CIE Chromatic Adaptation; Comparison of von Kries, CIELAB, CMCCAT97 and CAT02
Synonyms
Definition
According to the CIE International Lighting Vocabulary [1], chromatic adaptation is a visual process whereby approximate compensation is made for changes in the colors of stimuli, especially in the case of changes in illuminants. The effect can be predicted by a chromatic adaptation transform (CAT) which is used to predict the corresponding colors, a pair of color stimuli that have same color appearance when one is seen under one illuminant and the other is seen under the other illuminant.
Overview
CAT is used for many industrial applications. For example, it is highly desired to produce color constant merchandise, i.e., products do not change color appearance across different illuminants. A color inconstancy index named CMCCON02 was proposed by the Colour Measurement Committee (CMC) of the Society of Dyers and Colourists (SDC) [2]. CAT is a key element in the color inconstancy index. It was later become the ISO standard for textile applications [3]. Furthermore, chromatic adaptation is the most important function included in a color appearance model, which is capable of predicting color appearance under different viewing conditions such as illuminants, levels of luminance, background colors, and media (e.g., reflection, transmissive and selfluminous display). The CIE [4] recommended CIECAM02 for the application of the color management systems. For illumination engineering, a CAT is also required for predicting the color rendering properties between a test and a reference illuminant [5].

Step 1 Cone response transform
To model the physiological mechanisms of chromatic adaptation, one must express stimuli in terms of cone responses, denoted by R, G, and B or L, M, and S, suggestive of longwave (red), middlewave (green), and shortwave (blue) sensitivities, respectively. This is achieved by using a linear transform via a 3 by 3 matrix. Various transform functions have been proposed having different fundamental primaries.

Step 2 Chromatic adaptation mechanism
This step transforms cone responses of the test sample (R, G, B), under the test illuminant, defined by (R_{ w }, G_{ w }, B_{ w }), into the adapted cone responses (R_{ c }, G_{ c }, B_{ c }) under the reference illuminant, defined by R_{ rw }, G_{ rw }, and B_{ rw }. The transforms are different between different CATs.

Step 3 Reverse cone transformation
Using the reverse cone transform (an inverse matrix of Step 1) to calculate the corresponding cone responses (R_{ c }, G_{ c }, B_{ c } in Step 2), back to tristimulus values under the reference illuminant.
CIE TC152 technical report entitled “A review of chromatic adaptation transformations” [6] gave a comprehensive survey of the transforms and reported the testing results of the stateoftheart CATs using large accumulation of experimental datasets.
Four of them, the most well known, are introduced below. The notation used in each CAT is different from those used in its original version, but agree with those given in Fig. 1.
von Kries Chromatic Adaptation Transform
 Step 1 Calculate the R, G, B, R_{rw}, G_{rw}, and B_{rw} and R_{w}, G_{w}, and B_{w} using Judd’s cone transformation in Eq. 3:$$ \left[\begin{array}{c}\hfill R\hfill \\ {}\hfill G\hfill \\ {}\hfill B\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill 0,000\hfill & \hfill 1,000\hfill & \hfill 0,000\hfill \\ {}\hfill 0,460\hfill & \hfill 1,360\hfill & \hfill 0,100\hfill \\ {}\hfill 0,000\hfill & \hfill 0,000\hfill & \hfill 1,000\hfill \end{array}\right] \left[\begin{array}{c}\hfill X\hfill \\ {}\hfill Y\hfill \\ {}\hfill Z\hfill \end{array}\right] $$(3)

Step 2 Calculate the α, β, and γ von Kries coefficients and the R_{c}, G_{c}, and B_{c} values using Eqs. 1 and 2.
