How Big is a MPCD Unit?

[ChthonVII]

How big is a MPCD (minimum perceptible color difference) unit?

I gather (perhaps incorrectly) that MPCD is a unit of euclidean uv distance in the CIE 1960 UCS, to a given point from the nearest point on the black body curve. But I cannot for the life of me find the definition of 1 MCPD = ??? delta uv.

[KelSolaar]

Hello,

I don't think I ever seen it defined for CIE 1960 UCS, it is not typically a space where colour differences are measured and it is almost strictly relegated to colour temperature representation.

Cheers,

Thomas

[ChthonVII]

Whitepoints for CRT televisions and monitors were often specified with a color temperature plus a MCPD offset perpendicular to the black body curve. For instance, if you owned a CRT computer monitor in the 80s or 90s, there's a good possibility that the whitepoint was 9300K + 8 MCPD.

See, for instance, pp 277-78 in Poynton's Digital Video and HD: Algorithms and Interfaces, 2nd Edition:

An illuminant may be characterized by a single colour temperature number – the temperature of a blackbody radiator that exactly matches the chromaticity of the source. If the match is approximate, the term correlated colour temperature (CCT) is used.

Colour temperature is sometimes augmented by a second number giving the closest distance in the deprecated CIE 1960 [u, v] coordinates of the colour from the blackbody locus – the arcane “minimum perceptible colour difference” (MPCD) units. I consider it more sensible to specify colour temperature in kelvin for intuitive purposes, accompanied by [x, y] or [u’, v’] chromaticity coordinates.

Unfortunately, while Poynton tells what what a MPCD is conceptually, he doesn't tell us how to do the math. Hence my question: How big is a MCPD unit?

(Incidentally, by converting the commonly cited xy coordinates for 9300K + 8MPCD and 9300K + 27MPCD to 1960 UCS uv coordinates, and dividing the distance by 19, I get something around 0.0004.)

[tjdcs]

Hi @ChthonVII

I'm not familiar with that particular liturature and old CRT stuff... But based on some other historical research I've done, I can say that during the 80s and 90s there was a pretty big wreckoning to be done about what "perceptable color difference" meant and we are still going on and on about it today.

For the purpose of binning LEDs for illumination according to CIE TN 001:2014 specifies 1 JND = ∆u'v' = 0.0013, but for matching MacAdams ellipses, ∆u'v' = 0.0011. (Thanks Tim Kang for reminding me of this reference)

There are also some derived standards from the IES.

But very vitally, in truth... you can't give any single value for duv that is 1 "step" of color difference. The uv and u'v' spaces are quite bad in terms of their perceptual uniformity and the value for one step would be smaller at higher CCT values.

This kind of standard would probably be found in some old optical society of america papers. You might try searching those journals. If you find something interesting and are willing to provide an implementation to Colour, we may be able to buy the standard (no promises at this time though)

[ChthonVII]

Thank you, tjdcs.

I'm specifically looking for the archaic MPCD units historically used in the CRT industry. I am aware that the 1960 UCS is deprecated for good reason, and that these archaic units bear a poor relationship to the actual color distinguishing abilities of human beings.

Could you please provide me with a link for the 0.0011 MacAdams ellipse size? I've found this 1986 document that says a JND is about 1/3 of a MacAdams ellipse (page 22) -- which would be 0.000366... delta-uv, which is probably within a rounding error of the 0.0004 estimate I got from taking the distance between some commonly cited coordinates in my earlier post. (Assuming that "MPCD" and "JND" are used interchangeably.)

[ChthonVII]

Some progress:

According to CIE Technical Note 001-2014, the 0.0011 value for MacAdams ellipsis is in the CIE1976 colorspace. It shouldn't be hugely different in CIE1960 though, given how CIE1960 and CIE1976 are related. It might even be the same, since 0.0011 comes from approximately fitting a circle to the ellipses, and it may fit both well enough that the CIE1960 value was just kept for CIE1976. Maybe.

