# Optimizing the Spectral Characterisation of a CMYK Primer with Embedded CMY Printer Modelling
## 4 Results and Discussion
In addition to this, the colour coordinates of the 625 samples for CMYK models as well as the 125 samples (a subset of the 625 samples) for CMY models were plotted in CIELAB colour space, as shown in Figure 4. By that figure, the above statements are further validated. Meanwhile, another significant finding is that the colour gamut of the CMY printer in light and middle tones approximately matches that of the CMYK printer while for dark tones it is quite obvious that the gamut of CMY printer is much smaller, especially for the extreme dark tones. Note that although the embedded CMY printer modelling emphasised the sampling in middle tones and de-emphasised the sampling in dark tones, the corresponding accuracy did not vary considerably when compared to the CMYK models. In our opinion, several possible reasons mutually contribute to this phenomenon, including the modelling protocols of these three models, the magnitude of the spectral reflectance of different tones, the nonlinearity between the spectral accuracy and colorimetric accuracy as well as the measurement error in the extremely dark regions [19; 27]. Moreover, it should be mentioned that the CMY and CMYK models actually employed different sets of testing samples with different colour gamut for dark tones (very similar to the condition depicted in Figure 4), therefore the performance comparison for dark region in this condition is actually not very meaningful; regardless, the aim of this study is to optimise the performance of CYNSN-based forward and backward  
Figure 4: Colour coordinates (canvas paper) of the cellular samples for CMYK and CMY models in CIELAB space. (L-a plot, D50/2). Figure 3: Colour distribution of the training and testing samples for the canvas paper. models with black ink, so it is quite obvious that the colour gamut of a CMY printer is too small for the dark tone. As mentioned above, 100 in-gamut colour samples were reproduced in order to test the performance of different separation methods. Table 2 depicts the mean separation accuracy of the CMYK-BPn-CYNSN-based backward model and the CMY-CSN-based backward model for different colour tones on different substrates. As the superiority of CMYK-BPn-CYNSN-based spectral separation over that of CMYK-CYNSN model had been comprehensively proved by our previous work [19], in this study the CMYK-CYNSN model was not inverted. It is obvious in Table 2 that the results for these three substrates are quite consistent. For light tones, the separation accuracy of the CMY-based model always outperformed that of the CMYK based model while for middle tone colours, the improvement was not so significant. Meanwhile, as for the performance of the CMYK based separation, the accuracy of the dark tones was always higher than that of the middle tones while the accuracy for the light tones was always the worst. Such findings actually correlate well with the results of the forward modelling, as shown in Figure 2. Similarly, they could also be attributed to the nonuniform sampling of the CYNSN models as well as the strong light absorption of the black ink. In addition, from Table 2 it was found that the separation accuracy of CMY-based separation model exhibited much larger errors in dark tones. This could be explained by the fact that some of the colours in this region were so dark that they located outside the gamut of the embedded CMY printer, as indicated in Figure 4. To further illustrate this statement, three examples are provided in Figure 5, where the spectral colours from different colour tones were respectively reproduced by CMY-based separation and CMYK based separation. In the dark-tone case, the overprint of the CMY printer could not achieve a colour with extreme darkness. Fortunately, since the accuracy of CMYK based separation for the dark tones is already excellent and the proposed CMY modelling is only adopted in light and middle tones, there is no need to be concerned about this problem. Besides, the ink limitation settings as mentioned in Table 1 had strong influence on the accuracy of those models.