Encyclopedia of Color Science and Technology

2016 Edition
| Editors: Ming Ronnier Luo

CIECAM02

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-8071-7_6

Synonyms

Definition

CIECAM02 is a color appearance model that provides a viewing condition specific method for transforming between tristimulus values and perceptual attribute correlates. This model was first published [1] in 2002 by Division 8 of the International Commission on Illumination (CIE). CIECAM02 was developed for use in color management systems and was based on the previously published CIECAM97s color appearance model [2, 3]. The model provides a number of parameters for defining a viewing condition and also inverse equations for transforming perceptual attribute correlates back to tristimulus values for a given set of viewing conditions. In this way, CIECAM02 can be used to transform perceptual attribute correlates, such as lightness, chroma, and hue, across different viewing conditions.

Overview

A color appearance model [4, 5] transforms between colorimetry, which specifies if stimuli match, and perceptual attribute correlates, which are scales of lightness, chroma, and hue. To do so, CIECAM02 provides a set of viewing condition parameters in order to model specific color appearance phenomena, such as chromatic adaptation and simultaneous contrast. The resulting perceptual attribute correlates can then be used in research and engineering applications requiring a viewing condition independent color representation, such as color calibration of color printers.

The viewing conditions for CIECAM02 consist of the background, the adapting field, the surround, the white point, and the luminance of the adapting field. Figure 1 shows an example of a color stimulus, a background, and an adapting field. Note that this example is of a real-world situation of viewing a reflectance print. The central stimulus is a 2° region that corresponds to a portion of the print the size of a thumb viewed at arm’s length. The background is the 10° region surrounding the stimulus and is roughly the size of a fist viewed at arm’s length. The adapting field is everything else in the field of view.
CIECAM02, Fig. 1

An example of a colored stimulus, background, and adapting field. The stimulus subtends 2° or roughly the size of a thumb viewed at arm’s length. The background subtends 10° or approximately the size of a fist viewed at arm’s length. The adapting field is everything else in the field of view. The stimulus is shown as the central smaller black circle. The background is shown as the larger black circle. The adapting field is everything outside of the larger black circle

The luminance of the adapting field can be measured directly with an illuminance meter. To incorporate a gray-world assumption and convert to luminance, this is then divided by 5π. The surround setting for the model is categorical and follows roughly the specific application. Dark surrounds are those with no ambient illumination or viewing film projected in a darkened room. Dim surrounds are those in which the ambient illumination is not zero but is also less than 20 % of the scene, print, or display white point, such as home viewing of television with low light levels. Average surround is ambient illumination greater than 20 % of the scene, print, or display white point, such as viewing of surface colors in a light booth. The CIECAM02 model has a set of constants associated with each surround.

Finally the model has an associated white for all calculations. The selection of a white point is a subtle topic and the model suggests two approaches to this issue. First is to use an adopted white point or a computational white point for all calculations. An adopted white point is a fixed value, such as one based on a standard viewing condition or to ensure a specific final mapping for the white point. Second is an adapted white or the white point adapted by the human visual system for a given set of viewing conditions. An adapted white point is one which attempts to as closely as possible match the state of adaptation for a human observer. Note that adapted white points may require experimentation to infer their value, such as for a novel set of viewing conditions or situations with multiple illuminants. In cases where it is not possible to determine the adapted white point, use of an adopted or assumed white point can be convenient.

Given a set of viewing conditions and their associated parameters, it is then possible to compute the perceptual attribute correlates. Figure 2 shows an overall flowchart of the CIECAM02 model starting with input tristimulus values and adopted white point tristimulus values on the left.
CIECAM02, Fig. 2

Overall flowchart of the computational steps for calculating perceptual attribute correlates given input tristimulus values and a specific set of viewing conditions

The first step is to apply a matrix to convert the XYZ values to the CAT02 RGB space. The space was selected as a preferred color space to perform chromatic adaptation. This matrix can be written:
$$ {\mathrm{M}}_{\mathrm{CAT}02}=\left[\begin{array}{ccc}\hfill 0.7328\hfill & \hfill 0.4296\hfill & \hfill -0.1624\hfill \\ {}\hfill -0.7036\hfill & \hfill 1.6975\hfill & \hfill 0.0061\hfill \\ {}\hfill 0.0030\hfill & \hfill 0.0136\hfill & \hfill 0.9834\hfill \end{array}\right] $$
(1)
The result of applying this matrix to 1931 color matching functions is shown in Fig. 3. These curves can be compared to the CIE color matching functions, and it can be seen that these curves are qualitatively more narrow or sharpened. This matrix was derived using a set of corresponding color training data but excluding highly chromatic light sources.
CIECAM02, Fig. 3

The CAT02 matrix shown as a set of red, green, and blue sensitivity curves computed by applying Eq. 1 to the CIE 1931 color matching functions