Appendix 201 to VESA Flat Panel Display Measurements Standard Version 2.0 sounds like it has a definitive answer:

Besides the unit of 1960 (u, v) distance, there is another unit commonly used to quantify distance of a given light from the black-body locus. This is the minimum perceptible color difference (MPCD), defined as a distance of 0.004 (u, v) units. The value 0.004 was introduced in the early days of color television to specify a minimum perceptible difference in (u, v) under not-too-critical conditions.

The only problem here is that this is off from my estimate by a factor of ten -- It says 0.004, while I computed ~0.0004. I can think of three possibilities here:

1. Maybe it's a typo, and 0.0004 is correct. FPDM v2 cites to W.N. Sproson, Colour Science in Television and Display Systems , Adam-Hilger, 1983, page 42 for this figure. I'd like to check that reference, but I can't find a digital copy of this book anywhere.
2. Maybe the commonly cited x,y coordinates for "9300K+8mpcd" and "9300K+27mpcd" are really, really wrong in some way that makes them not 19mcpd apart. ("9300K+8mpcd is usually cited to 3 digits as 0.283, 0.298. Sometimes it's cited to 4 digits, but the 4-digit values vary a little. "9300K+27pmcd" is always cited to 3 digits as 0.281, 0.311.)
3. Maybe I botched typing the dead simple xy to uv conversion into libreoffice. Twice.

The MPCD/JND relationship doesn't make a lot of sense either way. In one case a MPCD is ~4 JND; in the other a MPCD is ~1/3 JNA.

[Edit: I just finally had the good sense to try running the math the other direction. If I take the x,y coordinates for "9300K + 27mpcd," convert them to u,v, move 27 * 0.004 in the +u,-v direction (which is vaguely close to the -MCPD direction), then convert back to x,y, the result is a purple color way the hell off the plankian locus. If I change it to 0.0004, I pretty much hit the plankian locus. At this point, I'm pretty sure it's got to be 0.0004. 0.004 is just too big.]

[ChthonVII]

And it turns out that sometimes MPCD was defined in the Judd UCS and not the CIE1960 UCS. (Source) Fuck me!

Google translate of the relevant section:

The Electronics and Mechanical Engineering Association requested that the white standard to be fabricated here have chromaticity coordinates x = 0.281, y = 0.311 (color temperature 9300°K + 27 MPCD) and have the characteristics of a luminance standard for color picture tubes. The chromaticity coordinates are specified on the Uniform Chromaticity Scale (UCS) of Judd3) (where C2 = 1.4380) so that the deviation from the blackbody radiation locus is +27 MPCD at a color temperature of 9300°K. The color temperature of a light source is defined as the temperature of the black body radiator that is closest to the chromaticity coordinates of the light source, considering the locus of the black body radiator at 9300°K on the UCS chromaticity diagram. Therefore, if the chromaticity diagram is different, for example on the 1960 CIEUCS chromaticity diagram10), the color temperature and MPCD of the light source will also be different. However, in accordance with the US standard JEDEC4), the design is carried out with this chromaticity coordinate as the target value. It was decided to carry out the following.

Edit: Found that definition rather fast! A Judd MPCD is 0.0005 Judd UCS units. Source. Now I just need to figure out (1) how to convert to/from Judd UCS, and (2) how to tell whether an author meant Judd MPCD or CIE1960 MPCD when they say "MPCD."

[KelSolaar]

If you find the formula, let us know, we can roll them in Colour with a reference to MPCD alongside.

[ChthonVII]

I believe I have it figured out.

Summary:

"Minimum perceptible color difference" or "MPCD" is a unit of distance in an obsolete uniform color space in a direction perpendicular to the Plankian (blackbody) locus at a given point. The positive MPCD direction goes away from the Plankian locus on the convex side, generally towards green. See [1], [2], and [3]. There are two different units named "MPCD." The more common, and more recent, usage is 0.0004 delta-uv in the CIE1960 Uniform Color Space. See [1] and [2]. The older, nearly forgotten usage is 0.0005 delta-uv in the Judd1935 Uniform Color Scale (or, rather, to be precise, in MacAdam's xy-to-uv transformation that is (nearly) equivalent to Judd's UCS). See [3] and [4]. I'm going to call these "CIE MPCDs" and "Judd MPCDs."

