Tuesday, May 17, 2022

The Oldest Hack in Color Engineering

(Send contributions to mbrill@datacolor.com)

When I was at MIT, I learned what it meant to call something “a hack.” The term referred to a patch in software (or hardware) that was ad hoc but clever and fixed a problem. There are many other definitions of “hack” (the noun), but I don’t use those here. To me, “hack” is not necessarily pejorative, but descriptive.

In color engineering there have been many hacks, originating even before the term “color engineering” was popular. Two rather good ones are Cal McCamy’s approximation for correlated color temperature of a light given its chromaticity [1] and the CIELAB L* function as an approximate inversion of a fifth-degree polynomial that characterized the Munsell Renotation System lightness scale [2].

Just for fun, I now ask you: What is the oldest hack in color engineering? One could nominate Newton’s representation of color as a closed circle. Newton must have been aware that the purples are not elementary colors that he could see with his prisms. But Newton and others may have adopted the circle as an instructive idealization, and that is not a hack.

To get the ball rolling (I expect hundreds of reader responses), I nominate the object-color tristimulus value (X, Y or Z, for any illuminant and observer you like). This quantity is defined as a specific ratio (see ASTM E-308, any edition). The numerator is the wavelength integral of the product of illuminant power density, reflectance and color-matching function (generally x-bar, y-bar or z-bar). The denominator is the wavelength integral of the product of the illuminant power density and the function y-bar. There’s also a factor of 100, but that doesn’t matter.

What problem does this definition cleverly solve? In a single stroke, it renders the object-color tristimulus value dimensionless and independent of the absolute light intensity, as is its cousin – the emissive-mode tristimulus value. (This latter fact emerges from the grounding of emissive-mode tristimulus values on the emissive-mode color-matching experiments that underlie basic colorimetry. In a short paper I just submitted to Color Research and Application, I explain how the titration in a color match leads to cancelation of all dimensions.) Creating the object-mode ratio makes the tristimulus values from reflected lights appear comparable to the values from emitted lights and emissive displays. Certainly color-matching equivalence classes of reflected lights are not disturbed by the ratio. But, as many color-management experts have warned, we should be careful in asserting exact colorimetric color reproduction between emissive and reflective media. For one thing, only the reflective tristimulus space has an unambiguous white point.

How is the object-color tristimulus value a hack? It is ad hoc, solves the units problem, and is clever enough to survive generations of standards bodies like the ASTM and the CIE. The ad hoc quality manifests when we observe that the object-color tristimulus values have a distinct and asymmetric dependence on Y wrought by the denominator, yet that asymmetry was not based on color matching (as should befit a true tristimulus value). Furthermore, as the current object-color tristimulus value is a ratio between two spectrum integrals, it will have a weird illuminant-invariance such as I have found for Von Kries adapted tristimulus values [3] and band ratios [4]. If the illuminant is restricted to a finite linear function space, changing its coefficients will not alter the object-color tristimulus value if the reflectance is outside a forbidden function subspace. There’s no room for such games in the emissive-mode tristimulus values.

So that is why I consider the object-color tristimulus value as a hack. My only remaining question is, how old is it? Wyszecki and Stiles [5] point to the dawn of the 1931 CIE system of colorimetry. I have not investigated further, but it’s entirely possible that this hack precedes not only the term “color engineering,” but also the name “tristimulus value” itself. I’ll leave that subject to serious historians in our ranks.

[1] McCamy CS, Color Res Appl 17 (1992), 142-144 (with erratum in Color Res Appl 18 (1993), 150.

[2] Newhall SM, Nickerson D and Judd DB, Final report of the OSA subcommittee on spacing of the Munsell colors, J Opt Soc Am 33 (1943), 385-418.

[3] Brill MH, Minimal Von-Kries illuminant invariance, Color Res Appl 33 (2008), 320-323.

[4] Brill MH, "Can color-space transformation improve color computations other than von Kries?" in:  Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach and B. E. Rogowitz, Editors, Proc. SPIE 1913,485-494 (1993).

[5] Wyszecki G and Stiles WS, Color Science, 1st ed. New York: Wiley, 1967, p. 279.

Michael H. Brill

Datacolor