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CIECAM02

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Color appearance model

This articleis missing information about numeric property. Please expand the article to include this information. Further details may exist on thetalk page.(February 2021)

Observing field model. Not drawn to scale.

Incolorimetry,CIECAM02 is thecolor appearance model published in 2002 by theInternational Commission on Illumination (CIE) Technical Committee 8-01 (Color Appearance Modelling for Color Management Systems) and the successor ofCIECAM97s.^[1] It has since been superseded by CIECAM16.^[2]

The two major parts of the model are itschromatic adaptation transform,CIECAT02, and its equations for calculating mathematical correlates for the six technically defined dimensions of color appearance:brightness (luminance),lightness,colorfulness,chroma,saturation, andhue.

Brightness is the subjective appearance of how bright an object appears given its surroundings and how it is illuminated.Lightness is the subjective appearance of how light a color appears to be.Colorfulness is the degree of difference between a color and gray.Chroma is the colorfulness relative to the brightness of another color that appears white under similar viewing conditions. This allows for the fact that a surface of a given chroma displays increasing colorfulness as the level of illumination increases.Saturation is the colorfulness of a color relative to its own brightness.Hue is the degree to which a stimulus can be described as similar to or different from stimuli that are described as red, green, blue, and yellow, the so-calledunique hues. The colors that make up an object’s appearance are best described in terms of lightness and chroma when talking about the colors that make up the object’s surface, and in terms of brightness, saturation and colorfulness when talking about the light that is emitted by or reflected off the object.

CIECAM02 takes for its input thetristimulus values of the stimulus, the tristimulus values of an adaptingwhite point, adapting background, and surround luminance information, and whether or not observers are discounting theilluminant (color constancy is in effect). The model can be used to predict these appearance attributes or, with forward and reverse implementations for distinct viewing conditions, to compute corresponding colors.

TheWindows Color System introduced inWindows Vista usesCanon's Kyuanos (キュアノス) technology for mappingimage gamuts between output devices, which in turn uses CIECAM02 for color matching.^[3]

Viewing conditions

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The inner circle is thestimulus, from which the tristimulus values should be measured in CIE XYZ using the2° standard observer. The intermediate circle is theproximal field, extending out another 2°. The outer circle is thebackground, reaching out to 10°, from which the relative luminance (Y_b) need be measured. If the proximal field is the same color as the background, the background is considered to be adjacent to the stimulus. Beyond the circles which comprise thedisplay field (display area,viewing area) is thesurround field (orperipheral area), which can be considered to be the entire room. The totality of the proximal field, background, and surround is called theadapting field (the field of view that supports adaptation—extends to the limit of vision).^[4]

When referring to the literature, it is also useful to be aware of the difference between the termsadopted white point (the computationalwhite point) and theadapted white point (the observer white point).^[5] The distinction may be important in mixed mode illumination, where psychophysical phenomena come into play. This is a subject of research.

Parameter decision table

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CIECAM02 defines three surround(ing)s – average, dim, and dark – with associated parameters defined here for reference in the rest of this article:^[6]

Surround condition	Surround ratio	F	c	N_c	Application
Average	S_R > 0.15	1.0	0.69	1.0	Viewing surface colors
Dim	0 <S_R < 0.15	0.9	0.59	0.9	Viewing television
Dark	S_R = 0	0.8	0.525	0.8	Using a projector in a dark room

S_R =L_sw /L_dw: ratio of the absolute luminance of thereference white (white point) measured in the surround field to the display area. The 0.2 coefficient derives from the "gray world" assumption (~18%–20% reflectivity). It tests whether the surround luminance is darker or brighter than medium gray.
F: factor determining degree of adaptation
c: impact of surrounding
N_c: chromatic induction factor

For intermediate conditions, these values can be linearly interpolated.^[6]

The absolute luminance of the adapting field, which is a quantity that will be needed later, should be measured with aphotometer. If one is not available, it can be calculated using a reference white:

L_{A}={\frac {E_{w}}{\pi }}{\frac {Y_{b}}{Y_{w}}}={\frac {L_{W}Y_{b}}{Y_{w}}}

whereY_b is the relative luminance of background, theE_w =πL_W is the illuminance of the reference white in lux,L_W is the absolute luminance of the reference white in cd/m², andY_w is the relative luminance of the reference white in the adapting field. If unknown, the adapting field can be assumed to have average reflectance ("gray world" assumption):L_A =L_W / 5.

Note: Care should be taken not to confuseL_W, the absoluteluminance of the reference white in cd/m², andL_w the red cone response in theLMS color space.

