Talk:Color difference

delta h in CIE 1994
In the CIE 1994 formula for delta_H_star_ab, shouldn't the last term read delta_C_star_ab rather than delta_C_star?

Gggustafson (talk) 16:20, 16 August 2011 (UTC)

In the proposed formulation, S_C and S_H depends only frome the first color, with the result that the distance of the first color from the second is not equal to the distance of the second color from the first, violating one of the most basic properties of any metric. Is there someone with acces to the actual CIE1994 standard document that could confirm? — Preceding unsigned comment added by 195.223.18.94 (talk) 13:29, 24 January 2020 (UTC)

delta h
In color difference 94, isn't the "h1 - h2" term adjusted so it is not greater than pi? h is an angle, if this is really using LCh coordinates. But I've seen other formulas that seem to calculate a dH term from a, b and C. I'm unsure about the accuracy of this section of the article now. DonPMitchell (talk) 16:17, 9 July 2009 (UTC)

I agree, the formula initially posted was wrong. We must use a delta H* that represents the difference in hue as an euclidian distance. Furthermore the original author posted a formula different from the one in the two references cited. I corrected this and added a reference to the best source possible, the CIE draft standard. SMandon (talk) 10:38, 23 March 2011 (UTC)

missing stars?
In the CIEDE2000 section, it looks like a1, a2, b1, and b2 are missing stars, but I'm not familiar enough with this stuff to say for sure. If they're not missing stars then it should be clarified what a1, a2, b1, and b2 are supposed to be. Hixie (talk) 06:28, 11 April 2011 (UTC)


 * You are right, the asterisks were missing (see ref #12), now added. Note that Bruce Lindbloom (ref #13) does not use the asterisks but naked 'a' and 'b'.--SiriusB (talk) 16:56, 20 January 2013 (UTC)

∆H' in the CIEDE2000 equation
In the initial square root of the sum of the squares formula, it references ∆H', but the following equations only reference ∆H'bar and ∆h'. I think it is referring to ∆h', but am not certain. These equations should be case sensitive, so could someone with more precise knowledge verify and correct the formula? PJV (talk) 17:30, 11 May 2011 (UTC)

I found in the references that the ∆H' must have been left out, it should be added:


 * $$\Delta H' = 2 \sqrt{C'_1C'_2}sin(\Delta h'/2)$$

(this is from http://www.brucelindbloom.com/index.html?Eqn_DeltaE_CIE2000.html, a reference of the article section)

PJV (talk) 19:18, 11 May 2011 (UTC)

I just looked over this comment again and the simpler way to say it is: $$\Delta \bar{H}'$$ should be changed to $$\Delta H'$$. Nothing refers to $$\Delta \bar{H}'$$, only $$\bar{H}'$$, and $$\Delta H'$$ is referenced but not defined. I'll change it soon if no one corrects me PJV (talk) 23:26, 15 November 2011 (UTC)


 * Yup, you’re right, $$\Delta \bar{H}^\prime$$ should be just $$\Delta H^\prime$$. Looks like just a typo. –jacobolus (t) 03:06, 16 November 2011 (UTC)

Similarly, I notice that the $$\bar{H}^\prime$$ and $$\Delta h^\prime$$ equations do not match the referenced source formulation, and I am unable to show that the posted equations are mathematically equivalent formulations.KlappCK (talk) 20:37, 24 March 2014 (UTC)

Degrees or radians?
I am having problems understanding from the article whether $$\bar{H}'$$ is in degrees or radians (For CIEDE2000)

This part seems to imply it is degrees, $$R_T = -2 \sqrt{\frac{\bar{C}'^7}{\bar{C}'^7+25^7}} \sin \left[ \frac{\pi}{6} \exp \left( -\left[ \frac{\bar{H}'-275^\circ}{25} \right]^2 \right) \right]$$

