all that.

Best regards,

Doug