 Step 3 Calculate the X_{c}, Y_{c}, and Z_{c} using Eq. 4:$$ \left[\begin{array}{c}\hfill {X}_{\mathrm{c}}\hfill \\ {}\hfill {Y}_{\mathrm{c}}\hfill \\ {}\hfill {Z}_{\mathrm{c}}\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill 2,954\hfill & \hfill 2,174\hfill & \hfill 0,220\hfill \\ {}\hfill 1,000\hfill & \hfill 0,000\hfill & \hfill 0,000\hfill \\ {}\hfill 0,000\hfill & \hfill 0,000\hfill & \hfill 1,000\hfill \end{array}\right] \left[\begin{array}{c}\hfill {R}_{\mathrm{c}}\hfill \\ {}\hfill {G}_{\mathrm{c}}\hfill \\ {}\hfill {B}_{\mathrm{c}}\hfill \end{array}\right] $$(4)
CIELAB
Although the CIELAB color space [8] was recommended by CIE in 1976 solely for quantifying color differences under daylight illuminants, it can also be used with other illuminants because it includes a von Kries type of transformation, i.e., by dividing the tristimulus values (X, Y, Z) of the sample by those (X_{ w }, Y_{ w }, Z_{ w }) of illuminant, respectively. The assumption made is that L*, a*, and b* values will be the same for a pair of color constants under a test and a reference illuminant.
CMCCAT97 Chromatic Adaptation Transformation
Lam and Rigg [9] investigated the color constancy for object colors with change of illuminants. They conducted a memorymatching experiment using 58 textile samples under illuminants D65 and A. A transformation was derived to fit the experimental data. The transform was named BFD transform, which is similar to the structure of Bartleson’s. At a later stage, this transform was enhanced by Luo and Hunt [10] to become CMCCAT97. It was also included in the first version of CIE color appearance model, CIECAM97 [11]. CMCCAT97 transform is given below.
 Step 1 Calculation of R, G, B, R_{ rw }, G_{ rw }, and B_{ rw } and R_{ w }, G_{ w }, and B_{ w } using Eq. 5:$$ \begin{array}{l}\left[\begin{array}{c}\hfill R\hfill \\ {}\hfill G\hfill \\ {}\hfill B\hfill \end{array}\right]=M\left[\begin{array}{c}\hfill X/Y\hfill \\ {}\hfill Y/Y\hfill \\ {}\hfill Z/Y\hfill \end{array}\right]\\ {}\phantom{\rule{0ex}{2em}} \mathrm{where}\\ {}\phantom{\rule{0ex}{3em}}M=\left[\begin{array}{ccc}\hfill 0.8951\hfill & \hfill 0.2664\hfill & \hfill 0.1614\hfill \\ {}\hfill 0.7502\hfill & \hfill 1.7135\hfill & \hfill 0.0367\hfill \\ {}\hfill 0.0389\hfill & \hfill 0.0685\hfill & \hfill 1.0296\hfill \end{array}\right]\end{array} $$(5)
 Step 2 Calculation of degree of adaptation (D) using Eq. 6:where F = 1 for surface samples seen under typical viewing conditions.$$ D=F\frac{F}{1+2{L}_a^{1/4}+{L}_a^2/300} $$(6)
D is set to one by assuming that the color of the illuminant is usually discounted during visual color inconstancy assessments for object colors. This is proposed by CMCCON97 [12].