But at the same time this part seems to (as far as I can tell) imply it is radians. $$ T = 1 - 0.17 \cos ( \bar{H}^\prime - \pi/6 ) + 0.24 \cos (2\bar{H}^\prime) + 0.32 \cos (3\bar{H}^\prime + \pi/30 ) - 0.20 \cos (4\bar{H}^\prime - 21 \pi/60) $$ Would it be possible for someone with more knowledge about this to clarify ? 109.189.51.196 (talk) 13:38, 29 December 2011 (UTC)


 * How important is it that it is degrees? Would converting everything to radians (taking care to make them in the range [0, 2pi] where appropriate, as is suggested for degrees currently) give an equivalent result? Most intrinsic functions seem to use radians rather than degrees, and it seems weird to go through degrees for the sake of it. NeruYume (talk) 01:31, 2 November 2012 (UTC)


 * Sadly, colorists use degrees rather than radians; its easy to add or subtract 360; 2&pi; not so much. The color difference definition and secondary sources use degrees, so this article should use degrees. WP is not a how-to guide. An earlier version of this article used radians (see above), but then stopped with the expression for RT (presumably due to the argument for the exponential; the specification used 25 instead of 25&deg; in the denominator; I made the degrees explicit). One may certainly rewrite the equations to use radians, but any software implementation should be tested against published values to make sure the implementation is correct. Many test cases are designed to trip up naive implementations. I don't see the radian-degree conversions as a big deal - a few extra multiplications that can be hidden using macros/functions such as  instead of  . Instead of using   directly, stick it in a function that not only does the degree conversion, but also checks for the degenerate case and returns 0 to 360&deg;; turns out that function is needed for some colorspace conversions anyway. The problem with not doing the conversions is the risk of messing up somewhere; if somebody sees a variable , then they may assume it is in degrees. Glrx (talk) 02:13, 4 November 2012 (UTC)

I do not understand this note: The formulae below should use degrees rather than radians; the issue is significant for RT. Can someone in the know just edit the section to make that note redundant, then remove it? — Preceding unsigned comment added by 2602:306:3398:dd10:793a:8ae4:aae9:d23c  (talk) 16 October 2017 (UTC)

Delta E and CIE76 sections omit CIELUV & others
These sections omit mention of CIELUV and the associated formulae, creating the false impression that CIELAB was the first and only CIE-sanctioned color space for calculating color differences in terms of Euclidean distance, circa 1976.

It also overlooks the many CIELUV/CIELAB predecessors and subsequent alternatives (e.g., Wandell's S-CIELAB). It should at least be mentioned that there are other color-difference measures and the entry restricts attention to the CIE-sanctioned ones.

Therealdp (talk) 14:04, 4 September 2013 (UTC)


 * Worse, I feel is that it omits any discussion of computability and the various approximations. If somebody came to the site and wanted to know about color differences they would be asked to implement a bunch of very cryptic formulae rather than noting the actual fairly good approximations or device dependent descriptions. Tat (talk) 15:22, 22 January 2017 (UTC)

I have problems with DE* ~ 2.3 for JND. I feel that this is a bad interpretation of the original article by Mahy et al. (Color Res. Appl. 1994, 19(2), 105). Table II of said article denotes the average ellipse radius, Řch, as 2.3 for CIELAB perceptibility/acceptability data of surface colors. The average eccentricity, Ēch, for this is 2.2 and 2.1 for perceptibility/acceptability for the same color system. The article clearly says: "The average radius over all the ellipses Řch on the other hand gives the average relation between a distance unit in the chromatic plane and a JND." This would imply that 1JND = Rch x DE*--> DE* = 0.43 for 1JND. For DE94(1,1,1) Rch = 1.0 which would put DE94 = 1.0 for 1JND. This correlates well with visual color discrimination done by various individuals in our laboratories. — Preceding unsigned comment added by 150.251.3.1 (talk) 17:39, 25 July 2018 (UTC)

a* in CIEDE2000
What is the variable a* in the CIEDE2000 formula? The a* in LAB? Thus, the formula needs both LAB and LCH (not that that is a problem since you get one from the other)? — Preceding unsigned comment added by 173.228.4.22 (talk) 20:18, 19 November 2015 (UTC)

