Color Theory: How to convert Munsell HVC to RGB/HSB/HSL
The hue specification you've given here is incomplete (4.5 should be 4.5Y etc). Since the link is dead, if anyone is interested, the specs are still alive here: http://web.archive.org/web/20071103065312/http://lib.umich.edu/dentlib/Dental_tables/Colorshadguid.html
The only free utility for Munsell conversion I could find was this:
http://web.archive.org/web/20020809130910/standards.gretagmacbeth.com/cmc/munsell.exe
Very old as you can see, but seems to work well. Current programs that can do this are not free:
- http://livingstonmanor.net/Munsell2/index.htm
- http://www.babelcolor.com/main_level/download.htm (this one has a free 14 day trial)
The current holders of the Munsell products are X-Rite, they probably have some conversion solutions as well.
Further, note that the link you supplied includes definitions for the same colors in other color coordinates - namely Yxy and CIE lab*. Both can be freely converted online at http://www.colorpro.com/info/tools/convert.htm or offline with this free color converter
Munsell Renotation System to sRGB Colourspace Conversion
Colour, our open source Python colour science package allows to perform that conversion.
From Munsell Renotation System to CIE xyY Colourspace
The following two definitions based on Centore (2012) method converts between Munsell Renotation System and CIE xyY colourspace:
- munsell_colour_to_xyY
- xyY_to_munsell_colour
From CIE xyY Colourspace to sRGB Colourspace
Converting from CIE xyY colourspace to sRGB colourspace is done by first converting to CIE XYZ tristimulus values and then to sRGB colourspace using the following definitions:
- xyY_to_XYZ
- XYZ_to_sRGB
Implementation
Here is an annotated complete example using the above definitions:
import colour
# The *Munsell Renotation System* colour we would like to convert
# to *sRGB* colourspace.
MRS_c = '4.2YR 8.1/5.3'
# The first step is to convert the *MRS* colour to *CIE xyY*
# colourspace.
xyY = colour.munsell_colour_to_xyY(MRS_c)
# We then perform conversion to *CIE xyY* tristimulus values.
XYZ = colour.xyY_to_XYZ(xyY)
# The last step will involve using the *Munsell Renotation System*
# illuminant which is *CIE Illuminant C*:
# http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/colorimetry/illuminants.ipynb#CIE-Illuminant-C
# It is necessary in order to ensure white stays white when
# converting to *sRGB* colourspace and its different whitepoint
# (*CIE Standard Illuminant D65*) by performing chromatic
# adaptation between the two different illuminant.
C = colour.ILLUMINANTS['CIE 1931 2 Degree Standard Observer']['C']
RGB = colour.XYZ_to_sRGB(XYZ, C)
print(RGB)
[ 0.96820063 0.74966853 0.60617991]
You can also perform the reverse conversion from sRGB colourspace to Munsell Renotation System:
import colour
C = colour.ILLUMINANTS['CIE 1931 2 Degree Standard Observer']['C']
RGB = (0.96820063, 0.74966853, 0.60617991)
print(colour.xyY_to_munsell_colour(colour.XYZ_to_xyY(colour.sRGB_to_XYZ(RGB, C))))
4.2YR 8.1/5.3
References
- Centore, P. (2012). An open-source inversion algorithm for the Munsell renotation. Color Research & Application, 37(6), 455–464. doi:10.1002/col.20715
It is rather involved. The short answer is, converting Munsell codes into RGB involves interpolation of empirical data in 3D that is highly non-linear. The only data set that is publicly available was collected in the 1930's. Free or inexpensive programs that I have found on the net have proved to be flawed. I wrote my own. But I am jumping ahead. Let's start with the basics.
Munsell codes are different in kind than those other codes, xyY, Lab, and RGB. Munsell notation describes the color of an object - what people experience when they view the object. (Isaac Newton was the first to realize that color is in the eye of the beholder.) Munsell conducted extensive experiments with human subjects and ingenious devices.
The other codes, i.e. xyY, Lab*, and RGB, describe light that has bounced off an object and passed through a convolultion with a rather simple mathematical model of a human eye. Some google-terms are "illuminant," "tri-stimulus," and "CIE standard observer."
Munsell describes the colors of objects as they are perceived under a wide variety of illuminants. Another google-term is "chromatic adaptation." Chromatic adaptation in the brain is automatic if the lighting is not too weird. It is really quite remarkable. Take a piece of typing paper outside under a blue sky. The paper looks white. Take it indoors and look at it under incandescent (yellowish) lights. It still looks white! Munsell tapped into that astonishing processing power empirically. Munsell codes also preserve perceived hue at different chromas. A sky-blue and a powder-blue that Munsell assigns the same hue notation, e.g. 5RP, will appear to the typical human with normal eyesight to be the same hue. More on that in the footnote.
