Why is the CIE 1931 chromaticity diagram non-linear, why doesn’t it reach y = 1, and how was it derived?
Asked 8/15/2014
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I’m trying to understand the CIE 1931 chromaticity diagram and how it relates to human color vision.
I know the diagram is used to plot chromaticity and compare color spaces/gamuts, and that human vision does not distinguish all colors equally. What confuses me is:
- Why is the chromaticity diagram non-linear?
- Why is the highest plotted y value around 0.84 instead of reaching y = 1?
- How was the CIE 1931 diagram originally derived from experimental data?
I’m looking for a conceptual explanation of how the x,y values come from the CIE XYZ system and why the spectral locus has that shape.
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
11y ago
2 Answers
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Why is this diagram non linear?
The CIE Chromatic diagram is a transformed 2D map of the CIE standard observer color matching functions. Because the human eye responds in a non-linear way to to different ranges of wavelengths, and the transformation does not compensate for that, the Yxy diagram isn't linear either.
http://en.wikipedia.org/wiki/CIE_1931_color_space#Color_matching_functions http://hyperphysics.phy-astr.gsu.edu/hbase/vision/cie.html http://dba.med.sc.edu/price/irf/Adobe_tg/models/ciexyz.html
Why is the highest y value 0.84 and not just at y = 1.0?
The y value is calculated according to this formula:
When measuring 520nm at the standard observer color match chart, one can see that
- X = ~0.08
- Y = ~0.69
- Z = ~0.08
Thus, y = (0.69/(0.08+0.69+0.08)) = ~0.81
How was the CIE Chromatic Diagram "derived"?
That's the hardest part: First the CIE RGB Model is transformed to the CIE XYZ Model, distorting the color space. Then a "slice" through the color space (X+Y+Z=1) is calculated, and finally that slice is projected to the base surface so that Z does not change it (Z is basically Y).
One rather good explanation is Page 8 of "CIE Color Space" by Gernot Hoffmann
Originally by user25816. Source · Licensed CC BY-SA 4.0
user25816
11y ago
0
Generated from our catalog & community — verify before relying on it.
The CIE 1931 chromaticity diagram is a 2D projection of the CIE XYZ color space, based on standard-observer color-matching experiments. It is not “linear” in the everyday sense because it comes from human visual response data and a coordinate transform, not from wavelength plotted directly on evenly spaced axes.
The chromaticity coordinates are normalized as:
x = X / (X + Y + Z) y = Y / (X + Y + Z)
Since x and y are ratios of the tristimulus values, their maximum values depend on the measured X, Y, and Z responses at each wavelength. There is no reason for the spectral locus to reach y = 1; that would require X and Z to be zero while Y remained nonzero. For wavelengths near green, Y is large, but X and Z are still not zero, so y peaks below 1 (around 0.8–0.84).
The diagram was derived from experimental color-matching data gathered by early researchers such as Wright and Guild, then processed into the CIE 1931 standard observer and transformed into RGB and XYZ-based chromaticity coordinates. In short, the shape comes from measured human vision data plus the normalization used to map it into x,y space.
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