It is, but only over a limited, but real world gamut. It wasn’t purely optimized to be perceptually uniform, although it is to a fair degree. Optimization (fitting) also pulled it in the direction of modelling viewing condition effects.
So it’s reasonable to use it for many tasks, but it shows its limits when you get near the edge of real world colors, or try to go beyond (i.e. ProPhoto primaries etc.)
No your assumption was correct! Perceptual uniformity is a required quality for a CAM or any Colour Model for that matter if you intend to use that model to make predictions about colours, measure colour differences, etc…
As @gwgill put it well (and described it somewhere above) the CIECAM02 suffers from having been fitted to a dataset that was probably not large enough. You end up with CAT02 generating negative values for some spectrally sharp colours or imaginary colours, thus related failures with Wide Gamut colourspaces, etc…
It is a very good CAM, maybe the best available to date (along the CAM16 flavour), so depending what you are doing it will make great predictions but when it fails, it does so greatly 
CAM02UCS (along the CAM16 flavour) is a good uniform colourspace based on CIECAM02.
For anybody wanting to get up to speed without reading Color Appearance Models by Fairchild (which I highly recommend you do anyway),
Luo, M. R., & Li, C. (2013). CIECAM02 and Its Recent Developments. In C. Fernandez-Maloigne (Ed.), Advanced Color Image Processing and Analysis (pp. 19–58). New York, NY: Springer New York. doi:10.1007/978-1-4419-6190-7
is a great compact read.
Cheers,
Thomas
Even if you are not specifically interested in Color Appearance Models, it has some great introductory chapters on color and color perception.
@KelSolaar and @gwgill - thanks! for the references and for letting me know that CIECAM02 really is more perceptually uniform than LAB.
Regarding the problem of having been fitted to a data set that wasn’t large enough, even in the digital darkroom my own interest is strictly in colors that can be printed or painted (using the same pigments artists use) without resorting to optical brighteners or other exotic ways to make colors brighter or more saturated. So a practical question is this: When working in a large RGB color space like Rec.2020 (sRGB excludes far too many paintable and printable colors), and keeping as far away from the primaries as required to avoid unprintable/not-paintable colors, how badly would the “fitted to a too-small dataset” affect using JCh? In case this question is just plain confused, please enlighten!
A couple of years ago I got a copy of Fairchild’s Color Appearance Models from our local library and read it. At the time my reaction was “That book needs actual pictures to illustrate the disadvantages of each model, that in turn led to the creation of the next model”. But I’ll check it out again and try rereading it, and also see if I can find a copy of the Luo paper - fortunately we have a university library nearby that allows non-students to use their resources.
Regarding the possibility (that would surely make @afre happy I’m guessing!) of perhaps adding code to GIMP that would allow picking colors using JCh (some version of), just how complicated are the equations, assuming one sets the “appearance model” parts to be as simple as possible? I’ve been looking for something for JCh that’s along the lines of Lindbloom’s explanation of the XYZ to LAB equations, such that I could focus more on “turn the equations into code” and less on “by the way what do these equations actually mean” - is there such a reference? I’ve looked at the ArgyllCMS code, but haven’t really been able to figure out where to start in terms of “What does this code actually do to modify the input XYZ values”, such that maybe I could write similar code for GIMP.
I think that would be nice to find a balance between making images and improving image-making software. Maybe schedule in a painting between rounds of coding?
Regarding subtractive rather than additive, I got the impression that the Wikipedia article was only talking about adding white light to monochromatic light, and not about mixing actual paint pigments on a surface and looking at the resulting color, so only applies to additively mixed colors. Anyway, I pulled out my oil pastels and mixed blue with white to make a fairly long more or less even gradient, and the apparent hue didn’t change much if at all, stayed blue all the way. But maybe the blue wasn’t violet enough.
On the other hand, mixing bright yellow oil pastel with black (or rather a mixture of black and white) does make olive green precisley as discussed on MacEvoy’s website. So is the Abney effect only about adding white light to monochromatic light? Or is it also about adding black pigment to make darker colors from bright pigments?
I had never heard of the Abney effect so thanks! for the link.