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Non-sanctioned nomenclature is not encyclopedic
Using notation not sanctioned by the CIE for a CIE Total Color Difference is not encyclopedic. With respect to the Mahy study, a proper reference is needed, and exactly what color difference he used must be specified. Otherwise, that section of text may be deleted as not properly referenced. Lovibond (talk) 21:58, 29 September 2017 (UTC)
 * You changed the meaning of the text. Glrx (talk) 19:36, 5 October 2017 (UTC)
 * The paragraph does not have a proper reference; a name (last name only, but the author is known to me) and a year do not constitute an acceptable citation. I cannot check whether the text is supported by a reliable reference. Please provide a proper citation, and explain what color difference is being referred to by Mahy. Until such time, the paragraph is deleted for lack of a reliable reference. Lovibond (talk) 15:25, 6 October 2017 (UTC)
 * Your edit did not remove the Mahy reference, so that is clearly not the issue. You edit did modify Mahy's JND finding, something that you still fail to recognize. Glrx (talk) 17:10, 12 October 2017 (UTC)

RGB Color weighting
RGB weights are for use with linear values. Since linear light isn't perceived linear then simple weights - as explained - is naive. If weighting that factors gamma was intended then the explanation for why it doesn't work is misleading or at least incomplete. If not, then the whole discussion of RGB component weighting needs to be rethought. — Preceding unsigned comment added by David Billen (talk • contribs) 23:01, 31 October 2017 (UTC)

Best color difference function
The best color difference function is Manhattan distance of R, G and B, weighted by 0.299, 0.587 and 0.114 respectively.

$$\text { rederror} \times 0.299 +\text { greenerror} \times 0.587 +\text { blueerror} \times 0.114$$

155.230.90.52 (talk) 09:34, 21 April 2018 (UTC)


 * Actually no, what you gotta do is convert sRGB to linear RGB, then use this formula

$$\text { lineardifference} = \text { rederror} \times 0.212671 +\text { greenerror} \times 0.715160 +\text { blueerror} \times 0.072169$$

then

$$\text { linearbrightness1} = \text { red1} \times 0.212671 +\text { green1} \times 0.715160 +\text { blue1} \times 0.072169$$ $$\text { linearbrightness2} = \text { red2} \times 0.212671 +\text { green2} \times 0.715160 +\text { blue2} \times 0.072169$$

then convert linearbrightness1 and linearbrightness2 to produce 2 new variables sRGBbrightness1 and sRGBbrightness2 then the final difference is:

$$\text { difference} = \text { lineardifference} \times (( \text { sRGBbrightness2} - \text { sRGBbrightness1} )\div( \text { linearbrightness2} - \text { linearbrightness1} )) $$

or, if linearbrightness1 and linearbrightness2 are the same, use the derivative of sRGB instead:

$$\text { difference} = \text { lineardifference} \times ( \text { derivativeof} ( \text { sRGBbrightness1} ) ) $$

2A01:119F:21D:7900:503A:C616:B438:9F40 (talk) 08:59, 1 August 2019 (UTC)


 * Can you provide any academic or research source material that suggests this is the best color difference function? ∆E2000 is mostly considered the best, with some people advocating for newer difference formulas based on CAM16 UCS. TDcolor (talk) 19:39, 21 June 2022 (UTC)

white versus yellow
Personal observation told me that in small areas (dozens) of pixels, white and yellow can under some circumstances be difficult to distinguish. I suspect this has to do with gamma values of monitors, and possibly age. Anyone information on that?

alex (talk) 08:08, 27 August 2018 (UTC)


 * white and yellow differ only by the blue channel, and also color differences are easier to distinguish on darker colors than on brighter colors. 2A01:119F:21D:7900:503A:C616:B438:9F40 (talk) 09:01, 1 August 2019 (UTC)

Formulas are not equivalent
Let's compare the results of calculations of two formulas.


