Thread: The math behind mixing colors

1. Originally Posted by przyk
A person in possession of such an eye could distinguish a mixture of blue and yellow light from green light, but not from orange.
OK, excellent point; if we could see pure yellow and pure blue but nothing else, we obviously could not equate mixing the two to a pure green source.
Originally Posted by rpenner
The CIE team is convinced that perceptually the majority of us have very similar perceptual spaces.
RPenner, you've been a great source of information. Does the CIE color model obey any mathematical foundation whatsoever, or is it "backed out" from whatever arbitrary system our eyes and minds have developed over time?

2. Well the LMS system is backed out from biology -- we actually do have pigments in the eye which absorb colors. The XYZ model was an arbitrary choice, with brightness (Y) based on human perception experiments and X and Z from data from color perception tests. The assumption of linearity has been tested and found to be pretty good for color mixing.

So in principle we can build a color matching machine from a light detector and 3 filters, or from a spectrophotometer and 3 wavelength-dependent weighting functions. We can understand why the practice is to see how a print pattern looks in the sunlight since the peculiar spectrum of fluorescent lighting and the narrowly tailored spectral reflectance of synthetic dyes can cause a pattern of colors to be perceived significantly differently under different lighting conditions.

// Edit -- Oh, it turns out someone already did a nice summary of how we got to XYZ from the older RGB data based on color-matching experiments with light.

http://en.wikipedia.org/wiki/CIE_193...YZ_color_space

3. Originally Posted by rpenner
Well the LMS system is backed out from biology -- we actually do have pigments in the eye which absorb colors. The XYZ model was an arbitrary choice, with brightness (Y) based on human perception experiments and X and Z from data from color perception tests. The assumption of linearity has been tested and found to be pretty good for color mixing.

So in principle we can build a color matching machine from a light detector and 3 filters, or from a spectrophotometer and 3 wavelength-dependent weighting functions. We can understand why the practice is to see how a print pattern looks in the sunlight since the peculiar spectrum of fluorescent lighting and the narrowly tailored spectral reflectance of synthetic dyes can cause a pattern of colors to be perceived significantly differently under different lighting conditions.
First, I have been impressed with the information you have presented on the research into the perception aspect of color. I should have known someone would have already done this but I had been unaware. As far as turning that into a color matching machine....

Computerized color matching systems are used throughout the paint industry. Even at home improvement stores. They do a fairly good job but even those used by major paint manufacturers are not spot on.

One of the problems is that they are unable to detect the differences between pigmented and ink dye based colors, as well as different pigment and dye systems. This results in an in ability to make a "spot" on match. In other words when paint is matched using such systems it is rarely close enough to the original color to use as a touch up. The color differences can even be enough that when used on separate walls near one another an untrained eye will see the difference in shade. In fact if you provide a color formula to a distributor and then return to have it computer matched they often cannot reproduce the color close enough for touch up from their own stock and color system.

Your mention of the lighting issue is another problem. Though it is likely possible to make those compensations the equipment I was aware of did not do a very good job of it. Different pigments and dyes react very differently under a variety of lighting conditions. I should mention also that at least here in California, the industry was transitioning away from pigmented paints and moving to almost completely dye based in store systems shortly after I retired. This was driven by economics, it is cheaper and in part to meet air quality regulations. So mix all your paint together before you start to paint.

This information is from experience and I do not know that it is the same system mentioned above. However, since I have experience with systems used by two of the largest paint manufacturers and distributors in California and neither could produce an exact match without knowledge of the original composition of the paint and colorants, it is a fair assumption that the technology was not sufficiently advanced to match the color matching capability of some of the old time painters. Few of which are any longer available.

I retired in 2005 so there may have been some advancement since then.

I don't know how the technology would fair in applications other than paint. I have known two people both old time painters now long gone who could tell the difference between a pigmented paint and dye. Even tell you which dyes or pigments would be needed to reproduce the color. Both were able to match paint close enough to touch up. That is really hard even if you know the original formula. You might say that both of them had a color sense comparable to perfect pitch in music.

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