Why Discrimination Varies by Hue — MacAdam Ellipses and Uniform Color Spaces
MacAdam ellipses are drawn large in the green region and small in the blue region. Learn why the size of a noticeable difference on the chromaticity diagram varies from color to color, and how color spaces evolved to correct it.
When you take the test, some hue families feel easy and others feel unusually hard. Individual differences play a part, but experiments since the 1940s have confirmed that human color discrimination naturally varies across the color space.
MacAdam ellipses
In 1942, David MacAdam picked 25 colors on the CIE 1931 xy chromaticity diagram and had an observer repeatedly adjust a comparison color until it matched a reference. When he measured the spread (standard deviation) of those matches in each direction, the shape turned out to be an ellipse.
The striking finding was that the size and orientation of the ellipses varied greatly from color to color. In the green region of the diagram the ellipses were very large, while in the blue–violet region they were very small. In other words, for the same xy distance, a difference near blue is noticed right away, whereas near green the colors have to be much farther apart before anyone notices.
The ellipses in the original experiment represent the standard deviation of matching, so a just noticeable difference (JND) is several times larger; it is commonly estimated at about 3 times. The experiment was limited by having a single observer, but later experiments with many observers confirmed the same trend.
Is it the eye or the coordinate system?
The uneven MacAdam ellipses are partly a problem with the coordinate system. The xy chromaticity diagram is a set of coordinates for matching colors, not a map designed to show the size of differences. Just as Greenland looks larger than it really is on a world map, the xy diagram inflates the green region.
This led to ongoing efforts to build uniform color spaces in which distance is proportional to perceived difference. The CIE 1960 UCS, the CIE 1976 u′v′ chromaticity diagram, and CIELAB and CIELUV are the results. In these spaces the MacAdam ellipses become much closer to circles, but never perfectly so. CIE94 and CIEDE2000 correct the remaining non-uniformity with formulas.
Why differences remain even with CIEDE2000
HueSense sets every round's difference with CIEDE2000, so if the formula were perfect, accuracy should be similar across hue families. There are still several reasons it is not.
- Small-field effect: The experiments behind CIEDE2000 mostly used fairly large samples. As squares get smaller, blue–yellow discrimination drops in particular (because S cones are scarce at the center of vision).
- Individual differences: Lens aging, cone ratios and mild color vision variations change discrimination in particular directions.
- Screen differences: If a screen cannot fully reproduce a certain region of color (limited gamut) or its gamma is off, color differences in that region look smaller or larger.
- Lightness differences: Yellow is a light color that sits in the L* range where we are less sensitive to lightness differences, and neutrals can only be told apart by lightness.
If one hue family comes out weak
If your accuracy in one hue family is low, first check the sample size. If you only answered a few rounds per family, it may be chance. It is better to take the test several times and see whether the same family is also low in your all-time accuracy.
If the pattern persists, try another device. If the same family stays weak across devices, it is likely a trait of your eyes; if it changes with the device, the screen is the more likely cause. If you consistently feel much weaker on the red–green side, the reliable step is to get a standard color vision test from an eye doctor. This test is not a diagnostic tool.
References
- MacAdam, D. L. (1942). Visual sensitivities to color differences in daylight. JOSA 32(5), 247–274
- CIE 15:2004 Colorimetry, 3rd edition — CIE 1976 UCS, CIELAB, CIELUV
- Luo, M. R., Cui, G., Rigg, B. (2001). Color Research & Application 26(5), 340–350