Anyway, @briend - you’ve convinced me of the value of your spectral subtractive mixing - anything that avoids that awful transition from blue to purple when mixing in white has got to be a step in the right direction .
Would you be willing to show some samples mixing magenta with cyan? I spent some time mixing oil pastels, using the nearest Crayola Portfolio yellow, cyan, and magenta working from MacEvoy’s page on triad color palettes handprint : "primary" triad palette, and was surprised by how much darker the purples, blues, and green-blues that you get from mixing the cyan and magenta oil pastels are, compared to the unmixed colors. Yes, I know, subtractive color mixing and all, of course the mixed color is darker. But “knowing” and “seeing” are two different things. So I’m curious as to how your spectral mixing algorithms handle colors like cyan and magenta (I think I already sent you approximate LCh values for the Portfolio pastels).
I googled for the “corrected” chromaticity diagram that the wiki page mentioned, and found this diagram from Fairchild’s book:
So I don’t know if we really have an answer as to why white and blue pigments will seem to maintain a constant hue. I wonder if the white paint was a perfect reflector and the illuminant was E, if this situation would change.
Yes! I win! I win! ;-). Kidding aside, I learned a lot just arguing. I was so focused on blue+yellow and how much better the spectral mixing “feels”, that I never even noticed how crazy the Abney effect was. I think the Abney effect accounts for the majority of my dissatisfaction with digital painting all these years. It’s one of those “once you see it, you can’t unsee it” things.
Sure! So, remember with oil pastels you’re probably making “layers” as well, which is more of a multiply rather than the weighted geometric mean a true mixing would yield. So here’s three gradients, the top is just a mix (weighted geometric mean) and the next two introduce that multiplication/layering aspect:
Here’s the same idea but on the canvas w/ brush settings, and a bit more intense multiplicative effect for the middle and bottom. It is much trickier to handle the multiplicative setting, because it is a compounding issue when dabs are being drawn on top of each other. Really need to implement a temporary stroke layer to fix this I think. Ideally most of these ideas could be implemented.
Cheers,
Brien
That may be true to some degree, but creating such data sets is hard work, and it may not be practical to extend them as wide as one would like, and is certainly impossible to extend them to imaginary colors!
One of the nice things about the Kunkel and Reinhard approach is that they start with a Neurophysiology inspired model, and fit it to the data. CIECAM02 appears to be less constrained by human feasibility, and more in the direction of arbitrary mathematical modeling. Within the gamut of the training data set, this difference isn’t of great significance, but I think the former approach is ley to getting more rational outputs near the edges or beyond the real world color boundary.
That is a really cool diagram - thanks! I tried experimenting with using GIMP’s LCh Hue-Chroma tool to see how many degrees I needed to rotate the blue layer with varying opacities of an overlaying white layer set to normal blend, to be able to say “yes, that looks like about the same hue” and sure enough the more white, the greater the required hue rotation.
Can you explain how “layers” is more of a multiply, compared to blending the two colors?
Actually for my “triad blending” experiment I sliced off chunks from the yellow, cyan, and magenta sticks and used a wooden ice cream stick to thoroughly blend the various color combinations.
Your rows go from sRGB magenta to sRGB cyan, and my magenta and cyan oil pastels surely aren’t even close to the resulting colors . But in terms of saturation, your top row is the closest.
Consider two identical grey paints. If you mix them in a bucket in any kind of ratio the resulting color is going to be identical. That’s the weighted geometric mean at work. For example, just considering one channel/wavelength; a grey paint might be 0.5; reflects 50% of light. So if you mix 1 part of this with 3 parts of an identical paint, the formula would resolve this way:
0.5^0.25 * 0.5^0.75 = 0.5 (the same)
However, if these paints were translucent (transmissive) and stacked as 2 layers, the formula would be more like
0.5 * 0.5 = 0.25. (much darker)
But changing modes like this flips the assumption of the illuminant being above the plane to behind the plane. There are a lot of problems to sort out. . . I really don’t want to make a ray tracer. . . but. . . 