The degree of adaptation is the next step in the model and is calculated given the surround setting and the luminance of the adapting field. The specific calculation for incomplete adaptation or D is shown in Eq. 2. The variable LA is the luminance of the adapting field and the value of F is a parameter that is computed from the surround setting.
$$ D=F\left[1-\left(\frac{1}{3.6}\right){e}^{\left(\frac{-{L}_A-42}{92}\right)}\right] $$
(2)
The results of using Eq. 2 with three different surround settings over luminance of adapting field values ranging from 0 to 800 cd/m2 are shown in Fig. 4. Essentially the surround limits the degree of adaptation and increases with larger values of LA. Complete adaptation is only achieved with the average surround with high LA values.
CIECAM02, Fig. 4

The degree of adaptation as computed for three surrounds and varying LA. A D value of 1 is complete adaptation to the white point, while values less than one are for incomplete adaptation

Given the input stimulus converted to CAT02 RGB space and a degree of adaptation, it is then possible to compute the chromatic adaptation. This can be done according to Eqs. 3, 4, and 5 below. The stimulus CAT02 values are shown as R, G, and B and the adopted or adapted white point as Rw, Gw, and Bw.
$$ {R}_c=\left[D\left(100/{R}_w\right)+1-D\right]R $$
(3)
$$ {G}_c=\left[D\left(100/{G}_w\right)+1-D\right]G $$
(4)
$$ {B}_c=\left[D\left(100/{B}_w\right)+1-D\right]B $$
(5)
The next step in the calculation of the forward CIECAM02 model is shown as the box HPE RGB in the center of the flowchart in Fig. 2. This is the conversion of Rc, Gc, and Bc above to the Hunt-Pointer-Estevez space. This can be done using a 3 by 3 matrix shown in Eq. 6:
$$ {\mathbf{M}}_{HPE}=\left[\begin{array}{ccc}\hfill 0.38971\hfill & \hfill 0.68898\hfill & \hfill -0.07868\hfill \\ {}\hfill -0.22981\hfill & \hfill 1.18340\hfill & \hfill 0.04641\hfill \\ {}\hfill 0.00000\hfill & \hfill 0.00000\hfill & \hfill 1.00000\hfill \end{array}\right] $$
(6)
A plot of the corresponding red, green, and blue sensitivity curves for the Hunt-Pointer-Estevez RGB space is shown in Fig 5. This graph shows the red and green curves with qualitatively broader and more overlapping than the red and green curves for the CAT02 RGB curves shown in Fig. 3. Effort was made during the formulation of the model to derive a single RGB space for both the chromatic adaptation and for the nonlinear compression, but the results were generally worse and ultimately the final model made use of the two different RGB spaces.
CIECAM02, Fig. 5

The HPE matrix shown as a set of red, green, and blue sensitivity curves computed by applying Eq. 6 to the CIE 1931 color matching functions

Given the Hunt-Pointer-Estevez RGB values, the next step is the nonlinear response compression. The specific nonlinearity used [6] in CIECAM02 is shown in Eqs. 7 through 9 and is shown graphically in Fig. 6. The R′, G′, and B′ values are the HPE values as computed with Eq. 6, and the FL value is a model parameter that is dependent on the viewing conditions.
CIECAM02, Fig. 6

The post-adaptation nonlinear response compression function as computed using Eq. 7. Similar curves result for Eqs. 8 and 9 for the calculation of G′a and B′a