Chromatic adaptation

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This section mayrequirecleanup to meet Wikipedia'squality standards. The specific problem is:Sharpened LMS should be just called RGB per original definition, Fairchild book, and CAM16 doc. Might need an explanation about how it's a funky LMS instead of an additive light model though. Please helpimprove this section if you can.(February 2021) (Learn how and when to remove this message)

Summary

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Convert to the "spectrally sharpened" CAT02 LMS space to prepare for adaptation.Spectral sharpening is the transformation of the tristimulus values into new values that would have resulted from a sharper, more concentrated set of spectral sensitivities. It is argued that this aids color constancy, especially in the blue region. (Compare Finlayson et al. 94, Spectral Sharpening:Sensor Transformations for Improved Color Constancy)
Perform chromatic adaptation using CAT02 (also known as the "modified CMCCAT2000 transform").
Convert to an LMS space closer to the cone fundamentals. It is argued that predicting perceptual attribute correlates is best done in such spaces.^[6]
Perform post-adaptation cone response compression.

CAT02

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Given a set oftristimulus values inXYZ, the correspondingLMS values can be determined by theM_CAT02transformation matrix (calculated using theCIE 1931 2° standard colorimetric observer).^[1] The sample color in thetest illuminant is:

{\begin{bmatrix}L\\M\\S\end{bmatrix}}=\mathbf {M} _{\mathit {CAT02}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}},\quad \mathbf {M} _{\mathit {CAT02}}={\begin{bmatrix}\;\;\,0.7328&0.4296&-0.1624\\-0.7036&1.6975&\;\;\,0.0061\\\;\;\,0.0030&0.0136&\;\;\,0.9834\end{bmatrix}}

Once in LMS, the white point can be adapted to the desired degree by choosing the parameterD.^[4] For the general CAT02, thecorresponding color in the reference illuminant is:

{\begin{aligned}L_{c}&={\Big (}{\frac {Y_{w}L_{wr}}{Y_{wr}L_{w}}}D+1-D{\Big )}L\\M_{c}&={\Big (}{\frac {Y_{w}M_{wr}}{Y_{wr}M_{w}}}D+1-D{\Big )}M\\S_{c}&={\Big (}{\frac {Y_{w}S_{wr}}{Y_{wr}S_{w}}}D+1-D{\Big )}S\\\end{aligned}}

where theY_w /Y_wr factor accounts for the two illuminants having the same chromaticity but different reference whites.^[7] The subscripts indicate the cone response for white under the test (w) and reference illuminant (wr). The degree of adaptation (discounting)D can be set to zero for no adaptation (stimulus is considered self-luminous) and unity for complete adaptation (color constancy). In practice, it ranges from 0.65 to 1.0, as can be seen from the diagram. Intermediate values can be calculated by:^[6]

D=F\left(1-\textstyle {\frac {1}{3.6}}e^{-(L_{A}+42)/92}\right)

where surroundF is as defined above andL_A is theadapting field luminance in cd/m².^[1]

log-log plot ofF_L vs.L_A (L_A ranges from 10⁻⁴ to 10⁴,F_L ranges from 10⁻⁴ to 10). The cube root approximation ofF_L is0.1715L_A^1/3

In CIECAM02, the reference illuminant has equal energyL_wr =M_wr =S_wr = 100) and the reference white is theperfect reflecting diffuser (i.e., unity reflectance, andY_wr = 100) hence:

{\begin{aligned}L_{c}&={\Big (}{\frac {Y_{w}}{L_{w}}}D+1-D{\Big )}L\\M_{c}&={\Big (}{\frac {Y_{w}}{M_{w}}}D+1-D{\Big )}M\\S_{c}&={\Big (}{\frac {Y_{w}}{S_{w}}}D+1-D{\Big )}S\\\end{aligned}}

Furthermore, if the reference white in both illuminants have theY tristimulus value (Y_wr =Y_w) then:

{\begin{aligned}L_{c}&={\Big (}{\frac {L_{wr}}{L_{w}}}D+1-D{\Big )}L\\M_{c}&={\Big (}{\frac {M_{wr}}{M_{w}}}D+1-D{\Big )}M\\S_{c}&={\Big (}{\frac {S_{wr}}{S_{w}}}D+1-D{\Big )}S\\\end{aligned}}

Post-adaptation

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After adaptation, the cone responses are converted to the Hunt–Pointer–Estévez space bygoing to XYZ and back:^[6]

{\begin{bmatrix}L'\\M'\\S'\end{bmatrix}}=\mathbf {M} _{H}{\begin{bmatrix}X_{c}\\Y_{c}\\Z_{c}\end{bmatrix}}=\mathbf {M} _{H}\mathbf {M} _{CAT02}^{-1}{\begin{bmatrix}L_{c}\\M_{c}\\S_{c}\end{bmatrix}}

