J. Eur. Opt. Society-Rapid Publ. 21, 36( 2025) 59
Table 4. Coefficients found for the 19 metrics analyzed with the ANOVA.
Metrics |
Low colorfulness group |
High colorfulness group |
|
Coeff |
p-value |
Coeff |
p-value |
M1 |
0.05 |
0.83 |
0.03 |
0.92 |
M2 |
0.15 |
0.33 |
0.18 |
0.31 |
M3 |
0.93 |
1.07 10 �3 |
0.61 |
0.01 |
M4 |
�3.04 |
4.45 10 �14 |
�3.25 |
1.53 10 �24 |
M5 |
1.41 |
2.66 10 �4 |
0.43 |
0.03 |
M6 |
�0.07 |
0.78 |
0.11 |
0.80 |
M7 |
0.21 |
0.33 |
0.15 |
0.41 |
M8 |
0.08 |
0.65 |
0.10 |
0.45 |
M9 |
�1.03 |
3.87 10 �5 |
�1.11 |
1.28 10 �6 |
M10 |
0.27 |
0.63 |
0.28 |
0.60 |
M11 |
1.03 |
0.01 |
�2.32 |
1.62 10 �6 |
M12 |
0.11 |
0.57 |
0.02 |
0.88 |
M13 |
0.01 |
0.98 |
�0.03 |
0.96 |
M14 |
0.14 |
0.87 |
0.45 |
0.04 |
M16 |
�0.36 |
0.02 |
�0.41 |
7.93 10 � ³ |
M17 |
�0.28 |
0.43 |
�0.34 |
0.07 |
SSIM |
�0.72 |
0.11 |
�0.19 |
0.54 |
MSE |
0.97 |
0.02 |
0.88 |
4.48 10 � ³ |
PSNR |
0.06 |
0.78 |
0.08 |
0.07 |
Table 5. Metrics kept for each group indicated with a cross.
|
Low colorfulness group |
High colorfulness group |
M4 |
X |
X |
M9 |
X |
X |
M3 |
X |
|
M5 |
X |
|
M11 |
|
X |
M16 |
|
X |
MSE |
|
X |
ANOVA partitions the total variance in the observer rankings into components attributable to each metric, providing insight into the relative importance of each metric. Specifically, the ANOVA test compares the variance explained by each metric to the residual variance to determine which metrics contribute significantly to the model.
For this analysis, the probability of a Type I error“ alpha” was set at 0.1, meaning that a metric was considered significant when there was less than a 10 % probability that the effect of the metric was due to chance. The p-value is a statistical measure that indicates the likelihood of getting the same results if there is no effect. Metrics with a p-value below 0.1 were identified as key predictors. These metrics were then used to create various models, each representing a different linear combination of the significant metrics. The Akaike Information Criterion( AIC) was used to determine the best model. AIC evaluates each model by considering both the goodness of fit and the number of parameters, favoring simpler models that adequately explain the data. Due to the limited sample size, the corrected AIC( AICc) was used, which adjusts the AIC for small sample sizes, ensuring a more accurate model selection.
The AICc model analysis shown that the metrics listed in Table 5 were the most promising since they showed p-values below 0.01.
The linear regression used with a simplified prediction model, as a linear combination of M4, M9, M3 andM5 for the low colorfulness group, gives:
pred ¼ 4:31 � 2:95M4 � 1:01M9 þ 0:90M3 þ 1:36M5 ð3Þ
And the linear combination of M4, M9, M11, M16 and MSE for the low colorfulness group yields:
pred ¼ 4:29 � 3:07M4 � 1:06M9 þ 2:25M11 � 0:41M16 þ 0:83MSE ð4Þ
These predictions give an overall R 2 value of 0.873. However, Figure 5 showsthatthereare3populationsofpoints: one with the two best gamuts, the printer and portrait gamuts, one with the experimental gamuts, and one with the bad gamut.
Figure 6 displays six simulated images from the original image( a) of Figure 3, with their subjective ranking compared with the ranking predicted by equations( 3)/( 4). It shows how well the metric is able to discriminate the