 Step 3 Calculation of the corresponding RGB cone responses using Eq. 7:$$ \begin{array}{l}{R}_C=\left[D\left({R}_{wr}/{R}_w\right)+1D\right]R\\ {}{G}_C=\left[D\left({G}_{wr}/{G}_w\right)+1D\right]G\\ {}{B}_C=\left[D\left({B}_{WR}/{B}_w^p\right)+1D\right]{\leftB\right}^p\end{array} $$(7)(when B is negative, B_{c} must be made negative)$$ \mathrm{where} p={\left({B}_w/{B}_{wr}\right)}^{0.0834} $$
 Step 4 Calculation of the corresponding tristimulus values using Eq. 6:$$ \begin{array}{l}\left[\begin{array}{c}\hfill {X}_c\hfill \\ {}\hfill {Y}_c\hfill \\ {}\hfill {Z}_c\hfill \end{array}\right]={M}^{1}\left[\begin{array}{c}\hfill {R}_cY\hfill \\ {}\hfill {G}_cY\hfill \\ {}\hfill {B}_cY\hfill \end{array}\right]\\ {}\end{array} $$(8)
CAT02 Transform
 Step 1 Calculation of R, G, B, R_{rw}, G_{rw}, and B_{rw} and R_{w}, G_{w}, and B_{w} using Eq. 7:where$$ \left[\begin{array}{c}\hfill R\hfill \\ {}\hfill G\hfill \\ {}\hfill B\hfill \end{array}\right]={\mathbf{M}}_{\mathrm{CAT}02}\left[\begin{array}{c}\hfill X\hfill \\ {}\hfill Y\hfill \\ {}\hfill Z\hfill \end{array}\right] $$(9)$$ {\mathbf{M}}_{\mathrm{CAT}02}=\left[\begin{array}{ccc}\hfill 0,7328\hfill & \hfill 0,4296\hfill & \hfill 0,1624\hfill \\ {}\hfill 0,7036\hfill & \hfill 1,6975\hfill & \hfill 0,0061\hfill \\ {}\hfill 0,0030\hfill & \hfill 0,0136\hfill & \hfill 0,9834\hfill \end{array}\right] $$
 Step 2 Calculation of degree of adaptation (D) using Eq. 8:where F is set to 1,0, 0,9, or 0,8 for “average,” “dim,” or “dark” surround condition, respectively, and L_{a} is the luminance of the adapting field. In theory D should range from 0 for no adaptation to the adopted white point to 1 for complete adaptation to the adopted white point. In practice the minimum D value will not be less than 0,65 for a “dark” surround and will exponentially converge to 1 for “average” surrounds. If D from Eq. 8 is larger than one, D should be set to one. For predicting color inconstancy of a sample using CMCCON02, D value should be set to one assuming a complete adaptation.$$ D=F\left[1\left(\frac{1}{3,6}\right){e}^{\left(\frac{{L}_{\mathrm{a}}42}{92}\right)}\right] $$(10)
 Step 3 Calculation of R_{c}, G_{c}, and B_{c} from R, G, and B (similarly R_{wc}, G_{wc}, B_{wc} from R_{w}, G_{w}, B_{w}):$$ \begin{array}{l}{R}_{\mathrm{c}}=\left[D\left({R}_{\mathrm{rw}}/{R}_{\mathrm{w}}\right)+1D\right]R\\ {}{G}_{\mathrm{c}}=\left[D\left({G}_{\mathrm{rw}}/{G}_{\mathrm{w}}\right)+1D\right]G\\ {}{B}_{\mathrm{c}}=\left[D\left({B}_{\mathrm{rw}}/{B}_{\mathrm{w}}\right)+1D\right]B\end{array} $$(11)
 Step 4 Calculation of the corresponding tristimulus values using Eq. 10:$$ \left[\begin{array}{c}\hfill {X}_{\mathrm{c}}\hfill \\ {}\hfill {Y}_{\mathrm{c}}\hfill \\ {}\hfill {Z}_{\mathrm{c}}\hfill \end{array}\right]={{\mathbf{M}}_{\mathrm{CAT}02}}^{1}\left[\begin{array}{c}\hfill {R}_{\mathrm{c}}\hfill \\ {}\hfill {G}_{\mathrm{c}}\hfill \\ {}\hfill {B}_{\mathrm{c}}\hfill \end{array}\right] $$(12)
Experimental Datasets Investigated by CIE TC152
List of classical experiments for each technique (Copyright of the Society of Dyers and Colourists)
Viewing field  Experiment  Year  References 

Haploscopic matching  
Simple  CSAJ  1991  [14] 
Complex  Breneman  1987  [15] 
Memory matching  
Simple  Helson et al.  1952  [7] 
Complex  Lam and Rigg  1985  [9] 
Braun and Fairchild  1996  [16]  
Magnitude estimation  
Simple  Kuo and Luo  1995  [17] 
Complex  Luo et al.  1991  
Luo et al.  1993 
Evaluation of CATs
The performance of chromatic adaptation transforms (Copyright of the Society of Dyers and Colourists)
Datasets/transform  Refer. illum.  Test illum.  No. of pairs  CIELAB  von Kries  CMC CAT97  CAT02 

Group 1: reflective  
CSAJC  D65  A  87  5.0  4.1  3.4  3.4 
Helson et al.  C  A  59  6.2  5.1  3.8  3.8 
Lam and Rigg  D65  A  58  5.0  5.0  3.4  3.6 