\mathbf {M} _{H}={\begin{bmatrix}\;\;\,0.38971&0.68898&-0.07868\\-0.22981&1.18340&\;\;\,0.04641\\\;\;\,0.00000&0.00000&\;\;\,1.00000\end{bmatrix}}

logL′_a vs. logL′ forL_A = 200 (F_L = 1)

Note that the matrix above, which was inherited from CIECAM97s,^[8] has the unfortunate property that since 0.38971 + 0.68898 – 0.07868 = 1.00001, 1⃗ ≠ M_H1⃗ and that consequently gray has non-zero chroma,^[9] an issue which CAM16 aims to address.^[10]

Finally, the response is compressed based on the generalized Michaelis–Menten equation (as depicted aside):^[6]

k={\frac {1}{5L_{A}+1}}

F_{L}=\textstyle {\frac {1}{5}}k^{4}\left(5L_{A}\right)+\textstyle {\frac {1}{10}}{(1-k^{4})}^{2}{\left(5L_{A}\right)}^{1/3}

F_L is the luminance level adaptation factor.

{\begin{aligned}L'_{a}&={\frac {400{\left(F_{L}L'/100\right)}^{0.42}}{27.13+{\left(F_{L}L'/100\right)}^{0.42}}}+0.1\\M'_{a}&={\frac {400{\left(F_{L}M'/100\right)}^{0.42}}{27.13+{\left(F_{L}M'/100\right)}^{0.42}}}+0.1\\S'_{a}&={\frac {400{\left(F_{L}S'/100\right)}^{0.42}}{27.13+{\left(F_{L}S'/100\right)}^{0.42}}}+0.1\end{aligned}}

As previously mentioned, if the luminance level of the background is unknown, it can be estimated from the absolute luminance of the white point asL_A =L_W / 5 using the "medium gray" assumption. (The expression forF_L is given in terms of 5L_A for convenience.) Inphotopic conditions, the luminance level adaptation factor (F_L) is proportional to the cube root of the luminance of the adapting field (L_A). Inscotopic conditions, it is proportional toL_A (meaning no luminance level adaptation). The photopic threshold is roughlyL_W = 1 (seeF_L–L_A graph above).

Appearance correlates

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CIECAM02 defines correlates for yellow-blue, red-green, brightness, and colorfulness. Let us make some preliminary definitions.

{\begin{aligned}C_{1}&=L_{a}^{\prime }-M_{a}^{\prime }\\C_{2}&=M_{a}^{\prime }-S_{a}^{\prime }\\C_{3}&=S_{a}^{\prime }-L_{a}^{\prime }\end{aligned}}

Thecorrelate for red–green (a) is the magnitude of the departure ofC₁ from the criterion for unique yellow (C₁ =C₂ / 11), and thecorrelate for yellow–blue (b) is based on the mean of the magnitude of the departures ofC₁ from unique red (C₁ =C₂) and unique green (C₁ =C₃).^[4]

{\begin{aligned}a&=C_{1}-\textstyle {\frac {1}{11}}C_{2}&=L_{a}^{\prime }-\textstyle {\frac {12}{11}}M_{a}^{\prime }+\textstyle {\frac {1}{11}}S_{a}^{\prime }\\b&=\textstyle {\frac {1}{2}}\left(C_{2}-C_{1}+C_{1}-C_{3}\right)/4.5&=\textstyle {\frac {1}{9}}\left(L_{a}^{\prime }+M_{a}^{\prime }-2S_{a}^{\prime }\right)\end{aligned}}

The 4.5 factor accounts for the fact that there are fewercones at shorter wavelengths (the eye is less sensitive to blue). The order of the terms is such that b is positive for yellowish colors (rather than blueish).

Thehue angle (h) can be found by converting the rectangular coordinate (a,b) into polar coordinates:

h=\angle (a,b)=\operatorname {atan2} (b,a),\ (0\leq h<360^{\circ })

To calculate the eccentricity (e_t) and hue composition (H), determine which quadrant the hue is in with the aid of the following table. Choosei such thath_i ≤h′ <h_i+1, whereh′ =h ifh >h₁ andh′ =h + 360° otherwise.

