This is an arcane question, but here's hoping.
It has been established empirically, that the luminance Y in the CIE color spaces is a function of the Munsell value V. It does not depend on hue or chroma. The function can be approximated by a 5th degree polynomial (Eq. 2 of ASTM Standard D 1535-08.)
double munV_to_cieY(const double V) {
// V is in [0,10]
// Y is in [0,100]
double Y = V*(1.1914+V*(-0.22533+V*(0.23352+V*(-0.020484+V*0.00081939))));
return Y;
}
It is the case that in the Munsell renotation data, which associates HVC triples with xyY triples, the Y in xyY is effectively multiplied by a mysterious 1.0257. I have verified that that is the case. I read somewhere, years ago, that the mystery number is due to some kind of mistake, but that is all I remember.
What was the mistake?
I want to know because I have a program that maps sRGB pixels to Munsell. Should I only use the 1.0257 when processing the renotation training data? Or should I also use it in the program per se?
Can someone tell me what's up with that 1.0257, or suggest a way to find out?
EDIT: I inverted the function, using a cubic spline. When applied to the renotation data that I have, here's what I get
V Y V'
1 1.21 1.022
2 3.126 2.031
3 6.55 3.037
4 12.00 4.046
5 19.77 5.056
6 30.03 6.064
7 43.06 7.076
8 59.1 8.085
9 78.66 9.092
I am trying to wrap my head around that.
Short answer is, the renotation Y-data are too high by a factor of 1.0257, but the quintic formula listed in the question is correct.
(The discrepancy is apparently related to the reflectance of 0.975 of magnesium dioxide, a white substance which one presumes was used somehow when analysing the color samples.)
A predecessor to the quintic above was fitted to the uncorrected renotation data. The ASTM standard contains a note to the effect that the correct quintic was obtained from the previous one by dividing the original by 1.0257 (I.e. multiplying each coefficient by 0.975.)