# Optimizing the Spectral Characterisation of a CMYK Primer with Embedded CMY Printer Modelling
## 4 Results and Discussion  
Table 1 reveals the maximum total ink amount for the 16 Neugebauer Primary Ramps, as defined in Equation (1), where canvas, glossy and water colour, respectively, refer to the Black Diamond 220 g canvas paper, the Canon 170 g glossy photo paper and the Pinnacle 245 g water colour paper. From this table, it is clear to see that the glossy paper could hold the most ink while the water colour paper held the least ink. Since the spectral reflectances of these three substrates do not vary significantly, the gamut of those substrates is mainly dependent on the maximum ink amounts. Therefore, the glossy paper exhibits the largest gamut while the water colour paper exhibits the smallest gamut. Figure 2 shows the spectral and colorimetric accuracy of the three forward models when predicting the 100 testing samples as described in Section 3. Note that for CMYK and CMY models, different groups of samples were adopted. Since the results regarding to these three substrates are quite consistent, only the case for the canvas papers is presented. The root mean square error (RMSE) [39] and the CIEDE2000 colour difference [31] under the D50/2 condition were adopted to denote the spectral and colorimetric accuracy respectively. As stated above, the light tone, middle tone and dark tone were defined by dividing the whole gamut with two thresholds, which refer to the lightness of (c = 0.3, m = 0.3, y = 0.3, k = 0) and (c = 0.7, m = 0.7, y = 0.7, k = 0). In this case, such two lightness values are 59 and 39 in CIELAB colour space (D50/2) respectively. From Figure 2, it is clear that our formerly proposed BPn-CYNSN model obviously outperformed the plain CYNSN model for the CMYK printer, which is consistent with our previous work [19]. Besides, it can be concluded that those models always encountered relatively large errors for light-tone regions while exhibiting the best performance for dark tones, which indeed highlights our concern upon the accuracy for light tones. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Primary**} & \multicolumn{3}{c}{**Maximum Total Ink Amount \(\boldsymbol{\Phi}_{total-max}\)**} \\ \cline{2-4}  & **Canvas** & **Glossy** & **Water Colour** \\ \hline Paper & (0, 0, 0, 0) & (0, 0, 0, 0) & (0, 0, 0, 0) \\ C & (0.9, 0, 0, 0) & (1, 0, 0, 0) & (0.7, 0, 0, 0) \\ M & (0, 0.8, 0, 0) & (0, 1, 0, 0) & (0, 0.65, 0,  
For the light-tone colours, the embedded CMY-CSN model exhibited the best performance despite the fact that this model is of the lowest level among the three (i.e., without Yule-Nielsen \(n\) value modification). As far as we are concerned, such a finding could be ascribed to the nonuniform sampling of those CYNSN models. Figure 3 depicts the colour distribution of the training and testing samples for the canvas paper, where the ordinate denotes the percentage of different colour tones. As described above, 625 samples were printed for the CMYK printer, whereas 125 samples were printed for the embedded CMY printer when building the cellular structure of these models. In addition, there were 100 testing samples for the CMYK and CMY models respectively. From Figure 3, it can be seen that the training and testing samples for the CMYK models mostly located in the dark tone regions due to the strong light absorption of the black ink. On the contrary, few light-tone colours were generated. As those models computed the printed reflectance by a weighted sum of those primary reflectances, such sampling overemphasised the dark tones while resulting in relatively large errors for the light tones. Similarly, as for the proposed embedded CMY printer modelling, as many more light-tone colours were generated, the prediction performance for this region should become significantly better. Figure 2: Spectral accuracy (**a**) and colorimetric accuracy (**b**) of different forward models for the canvas paper.