About CIE MPCDs:

The equations to convert from CIE1931 xy coordinates to CIE1960 UCS and back again are simple, well-known, and already implemented in Colour.

• u = 4x / (12y - 2x + 3)
• v = 6y / (12y - 2x + 3)
• x = 3u / (2u - 8v +4)
• y = 2v / (2u - 8v +4)

VESA FPDM ([1]) says that a MPCD is defined as 0.004 delta-uv. However, I am 99.9% certain that this must be a typo and that 0.0004 is the correct value. A value of 0.004 is simply too big to be correct. A shift of 0.004 delta-uv results in a flagrantly obvious color difference, rather than a minimally perceptible one, and shifting by a small multiple of 0.004 flies far across the chromaticity diagram. By contrast, 0.0004 gives very plausible results. See below.

About Judd MPCDs:

My conclusion here required more historical guesswork. We have two sources that mention MPCD in the Judd UCS, [3] and [4]. Both of these cite to [5]. However, [5] describes a trilinear coordinate space rather than a Cartesian one. (And the trilinear distance from 9300K to x = 0.281, y = 0.311 is nowhere near 27 * 0.0005, as [3] and [4], taken together, tell us it should be.) The inquiry is complicated here by the fact that there are three competing conversions from Judd's UCS to Cartesian coordinates, and it's not clear which one [3] and [4] are assuming (or even if they're assuming the same one).

1. Judd gave us a simple transformation in the appendix to [5]: x = (2b + g) / sqrt3; y = g, where b and g are two of the trilinear coordinates.
2. The xy-to-uv transformation provided in [6] that is equivalent to the Judd UCS. (However, I suspect that this equation was well known prior to 1944. Rather than an article on new research, [6] is a preview of a committee report chapter summarizing techniques that seem to have been well known in the field at the time. MacAdam explained the math behind [6] in [7] back in 1937. However, for his example in [7], he used a simplified version that latter became the CIE1960 UCS rather than the more complex equations shown in [6]. According to [8], Judd and MacAdam were both on the committee listed as the author of [6].)
3. A different xy-to-uv transformation, equivalent to the Judd UCS, provided in [9]. Also based on the math in [7].

I am reasonably certain that [3] and [4] were assuming the xy-to-uv transformation provided in [6], for the following reasons:

• Taken together, [3] and [4] tell us that the delta-uv distance from 9300K on the Plankian locus to x = 0.281, y = 0.311 should be 27 * 0.0005. Using the xy-to-uv transformation provided in [6] comes plausibly close to that (27 * ~0.00051), and slightly closer than the other possibilities.
• As noted above, [6] is a preview of a committee report chapter summarizing techniques that seem to have been well known in the field at the time, suggesting wide adoption.
• Latter-day sources, like wikipedia, conflate the xy-to-uv transformation provided in [6] with the Judd UCS, suggesting wide adoption. Also, if the wikipedia authors conflate [6] with [5], maybe the authors of [3] and [4] did too.
• The xy-to-uv transformation in [9] was dubbed "RUCS" by its authors. If the authors of [3] and [4] were using RUCS, presumably they would have called it by name.

The CIE1931 xy to uv equations in [6] are:

a = 0.4661;
b = 0.1593;
c = -0.15735;
d = 0.2424;
e = 0.6581;
u = (ax + by) / (y + cx +d)
v= ey / (y + cx +d)

The reverse transform is not provided in [6]. Solving by substitution, I get:

a = 0.4661;
b = 0.1593;
c = -0.15735;
d = 0.2424;
e = 0.6581;
y = dv / (e - v - ((c * (eu - bv)) / a))
x = y * ((eu - bv) / av)

These are ugly, and I hope someone with better algebra skills than I can simplify them into something prettier.

