## 2 Extraction of Spatial Domain Features from Digital Print Images
### Extraction of Chromaticity Features  
Chroma refers to the saturation or purity of a color, indicating its intensity. Changes in chroma can reflect the accuracy and consistency of color reproduction during printing.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\mathbf{X}\) & \(\mathbf{Y}\) & \(\mathbf{Z}\) \\ \hline \(redColorant_{Tag}\) & 0.4361 & 0.2225 & 0.0139 \\ \(greenColorant_{Tag}\) & 0.3851 & 0.7169 & 0.0971 \\ \(blueColorant_{Tag}\) & 0.1431 & 0.0606 & 0.7141 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Device ICC tag sheet.  
Figure 5: Tone reproduction curve.  
Color features are extracted from the A and B channels. The similarity of the A channel is as follows:  
\[S_{c}^{A}=\frac{1}{N}\sum_{i=1}^{N}\frac{2\times A_{s}(i)\times A_{o}(i)+C_{1}}{A _{s}(i)^{2}+A_{o}(i)^{2}+C_{1}}, \tag{5}\]  
In this equation, \(i\) represents the index of the image pixel, and \(N\) denotes the total number of pixels in the image. \(C_{1}\) serves as a stabilizing constant for the fractional term to prevent division by zero. Similarly, the chromaticity similarity in the \(B\) channel is described as follows:  
\[S_{c}^{B}=\frac{1}{N}\sum_{i=1}^{N}\frac{2\times B_{s}(i)\times B_{o}(i)+C_{1 }}{B_{s}(i)^{2}+B_{o}(i)^{2}+C_{1}}, \tag{6}\]  
The calculation of color feature similarity between \(I_{s}\) and \(I_{o}\) is outlined as follows:  
\[S_{C}=\frac{1}{N}\sum_{i=1}^{N}\left(\frac{2\times A_{s}(i)\times A_{o}(i)+C_{ 1}}{A_{s}(i)^{2}+A_{o}(i)^{2}+C_{1}}\times\frac{2\times B_{s}(i)\times B_{o}(i) +C_{1}}{B_{s}(i)^{2}+B_{o}(i)^{2}+C_{1}}\right), \tag{7}\]  
Different values of \(C_{1}\) will lead to differences in chromaticity similarity. In order to optimize the chromaticity metrics, the TID2013 dataset was tested to judge the effect of \(C_{1}\) values on chromaticity values via the Spearman Rank Order Correlation Coefficient (SROCC) metrics. The SROCC is used as a measure of the correlation between two variables. The SROCC value range is [\(-1\), \(1\)]; the closer it is to \(1\) or \(-1\), the more monotonicity is achieved. The results are shown in Figure 6. Figure 6a shows the change curve of the SROCC metrics with \(C_{1}\) taking the value of Figure 6b, which shows the change rate of the curve. From this analysis, it is concluded that the SROCC increases rapidly when the value of \(C_{1}\) increases from \(0\) to about \(40\), which indicates that the monotonicity between the color similarity and the true value increases as the value of the parameter increases. The rate of increase of the SROCC starts to slow down when the value of \(C_{1}\) is about \(40\), and enters into a smooth growth phase. When the parameter value continues to increase, the SROCC still shows a slow increasing trend, but the increase is smaller and close to linear growth. In practical applications, it may be necessary to find a balance between the performance improvement induced by the parameter value increase and the computational complexity. Too high a parameter value may not significantly improve the performance, while the computational cost will increase. All things considered, \(C_{1}=40\) is chosen in this paper.