Luo et al. (A)  D65  A  43  5.6  5.5  3.9  3.8 
Luo et al. (D50)  D65  D50  44  4.8  4.1  4.2  4.2 
Luo et al. (WF)  D65  WF  41  4.5  6.1  4.7  4.7 
Kuo et al. (A)  D65  A  40  5.6  5.8  3.6  3.5 
Kuo et al. (TL84)  D65  F11  41  3.3  3.9  2.8  2.6 
Group 1 weighted mean  5.1  4.9  3.7  3.7  
Group 2: nonreflective  
Braun and Fairchild  D65  3000 K 9300 K  66  5.5  5.2  3.7  3.6 
Breneman  D65  Various  107  8.2  8.0  5.6  5.5 
Group 2 weighted mean  7.2  6.9  4.9  4.8  
Overall weighted mean  5.7  5.7  4.0  3.9 
It was found [17] that the typical observer variation for studying chromatic adaptation was about 4 CMC (1:1) units. Hence, if a CAT has an error of prediction equal to or less than 4 units, it may be considered to be satisfactory. As shown in Table 2, the most accurate transform for each dataset (the underlined and bold value) is usually less than 4 units except for Luo et al. (WF) dataset. The ten datasets are divided into two groups: reflection and nonreflection samples. The Braun and Fairchild and Breneman datasets are included in the latter group. (Braun and Fairchild data were obtained by comparing between CRT and reflection printed colors, and Breneman data were based on projected transmissive colors.) The weighted mean for each CAT was calculated to represent the performance for each group or overall. The weighted mean was used to take into account the number of corresponding pairs in each dataset.
The results showed that for both data groups, CMCCAT97 and CAT02 outperformed von Kries and CIELAB with a big margin, and the former and the latter two gave similar degree of error of prediction. This implies that the former two and the latter two CATs gave very similar results. This implies that von Kries law alone is insufficient to develop a reliable CAT. The matrix in Step 1 of Fig. 1 is essential for a reliable CAT.
Also, CMCCAT07 was derived by fitting only one dataset, the Lam and Rigg. It also predicts well to the other datasets. This implies that all corresponding datasets agree reasonably well with each other. CAT02 can be considered as an improvement of CMCCAT97 because it is simpler and was developed by fitting all the datasets in Table 2.
Note that experimental errors would be expected to be random. When a diagram shows a consistent pattern in the errors of prediction of a particular color region, this is most likely to be due to a fault in the transform. See the example of the von Kries diagram at very colorful regions.
Figure 2a–d shows that there are large differences between the four different CATs in terms of predictive color shifts. For the von Kries transform (Fig. 2b), the predictive shifts only move along the a* direction, i.e., redgreen shift. Both von Kries and CIELAB gave reasonable predictions for the low chroma colors, but large predictive errors for high chroma colors. CMCCAT97 (Fig. 2c) gave a quite precise prediction for almost all colors with some exceptions in the colorful yellow and blue regions. The prediction of those regions was improved for CAT02 transform (Fig. 2d). It can also be seen that in general, the magnitudes and shifts for CAT02 are very similar to those of CMCCAT97 (see Fig. 2c). This indicates that although CMCCAT97 was derived to fit only the Lam and Rigg dataset, it gave almost the same performance as that CAT02 (see Table 2). This implies that there is great similarity between different datasets.
Future Directions
The CATs, especially CAT02, have been applied successfully in various applications. However, some shortcomings have been identified for some very saturated colors (close to the spectrum locus of the chromaticity diagram). Although these colors are rare in most applications, efforts from the CIE have been made to correct them [23].
CrossReferences
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