	Red	Yellow	Green	Blue	Red
i	1	2	3	4	5
h_i	20.14	90.00	164.25	237.53	380.14
e_i	0.8	0.7	1.0	1.2	0.8
H_i	0.0	100.0	200.0	300.0	400.0

{\begin{aligned}H&=H_{i}+{\frac {100(h^{\prime }-h_{i})/e_{i}}{(h^{\prime }-h_{i})/e_{i}+(h_{i+1}-h^{\prime })/e_{i+1}}}\\e_{t}&=\textstyle {\frac {1}{4}}\left[\cos \left(\textstyle {\frac {\pi }{180}}h+2\right)+3.8\right]\end{aligned}}

(This is not exactly the same as the eccentricity factor given in the table.)

Calculate the achromatic responseA:

A=(2L_{a}^{\prime }+M_{a}^{\prime }+\textstyle {\frac {1}{20}}S_{a}^{\prime }-0.305)N_{bb}

where

{\begin{aligned}&N_{bb}=N_{cb}=0.725n^{-0.2}\\&n=Y_{b}/Y_{w}\end{aligned}}

The correlate oflightness is

J=100\left(A/A_{w}\right)^{cz}

wherec is the impact of surround (see above), and

z=1.48+{\sqrt {n}}

The correlate ofbrightness is

Q=\left(4/c\right){\sqrt {\textstyle {\frac {1}{100}}J}}\left(A_{w}+4\right)F_{L}^{1/4}

Then calculate a temporary quantityt.

t={\frac {\textstyle {\frac {50\,000}{13}}N_{c}N_{cb}e_{t}{\sqrt {a^{2}+b^{2}}}}{L_{a}^{\prime }+M_{a}^{\prime }+\textstyle {\frac {21}{20}}S_{a}^{\prime }}}

The correlate ofchroma is

C=t^{0.9}{\sqrt {\textstyle {\frac {1}{100}}J}}(1.64-0.29^{n})^{0.73}

The correlate ofcolorfulness is

M=C\cdot F_{L}^{1/4}

The correlate ofsaturation is

s=100{\sqrt {M/Q}}

Color spaces

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The appearance correlates of CIECAM02,J,a, andb, form a uniformcolor space that can be used to calculatecolor differences, as long as a viewing condition is fixed. A more commonly used derivative is theCAM02 Uniform Color Space (CAM02-UCS), an extension with tweaks to better match experimental data.^[11]

CIECAM02 as a model of human visual processing

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Like many color models, CIECAM02 aims to model the human perception of color. The CIECAM02 model has been shown to be a more plausible model of neural activity in theprimary visual cortex, compared to the earlierCIELAB model. Specifically, both its achromatic responseA and red-green correlatea can be matched toEMEG activity (entrainment), each with their own characteristic delay.^[12]

References

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^^a ^b ^cFairchild, Mark D.; Luo, M. R.; Hunt, R. W. G. (August 2000)."A Revision of CIECAM97s for Practical Applications"(PDF).Color Research & Application.25 (4).Wiley Interscience:260–266.doi:10.1002/1520-6378(200008)25:4<260::AID-COL6>3.0.CO;2-9.The CIECAM97s model was adopted by the CIE in 1997 for color imaging applications. It includes forward and reverse modes. Some problems in using this model were found in recent field trials. This article suggests revision to the model in two respects: (a) to make the lightness (J) zero when the Y tristimulus value is zero, under all surround conditions; (b) to modify the chromatic induction factor (Nc) from 1.10 to 0.95 for the dim surround condition. To avoid confusion, it is suggested that the revised version of the model be designated CAM97s2. The article also describes an alternative mode to achieve a more nearly exact reversibility between the forward and reverse modes.
^Li, C.J.; Luo, M.R.; Brill, M.H.; Melgosa, M.; Pointer, M.R.; Teunissen, C.; Wei, M.T. (2022-03-01)."The CIE 2016 Colour Appearance Model for Colour Management Systems: CIECAM16".doi:10.25039/TR.248.2022. Archived fromthe original on 2025-06-28. Retrieved2025-07-16.
^“Windows Color System: The Next Generation Color Management System”Archived 2010-07-27 at theWayback Machine. Microsoft white paper. September 13, 2005.
^^a ^b ^cSchanda, János (2007). "The Future of Colorimetry in the CIE: Color Appearance".Colorimetry: Understanding the CIE System.Wiley Interscience. p. 359.ISBN 978-0-470-04904-4.
^Westland, Stephen; Ripamonti, Caterina (2004).Computational Colour Science Using MATLAB.John Wiley & Sons.ISBN 0-470-84562-7.
^^a ^b ^c ^d ^e ^fMoroney, Nathan; Fairchild, Mark D.; Hunt, Robert W.G.; Li, Changjun; Luo, M. Ronnier; Newman, Todd (November 12, 2002)."The CIECAM02 Color Appearance Model".IS&T/SID Tenth Color Imaging Conference.Scottsdale, Arizona: TheSociety for Imaging Science and Technology.ISBN 0-89208-241-0.
^Hunt, Robert W. G.; Changjun Li; M. Ronnier Luo (February 2005). "Chromatic Adaptation Transforms".Color Research & Application.30 (1).Wiley Interscience: 69.doi:10.1002/col.20085.Chromatic adaptation transforms (CATs) have appeared in different forms. The reasons for these forms, and the relationships between them, are described. The factors governing which type of CAT should be used in different applications are explained
^Ming Ronnier Luo & Robert William Gainer Hunt:The structure of the CIE 1997 colour appearance model
^Chunghui Kuo, Eric Zeise & Di Lai:Robust CIECAM02 implementation and numerical experiment within an International Color Consortium workflow
^Changjun Li, Zhiqiang Li, Zhifeng Wang, Yang Xu, Ming Ronnier Luo, Guihua Cui, Manuel Melgosa, Michael Henry Brill & Michael Pointer:Comprehensive color solutions: CAM16, CAT16, and CAM16-UCS
^Luo, M. Ronnier; Cui, Guihua; Li, Changjun (August 2006). "Uniform colour spaces based on CIECAM02 colour appearance model".Color Research & Application.31 (4):320–330.doi:10.1002/col.20227.S2CID 122917960.
^Thwaites, Andrew; Wingfield, Cai; Wieser, Eric; Soltan, Andrew; Marslen-Wilson, William D.; Nimmo-Smith, Ian (2018)."Entrainment to the CIECAM02 and CIELAB colour appearance models in the human cortex".Vision Research.145:1–10.doi:10.1016/j.visres.2018.01.011.doi:10.17863/CAM.21754.