@Elle here are a couple more samples from the palette you sent me. Plain spectral WGM for all 4 rows (no multiply stuff):
Below is a sample of two manual blends. The top is RGB, and the bottom is spectral. It’s a subtle difference in appearance, but what is unseen is how much easier it is to blend with the spectral model. For whatever reason, blending in RGB is more difficult; the swings between colors is much more sudden and abrupt. With the spectral model blending feels more dampened and smoothed out. It’s weird.
OK, I’m having trouble visualizing why multiply would be the correct formula for a translucent layer of paint of color 2 on top of an existing layer of paint of color 1. How translucent does color 2 need to be? Aren’t you describing “glazing”? When glazing for example translucent yellow paint (color 2) over dark green paint (color 1), is the resulting color darker or lighter than the original dark green paint?
What about mixing what MacEvoy calls “synthetic black”:
handprint : colormaking attributes and click on “black” at the top of the page, look in the notes for lamp black (PBk6 and PBk7).
When mixing the red, green, and blue oil pastels from my set of 12 Mungyo water-soluble oil pastels, the result really is “black” meaning a very dark color that anyone would look at on a white background and say “that’s black”, though after drying, or maybe just when looking under better light, it’s a dark gray.
@brien - would it be worth continuing an exploration of your spectral mixing colors compared to actual mixing of real media in a new thread over in the Digital Painting section of the forum? I’m very intrigued by how real paints actually mix to make colors, though my sample “real paints” are limited to various lines of oil pastels. For example, MacEvoy mentions somewhere that mixing yellow with black can make lovely shades of green, and by gosh he’s right, though surely “how green” and even “if green” depends on the particular black and yellow colors.
One aspect of mixing real paint is the lovely areas of “color texture” created by the “not completely blended” colors that results from applying and blending the colors on the substrate. This “textural colors” is something I’ve been experimenting with in GIMP, using things like more or less complicated gradients spanning several different colors, plus painting through a mask, and so on. But it seems to me that your spectral mixing might also allow “partial random mixing”, yes? no?
The topic came up once, a long time ago, in a different context, of using the xyY color space to create a color wheel.
Yesterday I wrote some code for babl to add conversions between XYZ and xyY, in the thought that it might be nice to add “xyY” to GIMP’s color picking tools, which would make visual exploration of things like “blue turns purple” a little more easy to do, not just for people who use command line tools like @KelSolaar 's wonderful colour-science, but also for ordinary users who are interested in color in the context of actual painting or image editing.
But then the question was “how to make a color wheel” from xyY. Obviously one can do a polar transform of the “xy” part of xyY, just as one can do a polar transform of the “ab” part of LAB or JAB to get C and h. But what would one call - how would one label - the xyY polar transform’s hue angle and square root of sum of x squared plus y squared?
Of course a prior question might be “how useful would such a wheel be in a painting/editing application”, other than for purely “what really happens” purposes, which of itself seems interesting and useful enough.
It’s a fair question.
Given the popularity of HSV interfaces, the clear answer is “quite useful”; we have to remember it is at the bottom of every UI whether we want to see it or not; it’s in every colour wheel ever used. The Abney effect is there too.
There is a an interesting side point to this which is one I’ve toiled with in attempting to deliver a “good” camera rendering transform. The question is “Where is the balance?”
If we take the Abney effect into account, we can use a contemporary JzAzBz to deliver perceptually uniform desaturation in rendering scene referred ratios to various outputs. Sadly though, grading / colorist work on such an image would then end up on the other side of the problem. Imagine trying to tweak a render of CGI / Vfx / photographic work after having run through such transforms, attempting to push or pull saturation around. Unless the JzAzBz[1] interface is built into the software (invertible, to get back to xyY), grading such an image will also result in colours losing their intention.
This is as relevant as anything given how critical desaturations are in a camera rendering transform.
