Tuesday, August 30, 2022

Response to Hue Angles ISCC 498


In the Hue Angles column Spring 2022 issue of the ISCC newsletter, Michael Brill offered a challenge for all his fellow chromo-historians: What is the oldest hack in color engineering? Dr. Brill’s nomination was the normalization of the tristimulus values against the illuminant.


I accept his challenge, and submit not one, but two related hacks, just to distinguish my entry from the hundreds of others who responded to the challenge.


I contend that the tristimulus functions are themselves a hack, well, actually two hacks. And since you can’t normalize tristimulus values until you have tristimulus values, I claim that my hacks are slightly older than the normalization hack proposed by Dr. Brill. 


To explain my proposed hacks, I need to give some thrilling backstory. There is a common misconception that the tristimulus functions (also referred to as the Standard Observer) that we know and love were developed to create color metrics that mimicked how we see color. Nope. Not true. There is another common misconception that the tristimulus functions were the best guess in 1931 as to the spectral response of the human eye. Sorry. That’s not true either. The backstory will explain both of those misconceptions.


Color measurement in the 1920s was considerably different than it is today. Today, we punch a button and a set of color coordinates comes out. In the 1920s, measurements were performed by a device called a tristimulus light mixing colorimeter[1]. The user would meticulously adjust the intensities of a red light source, a green light source, and a blue light source to match a sample. This was a time consuming and painstaking task and the human being was an integral part of the color measurement device. The settings of the three light sources were used as a proxy for the measured value of the color [3].

Conceptual drawing of a tristimulus light mixing colorimeter

The Such devices were difficult to use and had poor reproducibility. Someone came up with the clever idea that a spectrophotometer and gobs of arithmetic could be used to emulate a tristimulus colorimeter. I will tentatively say that this person was Deane Judd. At the very least, he was thinking about this in 1930 [4]. 


The aforementioned “gobs of arithmetic” required the creation of gobs of standardized data in the form of color matching functions. These color matching functions answered the question of “how would a hypothetical user adjust the hypothetical knobs of a hypothetical tristimulus colorimeter to match (for example) 530 nm light?”


Two scientists from England, John Guild and W. David Wright, independently took on the task of creating said gobs of data with the help of a total of 17 volunteers between them. Guild and Wright chose different versions of red, green and blue light sources, so their color matching functions were different. But once the correction was made for this difference, their data agreed reasonably well. The averaged data was massaged a bit and standardized in 1931 by the committee that is now known as the CIE. They called it the Standard Observer.


The idea of using a spectrophotometer and gobs of arithmetic to emulate a tristimulus colorimeter was clever. It was also ad hoc, that is, it served as a quick fix to a problem that was at hand. But it did not address the more general need for a way to emulate the human visual system. Hence, it qualifies as a hack. 


The committee now known as the CIE needed to decide which tristimulus colorimeter to emulate. Virtually any choice of red, green and blue lights would suffice. Golly gee, they could even substitute an exotic violet for the blue or a subtle chartreuse for the green. They decided to go even wilder and standardize on lights made from unobtanium[2]. Good golly gosh and gee willickers, since it’s all just computation anyway, who says the choice of standard stimuli for a standard tristimulus colorimeter even has to be physically possible?!??!? 


Being the wild and crazy guys they were, their choice of lights for the primary lights emitted negative amounts of light at certain wavelengths. Why? Their particular choice minimized the gobs of arithmetic needed to determine the tristimulus values that stood as proxy for color measurements. This is my second proposal for a primordial color engineering hack. It was clever and solved an immediate problem – hand calculation of colorimetric values. But once again, the bigger issue of emulating the eyeball went by the wayside.


The tristimulus functions [5]


I propose Seymour’s Rule of Hackery: Every good hack has an equal and opposite unforeseen consequence. As you would expect, there were unforeseen consequences that the 1931 committee did not foresee when they decided to emulate a long-since extinct color measuring device in a way that would save precious microseconds of computing time on any cell phone. Tune in to the next ISCC newsletter and you will see the unforeseen!



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

[2] Smith and Guild, The CIE colorimetric standards and their use, Trans. Opt. Soc. 33, 102 (1931-32), p. 89

[3] Seymour, John, Why does the a* axis point toward magenta instead of red?, Color Research and Application, 23 July, 2020

[4] Judd, Deane B., Reduction of Data on Mixture of Color Stimuli, Bureau of Standards Journal of Research, Vol 4 (1930)

[5] Judd, Deane B., The 1931 I. C. I. Standard Observer and Coordinate System for Colorimetry, JOSA Vol. 23, Oct. 1933


This article was written by John Seymour, who has to his credit several earlier pieces in the ISCC News and has (more famously) a blog at johnthemathguy.blogspot.com. Due to his immeasurable modesty, John has not signed his name, but I reveal his identity here. MHB

[1] Some of you may recognize the word tristimulus. The prefix tri- means three, and stimulus refers to the three flavors of lights in the device. A bit of foreshadowing for the perceptive reader.

[2] “A common observation about unobtainium is that it meets all requirements perfectly, other than not actually existing.”



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