# A Multi-Feature Automatic Evaluation of the Aesthetics of 3D Printed Surfaces
## 3 Proposed Approach  
Considering the above-discussed methods, over 100 various metrics and features were examined and their correlations with subjective MOS values were calculated for 107 images from the dataset considered in the paper. It is worth noting that some of the methods proposed in our earlier papers were initially verified for a smaller number of samples, hence the necessity of a reliable comparison of various approaches for the same dataset of images representing the photos of the 3D printed surfaces.  
In one of our previous conference papers [26], the simplified combination of some features as the weighted product with optimized exponent weights was proposed, leading to Pearson's Linear Correlation Coefficient with subjective scores reaching 0.8353. This was achieved for the combination of FSIM (for 4 blocks), averaged local entropy of depth maps, Hough transform-based metric (with the use of CLAHE), and the kurtosis of the HOG descriptor. On the other hand, the application of the same model for the combination of five SSIM-like IQA metrics made it possible to achieve the PLCC = 0.8565 [21]. The five metrics used in this weighted product, assuming the division of the assessed image into four blocks,were FSIM, CW-SSIM, MCSD, ESSIM, and GSIM. A similar correlation (PLCC = 0.8537) was obtained for the combination of the same metrics applying the division of the image into 16 fragments.  
Since the nonlinear combination of metrics using the weighted product may not be an optimal solution, we propose to extend this model using additionally the weighted sum of the same metrics. This approach does not increase the computational cost in a significant way, as for \(N\) metrics it requires only the additional \(N\) summation operations, \(N\) multiplications, and \(N\) operations related to raising to a power, which is the result of optimization of the model's parameters. The proposed model may be expressed as:  
\[Q_{\text{combined}}=\sum_{n=1}^{N}\left(a_{n}\cdot Q_{n}^{n}\right)+a_{N+1} \cdot\prod_{n=1}^{N}Q_{n}^{c_{n}}, \tag{1}\]  
where \(Q_{\text{combined}}\) denotes the proposed combined metric, and \(Q_{n}\) are the values of \(N\) elementary metrics. The variable \(n\) stands for the number of the elementary metric, and the parameters \(a_{n}\), \(b_{n}\), and \(c_{n}\), as well as \(a_{N+1}\), determine the weighting coefficients, which are obtained as the result of the optimization. The optimization is conducted with the use of the absolute value of the PLCC between the combined metric \(Q_{\text{combined}}\) and the MOS values for 107 samples as the goal function subject to maximization. For this purpose MATLAB(r) (ver. R2024a) fminsearch function may be used, which is based on the simplex search method, jointly with well-known gradient-based optimization methods. The operating principles of the proposed approach are illustrated in Figure 2.  
To find the best possible combination of metrics, the PLCC values obtained after the optimization of seven parameters (\(a_{1}\), \(a_{2}\), \(a_{3}\), \(b_{1}\), \(b_{2}\), \(c_{1}\), and \(c_{2}\)) for all combinations of two metrics (\(N=2\)) were checked. Then, the \"best\" combination of the two metrics was used together with all remaining metrics used as the third one and a similar optimization procedure was used--in this case the addition of an additional metric to the model causes the addition of three additional parameters (\(a_{n}\), \(b_{n}\), and \(c_{n}\)). The starting point for the  
Figure 2: Illustration of the idea of the proposed approach.  
optimization was the set of parameters leading to the highest PLCC value obtained without the additional metric. To verify the linearity of the relation between the combined metric and the subjective quality scores, the scatter plots were also analyzed. These obtained for the \"best\" combined metrics are presented in Section 4, together with the obtained correlation values and the results of the ablation study.