While checking some out-of-gamut tones on an xy Chromaticity Diagram I started to wonder how far two tones needed to be in order for an observer to notice a difference.  Were the tones in the yellow and red clusters below discernible or would they be indistinguishable, all being perceived as the same ‘color’?

Jumping the gun, here is the result of my investigation: a just noticeable difference for each of the 24 tones of a ColorChecker 24.  Details in the rest of the article.

MacAdam Ellipses

I knew about the ellipses that David MacAdam drew experimentally in the forties^[1].  Each ellipse indicates a range of colors at a luminance of 48 cd/m^2 that were deemed to be indistinguishable from the color in the center by his human subjects.

Not knowing the luminance of the brightest diffuse white does not tell us much about the level of adaptation of the subjects, so we do not know whether these results refer to what photographers would consider highlights, midtones or shadows.  In addition the ellipses are rather sparse and do not cover some areas of the diagram that I was interested in.

deltaE 2000 Ellipses

With the help of excellent toolkit OptProp^[2] I therefore let Matlab loose on a larger number of sample chromaticities using as the criterion of indistinguishability one unit of CIEDE2000^[3], which is said to represent a just noticeable color difference.  Since deltaE2000 varies with luminance (let’s call it Y in this post) I worked a number of examples varying Y.  Here is the result assuming a mid-tone Y value of 18 on a scale of zero to one hundred (click on it to see it full screen):

The black ellipses represent a less than 1 dE2000 change from the chromaticity at their center.  The white dashed line is Adobe RGB while the solid line is Rec. 2020, the largest-yet-still-inexistent monitor color space we are likely to be able to feast our eyes upon for the next few years.

Interestingly, it seems that in this case a just noticeable difference of 1 deltaE2000 is more stringent than what MacAdam’s human observers suggested for indistinguishable color change.   [Edit: Adam in the comments below mentions that MacAdam’s ellipses were plotted at 10x their measured size.  Aha, thanks Adam!]  I don’t know why there is a line of ellipses that looks like chromosomes, probably something to do with the peculiarities of the dE2000 formula.

While I was at it I also produced a version with u’v’ chromaticities, whose diagram is supposed to be more perceptually uniform (click on it to see it full screen):

This diagram appears indeed to produce ellipses whose sizes vary less extremely than in the previous one – but they obviously are still a long way from being truly uniform.

Lowering Y to 5, typical of lower mid-tones, produces slightly larger ellipses but still nowhere near the size seen in MacAdams’ picture:

They do get much larger in the shadows, so perhaps that is a hint as to the state of adaptation of MacAdam’s human subjects.   Here is a Y of 1,  6.6 stops below full scale:

Going the other way the ellipses get smaller but at slower pace and this makes sense of course given the logarithmic nature of dE2000, which is based on our response to brightness.  Here for instance is Y at 95, where the ellipses are a bit smaller than at a Y of 18:

Finally, these are 1 dE2000 ellipses for the ColorChecker 24, every ellipse refers to the Y level of the relative sample.  Keep in mind that what counts for such a just noticeable difference is the radius of the ellipse, not its area or diameter.

So there you go: when looking at a chromaticity diagram we can now relate 1 dE00 JND to a given chromaticity based on relative luminance.  And it seems that the chromaticities in the yellow and red clusters in Figure 1 should indeed be distinguishable, at least in the mid-tones.

Notes and References

<sub>1. See here for the wikipedia article on MacAdam ellipses.
2. You can find OptProp – A Color Properties Toolbox here.
3. CIEDE2000 is a modern measure of color difference, you find its definition here.</sub>