[3] tells us clearly that a Judd MPCD is 0.0005 units. (The hard question was, " In which Cartesian equivalent of the Judd UCS?")

Test Results

I implemented a C++ version of the foregoing in a project of mine. It gives the following results:

• For 9300K + 8 CIE MPCD, I get x=0.283013, y=0.297166. This is remarkably close to x=0.2831, y=0.2971 stated in [10].
• For 9300K + 8 Judd MPCD, I get x=0.283752, y=0.298031. This is reasonably close to x=0.2838, y=0.2984 stated in [11].
• The slight difference between CIE and Judd MPCD units probably accounts for the conflict between [10] and [11]. The authors were using different units!
• For 9300 + 27 Judd MPCD, I get x=0.281103, y=0.309955. This is reasonably close to x=0.281, y=0.311 stated in [4].

I believe the small differences between my results and the coordinates stated in the literature can be attributed to authors of these papers, working in the 1970s, relying on tables of rounded/truncated values for their calculations, whereas I today have a digital computer that uses 64 bits to represent each floating point value.

Sources

1. Charles Poynton, Digital Video and HD: Algorithms and Interfaces, 2nd Edition, pp. 277-78.
2. VESA Flat Panel Display Measurements Standard Version 2.0, Appendix 201.
3. B. R. Canty & G. P. Kirkpatrick, Color Temperature Diagram, J. Opt. Soc. Am., Vol. 51, No. 10, p. 1130 (Oct. 1961).
4. Yoshinobu Nayatani, Shoichi Hitani, Kyosuke Furukawa, Yutaka Kurioka and Isamu Ueda, Development of the White-Standard Apparatus for Color Cathode-ray Tubes , Television, Vol. 24, No. 2, p. 116 (1970). Machine translation of the relevant passage:

The Electronics and Mechanical Engineering Association requested that the white standard to be fabricated here have chromaticity coordinates x = 0.281, y = 0.311 (color temperature 9300°K + 27 MPCD) and have the characteristics of a luminance standard for color picture tubes. The chromaticity coordinates are specified on the Uniform Chromaticity Scale (UCS) of Judd) (where C2 = 1.4380) so that the deviation from the blackbody radiation locus is +27 MPCD at a color temperature of 9300°K. The color temperature of a light source is defined as the temperature of the black body radiator that is closest to the chromaticity coordinates of the light source, considering the locus of the black body radiator at 9300°K on the UCS chromaticity diagram. Therefore, if the chromaticity diagram is different, for example on the 1960 CIEUCS chromaticity diagram10), the color temperature and MPCD of the light source will also be different. However, in accordance with the US standard JEDEC4), the design is carried out with this chromaticity coordinate as the target value. It was decided to carry out the following.

5. Deane B. Judd, A Maxwell Triangle Yielding Uniform Chromaticity Scales, J. Opt. Soc. Am., Vol. 25, p. 24 (Jan 1935).
6. Committee on Colorimetry, Quantitative Data and Methods for Colorimetry, J. Opt. Soc. Am., Vol. 34, No. 11, p. 633 (Nov. 1944).
7. David L. MacAdam, Projective Transformations of I. C. I. Color Specifications, J. Opt. Soc. Am., Vol. 27, p. 294 (Aug 1937).
8. Sean F. Johnson, The Construction of Colorimetry by Committee, Science in Context, Vol. 9, No. 4, p. 387 (1996).
9. F. C. Breckenridge & W. R. Schaub, Rectangular Uniform-Chromaticity-Scale Coordinates, J. Opt. Soc. Am., Vol. 29, p. 370 (Sep 1939).
10. Yoshitomi Nagaoka, On the Color Reproduction and Reference White of Color Television, Journal of the Television Society, Vol. 33, No. 12, p. 1013 (1979).
11. Shigeru Yagishita, Kenji Nishino, Katsuhiro Ohta, and Takashi Ishii, Color Picture Tube with Built in Reference White for Color Master Monitors), Television, Vol. 31, No. 11, p. 883 (1977).