CIECAM02
In colorimetry, CIECAM02 is the color appearance model published in 2002 by the International Commission on Illumination Technical Committee 8-01 and the successor of CIECAM97s.
The two major parts of the model are its chromatic adaptation transform, CIECAT02, and its equations for calculating mathematical correlates for the six technically defined dimensions of color appearance: brightness, lightness, colorfulness, chroma, saturation, and hue.
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 grey. 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. The model can be used to predict these appearance attributes or, with forward and reverse implementations for distinct viewing conditions, to compute corresponding colors.
CIECAM02 is used in Windows Vista's Windows Color System.
Viewing conditions
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 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 is the surround field, which can be considered to be the entire room. The totality of the proximal field, background, and surround is called the adapting field.When referring to the literature, it is also useful to be aware of the difference between the terms adopted white point and the adapted 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 surrounds – average, dim, and dark – with associated parameters defined here for reference in the rest of this article:| Surround condition | Surround ratio | F | c | Nc | Application |
| Average | SR > 0.2 | 1.0 | 0.69 | 1.0 | Viewing surface colors |
| Dim | 0 < SR < 0.2 | 0.9 | 0.59 | 0.95 | Viewing television |
| Dark | SR = 0 | 0.8 | 0.525 | 0.8 | Using a projector in a dark room |
- : ratio of the absolute luminance of the reference white measured in the surround field to the display area. The 0.2 coefficient derives from the "gray world" assumption. 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
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 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 :.
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.
Chromatic adaptation
Summary
- 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.
- Perform chromatic adaptation using CAT02.
- Convert to an LMS space closer to the cone fundamentals. It is argued that predicting perceptual attribute correlates is best done in such spaces.
- Perform post-adaptation cone response compression.
CAT02
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 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 and reference illuminant. The degree of adaptation D can be set to zero for no adaptation and unity for complete adaptation. 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.
In CIECAM02, the reference illuminant has equal energy ) and the reference white is the perfect reflecting diffuser hence:
Furthermore, if the reference white in both illuminants have the Y tristimulus value then:
Post-adaptation
After adaptation, the cone responses are converted to the Hunt–Pointer–Estévez space by going to XYZ and back:Finally, the response is compressed based on the generalized Michaelis–Menten equation :
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 using the "medium gray" assumption. In photopic conditions, the luminance level adaptation factor is proportional to the cube root of the luminance of the adapting field. In scotopic conditions, it is proportional to LA. The photopic threshold is roughly .
Appearance correlates
CIECAM02 defines correlates for yellow-blue, red-green, brightness, and colorfulness. Let us make some preliminary definitions.The correlate for red–green is the magnitude of the departure of C1 from the criterion for unique yellow, and the correlate for yellow–blue is based on the mean of the magnitude of the departures of C1 from unique red and unique green.
The 4.5 factor accounts for the fact that there are fewer cones at shorter wavelengths. The order of the terms is such that b is positive for yellowish colors.
The hue angle can be found by converting the rectangular coordinate into polar coordinates:
To calculate the eccentricity and hue composition, determine which quadrant the hue is in with the aid of the following table. Choose i such that, where if and otherwise.
| Red | Yellow | Green | Blue | Red | |
| i | 1 | 2 | 3 | 4 | 5 |
| hi | 20.14 | 90.00 | 164.25 | 237.53 | 380.14 |
| ei | 0.8 | 0.7 | 1.0 | 1.2 | 0.8 |
| Hi | 0.0 | 100.0 | 200.0 | 300.0 | 400.0 |
Calculate the achromatic response A:
where
The correlate of lightness is
where c is the impact of surround, 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