## 2 Proposed Method
### Chromatic Adaptation Transform (CAT) Based on CMCCAT2000  
Chromatic adaptation is defined as the HVS' ability to adjust to changes in illumination in order to preserve the appearance of object colors. It allows us to perceive object colors stably and constantly even under different illuminations. However, digital imaging technology is far behind the HVS in chromatic adaptation. For example, a digital camera is unable to adapt to changes in illumination colors wholly and partially. In order to perform chromatic adaptation like the HVS, the computer vision has to take the changes in illumination colors into account and transform the tristimulus values of its captured image. Such transformations are called chromatic adaptation transforms (CATs). For this reason, the resulting image undergoes the CAT based on CMCCAT2000 [27]. The CMCCAT2000-based CAT operation is able to predict the mechanism of the HVS using all available data sets, which is more accurate than other versions. Using the tone-mapped image resulting from Equation (21), the transformation to estimate the chromatic adaptation is calculated as  
\[\left( \begin{array}{c}R\\ G\\ B\end{array} \right)=M\left( \begin{array}{c}X\\ Y\\ Z\end{array} \right)\left( \begin{array}{c}R_{w}\\ G_{w}\\ B_{w}\end{array} \right)=M\left( \begin{array}{c}X_{w}\\ Y_{w}\\ Z_{w}\end{array} \right),\left( \begin{array}{c}R_{w}\\ G_{w}\\ B_{w}\end{array} \right)=M\left( \begin{array}{c}X_{ur}\\ Y_{ur}\\ Z_{ur}\end{array} \right), \tag{22}\] \[M=\left( \begin{array}{ccc}0.7982&0.3389&-0.1371\\ -0.5918&1.5512&0.0406\\ 0.0008&0.0239&0.9753\end{array} \right),\]  
where \(R_{w}\), \(B_{w}\), \(G_{w}\) and \(X_{w}\), \(Y_{w}\), \(Z_{w}\) refer to \(R\), \(G\), \(B\) and \(X\), \(Y\), \(Z\) each for the white point. \(X_{ur}\), \(Y_{ur}\), and \(Z_{ur}\) refer to the reference white in reference illumination. Figure 3: Characteristic curve of the visual gamma values. The \(D\), which includes incomplete adaptation to be used in CMCCAT2000, is optimized to give the least color difference, and the last term in Equation (23) is included to consider dark luminance effects. The \(D\) value is given by the luminance value of test and reference adapting field (cd/m\({}^{2}\)), \(L_{A1}\) and \(L_{A2}\), and the surround luminance factor \(F\), as  
\[D=F[0.08\;log_{10}[0.5(L_{A1}+L_{A2})]+0.76-0.45(L_{A1}-L_{A2})/(L_{A1}+L_{A2} )], \tag{23}\]  
where  
\[F=0.2k^{4}(5L_{A})+0.1\Big{(}1-k^{4}\Big{)}(5L_{A})^{\frac{1}{3}}, \tag{24}\]  
\[L_{A}=L_{w}/5, \tag{25}\]  
\[k=\frac{1}{5L_{A}}, \tag{26}\]  
where \(L_{A1}\) and \(L_{A2}\) are the luminance values (cd/m\({}^{2}\)) of the reference adapting field, respectively. Both are the product of dividing the illuminance value in lux by \(\pi\) and multiplying it by \(Y_{b}/100\). Here, \(Y_{b}\) is any luminance factor other than the object's luminance. Most color appearance models (CAMs) assume that the observer has a single state of visual adaptation, but the important visual adaptation for appearance matching images is in fact affected by the surround conditions as well as luminous images. The effect of luminous images becomes more highlighted in dim or dark surroundings. Unfortunately, the method, CMCCAM2000, improves the issue of saturation or colorfulness but produces some unexpected artifacts, such as color or hue shift and color leakage. Hence, Equation (24) is used in the CAT instead of surround luminance (\(F=1\) for average surround, or \(F=0.8\) for dim- and dark-surround) to deal with a problem such as color shift and leakage, and a wide variety of conditions in a real scene. In Equation (23), if \(D\) is above 1 or below 0, it has to be set to 1 or 0. \(L_{A}\) is a function of adaptation luminance, and accounts for 20% of the adaptation white (\(L_{w}\)).