Color difference
In color science, color difference or color distance is the separation between two colors. This metric allows quantified examination of a notion that formerly could only be described with adjectives. Quantification of these properties is of great importance to those whose work is color-critical. Common definitions make use of the Euclidean distance in a device-independent color space.
Euclidean
sRGB
As most definitions of color difference are distances within a color space, the standard means of determining distances is the Euclidean distance. If one presently has an RGB (red, green, blue) tuple and wishes to find the color difference, computationally one of the easiest is to consider R, G, B linear dimensions defining the color space.
A very simple example can be given between the two colors with RGB values (0, 64, 0) ( ) and (255, 64, 0) ( ): their distance is 255. Going from there to (255, 64, 128) ( ) is a distance of 128.
When we wish to calculate distance from the first point to the third point (i.e. changing more than one of the color values), we can do this:
When the result should be computationally simple as well, it is often acceptable to remove the square root and simply use
This will work in cases when a single color WAS to be compared to a single color and the need is to simply know whether a distance is greater. If these squared color distances are summed, such a metric effectively becomes the variance of the color distances.
There have been many attempts to weigh RGB values to better fit human perception, where the components are commonly weighted (red 30%, green 59%, and blue 11%), however, these are demonstrably[citation needed] worse at color determinations and are properly the contributions to the brightness of these colors, rather than to the degree to which human vision has less tolerance for these colors. The closer approximations would be more properly (for non-linear sRGB, using a color range of 0–255):[1]
where:
One of the better low-cost approximations, sometimes called "redmean", combines the two cases smoothly:[1]
There are a number of color distance formulae that attempt to use color spaces like HSV or HSL with the hue represented as a circle, placing the various colors within a three-dimensional space of either a cylinder or cone, but most of these are just modifications of RGB; without accounting for differences in human color perception, they will tend to be on par with a simple Euclidean metric.[citation needed]
Uniform color spaces
CIELAB and CIELUV are relatively perceptually-uniform color spaces and they have been used as spaces for Euclidean measures of color difference. The CIELAB version is known as CIE76. However, the non-uniformity of these spaces were later discovered, leading to the creation of more complex formulae.
Uniform color space: a color space in which equivalent numerical differences represent equivalent visual differences, regardless of location within the color space. A truly uniform color space has been the goal of color scientists for many years. Most color spaces, though not perfectly uniform, are referred to as uniform color spaces, since they are more nearly uniform when compared to the chromaticity diagram.— X-rite glossary[2]
A uniform color space is supposed to make a simple measure of color difference, usually Euclidean, "just work". Color spaces that improve on this issue include CAM02-UCS, CAM16-UCS, and Jzazbz.[3]
Rec. ITU-R BT.2124 or ΔEITP
In 2019 a new standard for
where the components of this "ITP" is given by
- I = I,
- T = 0.5 CT,
- P = CP.
Other geometric constructions
The Euclidean measure is known to work poorly on large color distances (i.e. more than 10 units in most systems). A hybrid approach where a
CIELAB ΔE*
This section is missing information about acceptability difference values in industry.(July 2021) |
This section may require cleanup to meet Wikipedia's quality standards. The specific problem is: Should reorder chronologically (move CMC between 76 and 94, then rephrase accordingly) as it looks like an inspiration for the move to LCh. (February 2022) |
The
Perceptual non-uniformities in the underlying
All ΔE* formulae are originally designed to have the difference of 1.0 stand for a JND. This convention is generally followed by other perceptual distance functions such as the aforementioned ΔEITP.[11] However, further experimentation may invalidate this design assumption, the revision of CIE76 ΔE*ab JND to 2.3 being an example.[12]
CIE76
The 1976 formula is the first formula that related a measured color difference to a known set of CIELAB coordinates. This formula has been succeeded by the 1994 and 2000 formulas because the CIELAB space turned out to be not as perceptually uniform as intended, especially in the saturated regions. This means that this formula rates these colors too highly as opposed to other colors.
Given two colors in CIELAB color space, and , the CIE76 color difference formula is defined as:
corresponds to a JND (just noticeable difference).[12]
CIE94
The 1976 definition was extended to address perceptual non-uniformities, while retaining the CIELAB color space, by the introduction of application-specific weights derived from an automotive paint test's tolerance data.[11]
ΔE (1994) is defined in the
where
and where kC and kH are usually both unity, and the weighting factors kL, K1 and K2 depend on the application:
graphic arts textiles 1 2 0.045 0.048 0.015 0.014
Geometrically, the quantity corresponds to the arithmetic mean of the chord lengths of the equal chroma circles of the two colors.[16]
CIEDE2000
Since the 1994 definition did not adequately resolve the
- A hue rotation term (RT), to deal with the problematic blue region (hue angles in the neighborhood of 275°):[19]
- Compensation for neutral colors (the primed values in the L*C*h differences)
- Compensation for lightness (SL)
- Compensation for chroma (SC)
- Compensation for hue (SH)
- Note: The formulae below should use degrees rather than radians; the issue is significant for RT.
- The kL, kC, and kH are usually unity.