CIE xyY, Lab*, and RGB mean nothing unless an illuminant is specified. Chromatic adaptation for illuminants in the mathematical model is computationally difficult. (Rough but simple approximations can be done using the "Bradford matrices.") The RGB that we use is by default "sRGB," which specifies an illuminant called D65. D65 is something like a cloudless day at noon. The Lab numbers listed by the OP are probably relative to D50, which is more like afternoon or morning light. The xyY numbers might be relative to D50, or they might be relative to an old standard called C. I am not going to check. C was the light from a standard lighting fixture that was relatively inexpensive to build in the 1930's. It is obsolete. But C plays a key role in the answer to the question.
In the 1930's, color scientists were developing the mathematical models. One of the things they did was to take a standard Munsell Book of Color, shine illuminant-C light on the colored chips in the book, and record the data in xyY format. That data-set, called the "Munsell Renotation Data," is the only one that is freely available. Others surely exist, but they are closely held secrets.
Good news though. The data set works good. The Munsell authority today is a company called Gretag Macbeth. I imagine they have voluminous data related to the color-chips they sell. The only numbers I know of that they publish are the D50 Lab and D65 sRGB numbers for a small set of colors on their "Color Checker" cards. I wrote an interpolator based on the old renotation data. It agrees with the numbers for the Color Checker card almost exactly. I regret to inform that so far I have only written code for the conversion that goes the opposite direction from what the OP requested (a year ago, as I type this). It goes from sRGB to Munsell. I click on an image, and the program displays the sRGB and Munsell notations for the area clicked upon. I use it for oil painting.
Footnote: CIE has a standard that is analogous to Munsell. It is called LCh subscripted with a,b. It is Lab* in polar coordinates. The hues are in degrees. Chroma numbers are approximately 5 times the C in Munsell HVC. LCh has its problems though. If you have ever used a photo editor to pump up the vividness of the sky, only to see the blue turn to purple, the program was probably using LCh. When I started writing my program, I was unaware that Bruce Lindloom had done work that parallels what I was doing. His web site was invaluable to me as I finished the project. He designed a space he calls UPLab, which is LCh straightened out to align with Munsell. I had already re-invented LCh and (essentially) UPLab before I discovered Mr. Linbloom's site, but his knowledge of the subject far exceeds mine.
For completeness, here's the archive.org version of my page, that contains the colors in 3 colorspaces, Munsell, Yxy and Lab:
Vita shade-guide colors
_________________________________________________________________
Munsell Chromaticity
notation coordinates CIE L* a* b*
(ref 151) (ref 152) (ref 151)
_____________ _____________________ ___________________
Shade H V C Y x y L* a* b*
_________________________________________________________________
A1 4.5Y 7.80/1.7 55.92 0.3352 0.3459 79.57 -1.61 13.05
A2 2.4Y 7.45/2.3 49.95 0.3468 0.3539 76.04 -0.08 16.73
A3 1.3Y 7.40/2.9 48.85 0.3559 0.3593 75.36 1.36 19.61
A3.5 1.6Y 7.05/3.2 44.12 0.3627 0.3657 72.31 1.48 21.81
A4 1.6Y 6.70/3.1 38.74 0.3633 0.3658 68.56 1.58 21.00
B1 5.1Y 7.75/1.6 54.76 0.3336 0.3447 78.90 -1.76 12.33
B2 4.3Y 7.50/2.2 50.97 0.3437 0.3549 76.66 -1.62 16.62
B3 2.3Y 7.25/3.2 46.91 0.3611 0.3669 74.13 0.47 22.34
B4 2.4Y 7.00/3.2 43.38 0.3620 0.3678 71.81 0.50 22.15
C1 4.3Y 7.30/1.6 47.16 0.3361 0.3462 74.21 -1.26 12.56
C2 2.8Y 6.95/2.3 42.12 0.3487 0.3563 70.95 -0.22 16.72
C3 2.6Y 6.70/2.3 39.11 0.3499 0.3569 68.83 -0.01 16.68
C4 1.6Y 6.30/2.7 33.77 0.3600 0.3622 64.78 1.59 18.66
D2 3.0Y 7.35/1.8 48.71 0.3391 0.3473 75.27 -0.54 13.47
D3 1.8Y 7.10/2.3 44.48 0.3482 0.3534 72.55 0.62 16.14
D4 3.7Y 7.05/2.4 43.45 0.3492 0.3591 71.86 -1.03 17.77
_________________________________________________________________
H hue
V value
C chroma
Y lightness
x and y hue and chroma
L* lightness
a* hue and chroma on a red/green scale
b* hue and chroma on a yellow/blue scale
References
- 151 O'Brien, W.J., Groh, C.L., and Boenke, K.M. A new, small- color-difference equation for dental shades. J.Dent. Res. 69:1762-1764, 1990.
- 152 O'Brien, W.J., Groh, C.L., and Boenke, K.M. Unpublished data. University of Michigan School of Dentistry, Ann Arbor.