## 3 Color Acquisition Based on a Digital Camera and the CDS  
### Colorimetric Characterization of a Digital Camera  
In order to get the CIE chromaticity values from the paintings on the ancient architectures, we propose using a digital RGB camera to capture the RGB images of the paintings and then transforming them into XYZ values. Therefore, the colorimetric characterization model from the RGB space to the XYZ space should be established before the measurement. Figure 6: Illustration of the lookup table between CDS notations and CIE chromaticity values. One side of the table contains the notations of the CDS. The other side contains the chromaticity coordinates of CIE1976L*a*b* and CIE1931 xy. Figure 7: The CIE1931 xy coordinates of the 80 samples (the red dots) from the CDS hue circle of the CDS atlas, and 40 samples (the blue dots) from the hue circle of the NCS atlas, and 20 samples (the green dots) from the [PERSON] book. Until now, different methods of the colorimetric characterization of digital cameras have been put forward [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25], such as the polynomial formula [23; 24; 25], the artificial neural-network [25; 26; 27; 28; 29; 30; 31], the look-up-table [32], and so on. Among them, the method of the polynomial formula has been widely used because the configuration of the polynomial formula model is rather simple. More importantly, the high-order polynomial transformations such as the cubic and the quartic can obtain a desirable color conversion accuracy in the wide-color-gamut [25]. Therefore, in our work, we propose using the polynomial transform method to set up the color conversion model. The general expression of polynomial transform is shown in Formula (1). \[\left\{ \begin{array}{c}[X,Y,Z]^{\rm T}=A\cdot\left[1,R,G,B,RG,RB, BG,R^{2},G^{2},B^{2},R^{3},G^{3},B^{3},RGB\cdots\right]^{T}\\ A=\left[\begin{array}{cc}a_{1}&a_{2}\cdots&a_{n}\\ b_{1}&b_{2}\cdots&b_{n}\\ c_{1}&c_{2}\cdots&c_{n}\end{array}\right]\end{array} \right. \tag{1}\]  
where \(A\) is a constant matrix of three lines by \(n\) rows, and \(n\) is the number of terms in the polynomial formula. For example, in the linear, the quadratic, the cubic, and the quartic polynomial formulas, the values of \(n\) are 4, 10, 20, and 38, respectively. The elements of matrix \(A\) can be estimated by the training procedure. There are different kinds of training algorithms including the least square method [15; 16; 20], the Wiener estimation method [33], and principal component analysis [34]. In the paper, the least square method was used to estimate the elements of matrix \(A\). It should be noted that, in our study, not only were the polynomial formulas proposed for establishing the color conversion models for a digital camera, but the CDS color samples were also proposed as the training set and the testing set of the models. Considering that the gamut of the CDS system is wider than that of other color systems such as the Munsell or the NCS, it is a good choice for us to use the CDS to measure and evaluate the high chromatic samples on ancient Chinese architectures. Before the training, the training sets of (Ri, Gi, Bi) and (Xi, Yi, Zi) should be collected. Figure 8 shows the principle of colorimetric characterization for the digital RGB camera based on the CDS samples. During the colorimetric characterization, 40 pages of the CDS atlas were captured, respectively, by the digital camera, and the (Ri, Gi, Bi) values of 2740 CDS samples could be collected. On the other hand, the corresponding (Xi, Yi, Zi) values of 2740 CDS samples could be looked up from the CDS lookup table. Note that the light source for the CDS samples should be similar to that of the on-site paintings. For example, an artificial D65 light source can be used. Figure 8: The illustration of the colorimetric characterization of the RGB camera based on the CDS samples, and the colorimetric measurement of the paintings on the ancient architecture using the RGB camera and the CDS lookup table.