External links

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Colorlab MATLAB toolbox for color science computation and accurate color reproduction (by Jesus Malo and Maria Jose Luque, Universitat de Valencia). It includes CIE standard tristimulus colorimetry and transformations to a number of non-linear color appearance models (CIELAB, CIECAM, etc.).
Excel spreadsheet with forward and inverse examples Archived 2007-01-09 at theWayback Machine, by Eric Walowit and Grit O'Brien
Experimental Implementation of the CIECAM02 Color Appearance Model in a Photoshop Compatible Plug-in (Microsoft Windows Only), by Cliff Rames.
Notes on the CIECAM02 Colour Appearance Model. Source code in C of the forward and reverse transforms, by Billy Biggs.
CIECAM02 Java applet, by Nathan Moroney
Although Java applets no longer run on any major browser, this page also offers command line executables for Windows, Mac OS X and HP-UX. Although undocumented on the page itself, the use of these executables isn't all that hard, for example on Windows:
>%TEMP%\cam02vcecho 95.01 100 108.82 200 18 1&&>%TEMP%\cam02xyzecho 40 20 10&&ciecam02 0 1 0%TEMP%\cam02vc%TEMP%\cam02xyzcon
And similarly for other platforms. The first three numbers are the white point to use, then the average surround lighting, in this case 200 cd/m², then the relative luminance of the surround on the same scale as the white point, in this case 18%, then the surround conditions, where 1 = average, 2 = dim and 3 = dark, and then XYZ coordinates of the color to check. The result will be the JCh coordinates. The bits 0 1 0 mean ‘forward, verbose, calculate D’, so change the first to 1 to convert from JCh to XYZ, the second to 0 to not print the intermediate values in the calculation, or the last to 1 to force the D parameter to 1.

v t e Color space
List of color spaces Color models
CAM	CIECAM02 iCAM CAM16 CIECAM16
CIE	XYZ (1931) RGB (1931) YUV (1960) UVW (1964) CIELAB (1976) CIELUV (1976) CIECAM02 CIECAM16
RGB	RGB color spaces sRGB rg chromaticity Adobe Wide-gamut ProPhoto scRGB DCI-P3 Rec. 601 SMPTE 240M/"C" Rec. 709 Rec. 2020 Rec. 2100
Y′UV	YUV PAL YDbDr SECAM YIQ NTSC YCbCr Rec. 601 Rec. 709 Rec. 2020 Rec. 2100 ICtCp Rec. 2100 YPbPr MAC xvYCC YCoCg
Other	CcMmYK CMYK ColorADD Coloroid LMS Hexachrome HSL, HSV HCL Imaginary color Oklab OSA-UCS PCCS RG RYB HWB YJK TSL
Color systems and standards	ACES ANPA Colour Index International CI list of dyes DIC Federal Standard 595 HKS ICC profile ISCC–NBS Munsell NCS Ostwald Pantone RAL list JIS Z8102 [ja]
For the vision capacities of organisms or machines, see Color vision.