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-called unique 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 the tristimulus values of the stimulus, the tristimulus values of an adapting white point, adapting background, and surround luminance information, and whether or not observers are discounting the illuminant (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.
The inner circle is the stimulus, from which the tristimulus values should be measured in CIE XYZ using the 2° standard observer. The intermediate circle is the proximal field, extending out another 2°. The outer circle is the background, reaching out to 10°, from which the relative luminance (Yb) 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 the display field (display area, viewing area) is the surround field (or peripheral area), which can be considered to be the entire room. The totality of the proximal field, background, and surround is called the adapting field (the field of view that supports adaptation—extends to the limit of vision).
When referring to the literature, it is also useful to be aware of the difference between the terms adopted white point (the computational white point) and the adapted white point (the observer white point). The distinction may be important in mixed mode illumination, where psychophysical phenomena come into play. This is a subject of research.
Parameter decision table
CIECAM02 defines three surround(ing)s – average, dim, and dark – with associated parameters defined here for reference in the rest of this article:
SR > 0.15
Viewing surface colors
0 < SR < 0.15
SR = 0
Using a projector in a dark room
SR = Lsw / Ldw: ratio of the absolute luminance of the reference 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
Nc: chromatic induction factor
For intermediate conditions, these values can be linearly interpolated.
The absolute luminance of the adapting field, which is a quantity that will be needed later, should be measured with a photometer. If one is not available, it can be calculated using a reference white:
where Yb is the relative luminance of background, the Ew = πLW is the illuminance of the reference white in lux, LW is the absolute luminance of the reference white in cd/m2, and Yw 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): LA = LW / 5.
Note: Care should be taken not to confuse LW, the absolute luminance of the reference white in cd/m2, and Lw the red cone response in the LMS color space.
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 Colour 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.
Once in LMS, the white point can be adapted to the desired degree by choosing the parameter D. For the general CAT02, the corresponding color in the reference illuminant is:
where the Yw / Ywr factor accounts for the two illuminants having the same chromaticity but different reference whites. 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:
where surround F is as defined above and LA is the adapting field luminance in cd/m2.
log-log plot of FL vs. LA (LA ranges from 10−4 to 104, FL ranges from 10−4 to 10). The cube root approximation of FL is 0.1715LA1/3
In CIECAM02, the reference illuminant has equal energy Lwr = Mwr = Swr = 100) and the reference white is the perfect reflecting diffuser (i.e., unity reflectance, and Ywr = 100) hence:
Furthermore, if the reference white in both illuminants have the Y tristimulus value (Ywr = Yw) then:
Note that the matrix above, which was inherited from CIECAM97s, has the unfortunate property that since 0.38971 + 0.68898 – 0.07868 = 1.00001, 1⃗ ≠ MH1⃗ and that consequently grey has non-zero chroma, an issue which CAM16 aims to address.
Finally, the response is compressed based on the generalized Michaelis–Menten equation (as depicted aside):
FL is the luminance level adaptation factor.
As previously mentioned, if the luminance level of the background is unknown, it can be estimated from the absolute luminance of the white point as LA = LW / 5 using the "medium gray" assumption. (The expression for FL is given in terms of 5LA for convenience.) In photopic conditions, the luminance level adaptation factor (FL) is proportional to the cube root of the luminance of the adapting field (LA). In scotopic conditions, it is proportional to LA (meaning no luminance level adaptation). The photopic threshold is roughly LW = 1 (see FL–LA graph above).
CIECAM02 defines correlates for yellow-blue, red-green, brightness, and colorfulness. Let us make some preliminary definitions.
The correlate for red–green (a) is the magnitude of the departure of C1 from the criterion for unique yellow (C1 = C2 / 11), and the correlate for yellow–blue (b) is based on the mean of the magnitude of the departures of C1 from unique red (C1 = C2) and unique green (C1 = C3).
The 4.5 factor accounts for the fact that there are fewer cones 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).
The hue angle (h) can be found by converting the rectangular coordinate (a, b) into polar coordinates:
To calculate the eccentricity (et) and hue composition (H), determine which quadrant the hue is in with the aid of the following table. Choose i such that hi ≤ h′ < hi+1, where h′ = h if h > h1 and h′ = h + 360° otherwise.
(This is not exactly the same as the eccentricity factor given in the table.)
Calculate the achromatic response A:
The correlate of lightness is
where c is the impact of surround (see above), and
The correlate of brightness is
Then calculate a temporary quantity t,
The correlate of chroma is
The correlate of colorfulness is
The correlate of saturation is
The appearance correlates of CIECAM02, J, a, and b, form a uniform color space that can be used to calculate color differences, as long as a viewing condition is fixed. A more commonly-used derivative is the CAM02 Uniform Color Space (CAM02-UCS), an extension with tweaks to better match experimental data.
CIECAM02 as a model of human visual processing
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 the primary visual cortex, compared to the earlier CIELAB model. Specifically, both its achromatic response A and red-green correlate a can be matched to EMEG activity (entrainment), each with their own characteristic delay.
^ abcFairchild, Mark D.; Luo, M. R.; Hunt, R. W. G. (August 2000). "A Revision of CIECAM97s for Practical Applications"(PDF). Color Research & Application. Wiley Interscience. 25 (4): 260–266. doi:10.1002/1520-6378(200008)25:4<260::AID-COL6>3.0.CO;2-9. Archived from the original(PDF) on 2013-09-22. Retrieved 2008-02-09. 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.
^Hunt, Robert W. G.; Changjun Li; M. Ronnier Luo (February 2005). "Chromatic Adaptation Transforms". Color Research & Application. Wiley Interscience. 30 (1): 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.
Schlömer, Nico (2018). Algorithmic improvements for the CIECAM02 and CAM16 color appearance models. arXiv:1802.06067.
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.).
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:
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 colour 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.