$$ {R}_a^{\prime }=\frac{400{\left({F}_L{R}^{\prime }/100\right)}^{0.42}}{\left[27.13+{\left({F}_L{R}^{\prime }/100\right)}^{0.42}\right]}+0.1 $$
(7)
$$ {G}_a^{\prime }=\frac{400{\left({F}_L{G}^{\prime }/100\right)}^{0.42}}{\left[27.13+{\left({F}_L{G}^{\prime }/100\right)}^{0.42}\right]}+0.1 $$
(8)
$$ {B}_a^{\prime }=\frac{400{\left({F}_L{B}^{\prime }/100\right)}^{0.42}}{\left[27.13+{\left({F}_L{B}^{\prime }/100\right)}^{0.42}\right]}+0.1 $$
(9)
The final steps in the forward CIECAM02 model are the computation of the perceptual attribute correlates. First an intermediate set of opponent coordinates, a and b, are computed according to Eqs. 10 and 11. It should be emphasized that these values of a and b are preliminary and should not be used directly. The value of h or hue is computed using the arctangent of b divided by a. A table of constants is used to compute H or hue quadrature. The resulting H values for red, yellow, green, and blue are 100, 200, 300, and 400, respectively.
$$ a={R}_a^{\prime }-12{G}_a^{\prime }/11+{B}_a^{\prime }/11 $$
(10)
$$ b=\left(1/9\right)\left({R}_a^{\prime }+{G}_a^{\prime }-2{B}_a^{\prime}\right) $$
(11)
The perceptual attribute correlates for lightness and brightness can then be calculated. First the achromatic signal or A is computed according to Eq. 12. The Ra, Ga, and Ba values are the nonlinearly compressed values from Eqs. 7 through 9. Next the computation of J or lightness is shown in Eq. 13, while the computation of Q or brightness is shown in Eq. 14. The c and z values are additional model parameters as computed based on the viewing conditions.
$$ A=\left[2{R}_a^{\prime }+{G}_a^{\prime }+\left(1/20\right){B}_a^{\prime }-0.305\right]{\mathrm{N}}_{\mathrm{bb}} $$
(12)
$$ J=100{\left(A/{A}_w\right)}^{cz} $$
(13)
$$ Q=\left(4/c\right)\sqrt{{J}\!\left/ \!{100}\right.}\left({A}_w+4\right){F}_L^{0.25} $$
(14)
Finally given the correlates for hue, lightness, and brightness, it is possible to calculate the perceptual attribute correlates for chroma, colorfulness, and saturation. First a temporary variable t is computed using Eq. 15. Next C or chroma is calculated using Eq. 16. Colorfulness or M and saturation s can then be computed using Eqs. 17 and 18.
$$ t=\frac{\left(50,000/13\right){N}_c{N}_{cb}{e}_t{\left({a}^2+{b}^2\right)}^{1/2}}{R_a^{\prime }+{G}_a^{\prime }+\left(21/20\right){B}_a^{\prime }} $$
(15)
$$ C={t}^{0.9}\sqrt{J/100}{\left(1.64-{0.29}^n\right)}^{0.73} $$
(16)
$$ M=C{F}_L^{0.25} $$
(17)
$$ S=100\sqrt{{M}\!\left/ \!{Q}\right.} $$
(18)
The result of the preceding calculations is then a set of perceptual attribute correlates for the given input values and viewing conditions. Note though that this does not define a rectangular coordinate system, such as the a* and b* values for CIELAB [7]. Instead a set of correlates such as lightness, chroma, and hue must first be computed and used as polar coordinates. The rectangular coordinates can be computed using Eqs. 19 and 20. Similar coordinates can be calculated for lightness and saturation, with subscript s, and brightness and colorfulness, with subscript M.
$$ {a}_c=C\cdot \cos (h) $$
(19)
$$ {b}_c=C\cdot \sin (h) $$
(20)
The inverse CIECAM02 equations are beyond the scope of this entry, but reference 1 contains the full steps for inverting the above equations. This allows tristimulus values to be computed given input perceptual attribute correlates and viewing conditions.
The CIECAM02 color appearance model can then be used in situations requiring a viewing condition independent color encoding. It also could be considered in cases where CIELAB or CIELUV [7] lacks perceptual uniformity. For example, the CIELAB blue hue lacks hue constancy and tends toward purple as it approaches the neutral axis. This can be problematic in many circumstances, such as when gamut mapping colors from a display to a printer. The CIECAM02 space is considerably more uniform in this case. Two example gradients are shown in Fig. 7. The CIELAB gradient shown on the top has a clear tendency to purple as it goes to gray while the CIECAM02 gradient on the bottom does not. Both color spaces have constant hue angles for these colors but CIECAM02 is significantly improved.
CIECAM02, Fig. 7

Light gray to deep blue constant hue angle gradients for CIELAB, shown at the top, and CIECAM02 shown at the bottom. The left- and right-hand side colors are the same XYZ values and have constant respective hue angles, but the top gradient for CIELAB tends to a purplish tone in the center of the gradient

It is useful to further compare and contrast CIELAB and CIECAM02. CIELAB has as input the stimulus XYZ values and the white point XYZ values. CIECAM02 has as input the stimulus and white XYZ values and also luminance of the adapting field, the luminance of the background, and the surround setting. CIELAB has a chromatic adaptation transform that consists of a complete von Kries transform in XYZ space, while CIECAM02 has a complete or incomplete von Kries transform in CAT02 RGB space. CIELAB has a cube-root nonlinearity, while CIECAM02 uses a modified hyperbolic function as the nonlinearity. CIELAB uses XYZ data to compute the opponent signal, while CIECAM02 is based on a Hunt-Pointer-Estevez space. Finally CIELAB can be used to compute lightness, chroma, and hue correlates, while CIECAM02 can be used to compute these values as well as brightness, colorfulness, saturation, and hue quadrature values. However, CIELAB has benefited from the additional research in advanced color difference equations and as a result has advanced color difference metrics such as ΔE94 and ΔE 2000 which CIECAM02 does not have. There are encouraging results [8] though for using CIECAM02-based color difference equations.

Future Directions

CIECAM02 has been a useful and valuable addition to color appearance modeling research. It has provided a single reference point for ongoing research in the area of color appearance modeling. However, a number of researchers have pointed to specific aspects of the complexity that are problematic in some cases. For example, for the darkest colors, it may not be possible to invert the calculations for highly saturated inputs. These values may be outside the spectral locus, but for color management applications that use a fixed intermediate grid of coordinates, this is a shortcoming. Therefore, it seems likely that future work will continue in the area of color appearance modeling, with a future focus on robustness [8] and perhaps simplicity. In spite of these limitations, there is already work integrating CIECAM02 with color management systems, such as the International Color Consortium (ICC) [10, 11]. There has also been work [12] to consider how the model could be further extended to encompass a wider range of viewing conditions, such as mesopic illumination levels. Finally, there is also research [13] in the area of how the model could be used with complex stimuli to create an image appearance model.

Cross-References

References

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Hewlett-Packard LaboratoriesPalo AltoUSA