[1] CIC 31 Home
A Colour Appearance Model based on Jzazbz Colour Space , Muhammad Safdar1,2,3, Jon Hardeberg1, Guihua Cui4, Youn Kim5, and Ming Luo2,6; 1Norwegian University of Science and Technology (Norway), 2Zhejiang University (China), 3COMSATS Institute of Information Tehnology (Pakistan), 4>]Wenzhou University (China), 5Huawei Technologies Co., Ltd. (China), and 6University of Leeds (UK)
OK, given that an yY color wheel is or might be interesting, that brings me back to the practical coding questions:
In case the question I’m trying to ask isn’t clear (so often apparently it isn’t ), I’m talking about what would go in the user interface, assuming GIMP or Mypaint or some other image editing program actually had an xyY color wheel. What would be the name/label in the user interface for:
Are there already standard labels and terminology for a polar transform of xyY?
I don’t think so, although given that Lab / Lch are essentially nothing more than xyY bent according to MacAdams , I wouldn’t expect there to be too much of a difference once back in the RGB encoding model in terms of visual appearances. It would amount to encoding efficiency of the circle.
I suppose you could use xyY to more quickly identify dominant wavelength and an idea of spectral purity of such a wavelength?
Are the circles themselves being managed via rolling through ICC transforms so folks on proper sRGB displays seeing D65 renderings?
OK, if there aren’t such standard labels for a polar transform of xyY I’ll just use xy hue angle and xy chroma.
Well, maybe you could. I couldn’t. I just coded up Bruce Lindbloom’s equations for XYZ<->xyY. The next step is to add code for a polar transform, and then add code to GIMP for the color picking tools.
Keep in mind that just because I write such code - if indeed I manage to get all the way through to writing code for the actual color picking tools - doesn’t mean any patch I might submit to babl and/or GIMP will actually be accepted into the code base.
GIMP is an ICC-profile color-managed editing application and the color picking tools are color-managed. What you’d see in the interface would be just what’s already there, along with an extra set of sliders in the color picking tools.
Coding up an actual panel with an xy circle similar to the HSV circle - that’s beyond my coding skills. But pie-in-the-sky speculation, wouldn’t it be nice to have a panel with xy polar transform graph atop the horseshoe with its little wavelength markers.
While it’s a bit challenging to see in the image, the left triangle is atop of the xyY plot.
Layers that are partially transparent would make the resulting color darker than if you actually mixed those two paints together I think, because the light is traveling through the material, both layers, reflecting off the base paper, and then it has to make its way back through both layers of translucent paint again. Of course there is some combination of reflection as well during all of these. The idea is some super simple version of this:
I think a new thread would be a great idea to think about some very inexpensive way to have these effects real-time without actually building a ray tracer 
So, I was so annoyed with the Abney effect (thanks @anon11264400) that I added the pigment model as the default adjuster method to my fork of mypaint. So to change brightness I just “mix in” white/black paint. And to desaturate I mix in an appropriate grey paint. I use CAM16 to determine the white, black, and grey for a particular white point and color (grey is just the brush color fully desaturated (colorfulness=0).
So if I set my overall color temperature to the warmer side, I’ll get warm tints, tones, and shades. It works pretty well really if you want a traditional painter’s workflow, and seems to largely avoid the Abney shift. I also added some statefulness; if you start with a particular color at a particular saturation, you can desaturate it all the way to grey and then re-saturate it all the way back to your starting color (but not more saturated.
If you think about it, it’s not the end points that are hard. We know colors will end up grey, white, black. . . and we know the beginning point, it’s the darn color you picked from the palette. So it’s just “the journey” from the saturated color to the desaturated that is difficult. Maybe JzAzBz would make this simpler, but then again maybe the idiosyncrasies of a pigment model is desirable as well.
I am not entirely certain why the spectral approach is avoiding Abney, unless it just so happens that your spectral upsampling ends up being right smack dab in the sweet spot of spectral widths to avoid it, as per the paper. Fascinating none-the-less.
Are the results the same with Hero Wavelength approach? Is there a sharper, narrower band approach to upsampling to test the hypothesis?
Elle: do you have access to Daniel V Thompson, Jr The practice of tempera painting? Glaze, solid, and scumble yield different effects – and which effect you will obtain depends on whether you paint a light colour (thinly!) onto a dark one, or vice versa.
Have fun!
Claes in Lund, Sweden
@briend - Would you mind starting the new thread, and maybe posting the link here?
Hmm, checking our local public library and one of the local college libraries, no. I might try interlibrary loan. Thanks! for the reference.