 * $$\bar r = {{250 + 128 } \over 2} = 189$$
 * $$\Delta R = 250 - 128 = 122$$
 * $$\Delta G = 249 - 129 = 120$$
 * $$\Delta B = 248 - 130 = 118$$

Formula 1:
 * $$\Delta C = \sqrt {\left( {2 + {{\bar r} \over {256}}} \right) \times \Delta R^2 + 4 \times \Delta G^2  + \left( {2 + {{255 - \bar r} \over {256}}} \right) \times \Delta B^2 }

= \sqrt {\left( {2 + {{189} \over {256}}} \right) \times 122^2 + 4 \times 120^2  + \left( {2 + {{255 - 189} \over {256}}} \right) \times 118^2 } = \sqrt {129794.359375}$$

Formula 2:
 * $$\Delta C = \sqrt {2 \times \Delta R^2 + 4 \times \Delta G^2 + 3 \times \Delta B^2 +  {{\bar  r \times (\Delta R^2 - \Delta B^2) } \over {256}} }

= \sqrt {2 \times 122^2 + 4 \times 120^2 + 3 \times 118^2 +  {{189 \times (122^2 - 118^2) } \over {256}} } = \sqrt $$ As you can see, the formulas give different results. KyberPrizrak (talk) 07:38, 4 March 2019 (UTC)


 * Please note the MathJax/LaTeX implementation used in Wikipedia understand the Western notation with a decimal DOT for separating a fraction part: → $123.456$ but not the Eastern decimal COMMA: → $123,456$. If you want to force a comma, surround it with curly braces to avoid a space after it: → $123{,}456$. But be aware many readers may get confused with such notation in English-language text. --CiaPan (talk) 08:32, 4 March 2019 (UTC)


 * The source does not have the second formula, so some editor did the manipulation that dropped a $&minus;&Delta;B^{2}/256$ term. I deleted the second formula. Glrx (talk) 18:10, 4 March 2019 (UTC)

Weighted Euclidean RGB Difference is questionable?
Is there any source on this sqrt(2*ΔR^2 + 4*ΔG^2 + 3*ΔB^2) weighted equation? I've been experimenting with my own weighted equations using MacAdam ellipses of just noticeable difference and it seems that these weights are almost backwards. Green has the largest ellipses of just noticeable difference, red the second largest, and blue the smallest, thus green should have the smallest number, red the second smallest, and blue the largest since the ellipse size is inversely proportional to how good human vision is at differentiating between hues in that area.

My own results are more like sqrt(9*ΔR^2 + 5*ΔG^2 + 11*ΔB^2) based on the reciprocal of the major radii of the ellipses in the sRGB primaries areas or sqrt(15*ΔR^2 + 11*ΔG^2 + 17*ΔB^2) based on the reciprocal of the width of ellipses in the sRGB primaries measured perpendicular to lines radiating from D65 white as an approximation of hue. — Preceding unsigned comment added by TorridGristle (talk • contribs) 13:31, 26 June 2019 (UTC)

These results actually don't seem to work all that well, however using the distance from D65 to a ring of Munsell hues as weights seems to work better. 0.80769 Red, 1.00000 Green, 0.63636 Blue. — Preceding unsigned comment added by TorridGristle (talk • contribs) 15:41, 27 June 2019 (UTC)


 * The thing is, distinguishing values of, say, Green is NOT the same as "differentiating between hues in that area". When green transitions into yellow, it is the RED channel that differs, not the GREEN channel. When green transitions into cyan, it is the BLUE channel that differs, not the GREEN channel. 2A01:119F:21D:7900:503A:C616:B438:9F40 (talk) 08:40, 1 August 2019 (UTC)
 * There is a source. But it's a source written by a programmer that tweaked the numbers based on vibes, so any disagreement is really not a surprise. I would not, however, just use the hue: humans care about how bright it is too, and how saturated it is. Artoria2e5 🌉 14:33, 23 January 2024 (UTC)

BT.2124 : Objective metric for the assessment of the potential visibility of colour differences in television (delta ITP)
We should write about it. CALMAN (I think) is already using it and said it is better. https://www.youtube.com/watch?v=t9ntP01MceQ&t=502 https://www.itu.int/rec/R-REC-BT.2124/en ZBalling (talk) 03:14, 27 November 2019 (UTC)