# Optimizing the Spectral Characterisation of a CMYK Primer with Embedded CMY Printer Modelling
## 4 Results and Discussion
From Tables 1 and 2, it is obvious that the glossy paper, which holds the most black ink, always suffered from the largest errors. Such a finding, as mentioned above, should be attributed to the measuring error of the colour measurement device for extremely dark tones [19; 27; 28]. Meanwhile, it was found that for the glossy paper, the errors of the CMY model in dark tones were relatively smaller than those of the other substrates. A possible explanation is that the moderate ink limitation of the CMY inks for this substrate to some extent enabled three such inks to synthesize the colour of the black ink. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**CMYK-BPn-CYNSN**} & \multicolumn{2}{c}{**CMY-CSN**} \\ \cline{3-6}  & & **RMS** & **DE2000** & **RMS** & **DE2000** \\ \hline \multirow{3}{*}{Canvas} & Light Tone & 0.017 & 1.48 & 0.009 & 0.96 \\  & Middle Tone & 0.008 & 0.96 & 0.008 & 0.83 \\  & Dark Tone & 0.004 & 0.69 & 0.028 & 4.37 \\ \hline \multirow{3}{*}{Glossy} & Light Tone & 0.019 & 1.78 & 0.013 & 0.99 \\  & Middle Tone & 0.014 & 1.39 & 0.008 & 1.05 \\  & Dark Tone & 0.004 & 1.48 & 0.007 & 2.70 \\ \hline \multirow{3}{*}{Water Colour} & Light Tone & 0.016 & 1.26 & 0.011 & 1.09 \\  & Middle Tone & 0.009 & 0.99 & 0.006 & 0.89 \\ \cline{1-1}  & Dark Tone & 0.005 & 0.92 & 0.060 & 8.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean separation accuracy of CMYK-BPn-CYNSN-based backward model and CMY-CSN-based backward model. Figure 6 further demonstrates why the proposed method adopted the embedded CMY model for the characterisation in light and middle tones while maintaining the CMYK model for the dark tones. In this figure, taking the canvas paper as an example, the relationship between the backward accuracy and the final separation accuracy for different colour tones are illustrated. It is quite clear that the testing colour samples are more uniform among different colour tones when compared to the case of Figure 3, because we have modified the sampling for test colour samples as described in Section 3. As stated before, current separation methods always inverted the CYNSN models based on the backward accuracy, which merely refers to the smallest error between the target and the predicted colour according to the forward model. However, if the forward model is prob  
Figure 5: Examples of spectral colour reproduction. L denotes the lightness values in CIELAB space (D50/2), BPn represents the CMYK-BPn-CYNSN-based colour separation while CSN represents the CMY-CSN-based colour separation. Figure 6: The relationship between the backward accuracy and the final separation accuracy for the light tone, middle tone and dark tone for the canvas paper. The squares in dark colour represent the samples reproduced by the CMYK-BPn-CYNSN-based colour separation while the triangles in light colour represent the samples reproduced by the CMY-CSN-based colour separation. The dashed lines denote the least-squares fit for each scatter plot. The samples in the dashed ellipses represent the ones with sound backward accuracy but relative lower final accuracy, mainly for the CMYK-BPn-CYNSN-based colour separation. separation may not target the optimal control values. In that condition, a failure in final colour reproduction will occur. From Figure 6, it can be concluded that other than the case of the CMY-CSN-based colour separation for dark tone colours, there is always some obvious difference between the values of the backward accuracy and the final accuracy. (For instance, the samples in the dashed ellipses in Figure 6, which exhibit sound backward accuracy but relative lower final accuracy.) Such a finding indeed highlights the importance of the accuracy of the forward model. In other words, when the final colour separation accuracy is within a small error range (e.g., mean RMSE less than 0.02, mean DE2000 less than 2), the influence of the errors of the forward model should not be neglected when the highest precision is required.