- Note: The inverse tangent (tan−1) can be computed using a common library routine
atan2(b, a′)
which usually has a range from −π to π radians; color specifications are given in 0 to 360 degrees, so some adjustment is needed. The inverse tangent is indeterminate if both a′ and b are zero (which also means that the corresponding C′ is zero); in that case, set the hue angle to zero. See Sharma 2005, eqn. 7. - Note: The example above expects the parameter order of atan2 to be
atan2(y, x)
. See implementation in [20]
- Note: The inverse tangent (tan−1) can be computed using a common library routine
- Note: When either C′1 or C′2 is zero, then Δh′ is irrelevant and may be set to zero. See Sharma 2005, eqn. 10.
- Note: When either C′1 or C′2 is zero, then H′ is h′1+h′2 (no divide by 2; essentially, if one angle is indeterminate, then use the other angle as the average; relies on indeterminate angle being set to zero). See Sharma 2005, eqn. 7 and p. 23 stating most implementations on the internet at the time had "an error in the computation of average hue".
CMC l:c (1984)
In 1984, the Colour Measurement Committee of the
The distance of a color to a reference is:[22]
CMC l:c is designed to be used with
Tolerance
Tolerancing concerns the question "What is a set of colors that are imperceptibly/acceptably close to a given reference?" If the distance measure is perceptually uniform, then the answer is simply "the set of points whose distance to the reference is less than the just-noticeable-difference (JND) threshold". This requires a perceptually uniform metric in order for the threshold to be constant throughout the gamut (range of colors). Otherwise, the threshold will be a function of the reference color—cumbersome as a practical guide.
In the
More generally, if the lightness is allowed to vary, then we find the tolerance set to be ellipsoidal. Increasing the weighting factor in the aforementioned distance expressions has the effect of increasing the size of the ellipsoid along the respective axis.[24]
See also
Footnotes
Notes
- quasimetric. Specifically, both depend on only.
References
- ^ a b "Colour metric". Compu Phase.
- ^ "Color Glossary". X-Rite.
- .
- ^ "What Is ICtCp – Introduction?" (PDF). Dolby. Version 7.1. Archived (PDF) from the original on 2016-05-08.
- ^ "Objective metric for the assessment of the potential visibility of colour differences in television" (PDF). BT Series: Broadcasting service (television). International Telecommunication Union. January 2019. Recommendation ITU-R BT.2124-0.
- S2CID 209914019.
- ISBN 9783110154313. Retrieved 2014-12-02.
- ISBN 9780470849026. Retrieved 2014-12-02.
- ISBN 9780132777957.
- ^ Evaluation of the CIE Color Difference Formulas
- ^ a b "Delta E: The Color Difference". Colorwiki.com. Retrieved 2009-04-16.
- ^ ISBN 0-8493-0900-X.
- ^ Lindbloom, Bruce Justin. "Delta E (CIE 1994)". Brucelindbloom.com. Retrieved 2011-03-23.
- ^ "Colour Difference Software by David Heggie". Colorpro.com. 1995-12-19. Retrieved 2009-04-16.
- ^ Colorimetry - Part 4: CIE 1976 L*a*b* Colour Space (Report). Draft Standard. CIE. 2007. CIE DS 014-4.3/E:2007.
- ISBN 978-1-4419-1196-4.
- .
- ^ Lindbloom, Bruce Justin. "Delta E (CIE 2000)". Brucelindbloom.com. Retrieved 2009-04-16.
- ^ The "Blue Turns Purple" Problem, Bruce Lindbloom
- ^ Sharma, Gaurav. "The CIEDE2000 Color-Difference Formula". "Excel spreadsheet" hyperlink. Retrieved 2023-10-24.
- ^ Meaning that the lightness contributes half as much to the difference (or, identically, is allowed twice the tolerance) as the chroma
- ^ Lindbloom, Bruce Justin. "Delta E (CMC)". Brucelindbloom.com. Retrieved 2009-04-16.
- ^ "CMC" (PDF). Insight on Color. 8 (13). 1–15 October 1996. Archived from the original (PDF) on 2006-03-12.
- ^ Susan Hughes (14 January 1998). "A guide to Understanding Color Tolerancing" (PDF). Archived from the original (PDF) on 10 October 2015. Retrieved 2014-12-02.
Further reading
- Robertson, Alan R. (1990). "Historical development of CIE recommended color difference equations". Color Research & Application. 15 (3): 167–170. ]
- Melgosa, M.; Quesada, J. J.; Hita, E. (December 1994). "Uniformity of some recent color metrics tested with an accurate color-difference tolerance dataset". PMID 20963027.
- McDonald, Roderick, ed. (1997). Colour Physics for Industry (2nd ed.). ISBN 0-901956-70-8.
External links
- Bruce Lindbloom's color difference calculator. Uses all CIELAB metrics defined herein.
- The CIEDE2000 Color-Difference Formula, by Gaurav Sharma. Implementations in MATLAB and Excel.
- Explore the Spectrum with Colors in Between, by Bettie M. Cobb.