## 4 Proposed Approach
Such side-view mounting of a camera makes it possible to acquire images with visible individual layers of the filament, as illustrated in Figure 1.  
The idea of the calculation of the mutual similarity requires the division of the image representing the manufactured sample into regions and the application of the IQA formula for each pair of such obtained blocks. In the conducted experiments the division into 4, 9, and 16 square blocks has been assumed, although the best results have been obtained for 16 blocks (grid of \(4\times 4\) regions) requiring 120 mutual comparisons. Since the division of the surface into regions is fixed, we may expect the same or very similar orientations of the patters in each region. Hence, due to the use of the mutual similarity based on the comparison of regions, a potential influence of the position and the orientation of the cropping regions would be significantly reduced. Due to the use of the sliding window approach in the SSIM-based quality metrics, the structural changes introduced by such relatively small rotations or translations influence the final results of individual (elementary) metrics not as much as the presence of physical distortions of the 3D printed surface. Additionally, a phase-shifting by a few pixels to adjust the phase of the compared patterns may also be applied as presented in one of our earlier papers [56]. The influence of the color of individual samples has been reduced using the color to grayscale conversion according to ITU Recommendation ITU-R BT.601-7 [57] (using the _rgb2 gray_ function in MATLAB(r)). The illustration of the idea of the mutual similarity is presented in Figure 2, where two examples for the division into 4 and 9 regions are presented with the necessary 6 and 36 mutual similarity calculations. The number of similarities may be expressed as  
\[k=\frac{M\cdot(M-1)}{2}\, \tag{7}\]  
where \(M\) is the number of regions. Therefore, the average mutual similarity values obtained for the elementary metrics may be considered as the no-reference equivalents of the FR IQA metrics applied for the quality assessment of the 3D printed surfaces. Since we do not use the \"pristine\" reference images, we cannot apply FR IQA methods directly. Therefore, we have divided the images into parts (regions) and compare these regions using the FR IQA methods to make a workaround of the lack of the reference images. Hence, formally we can classify our approach as an NR (\"blind\") IQA approach, although all metrics used internally belong to the group of FR methods. Such obtained quality scores have been used as the input metrics for the combinations according to Formula (6). The optimized weights have been obtained by the maximization of the Pearson's Linear Correlation Coefficient (PLCC) between the objective and subjective scores (expressed as MOS values in the developed database), representing the prediction accuracy. Since it has been assumed that the nonlinear combination of elementary metrics should compensate the potentially nonlinear perception of distortions, no fitting functions have been used, differently than for the general-purpose IQA being typically applied according to recommendations of the Video Quality Experts Group (VQEG). Additionally, two rank order correlations have been calculated, representing the prediction monotonicity, namely Spearman Rank Order Correlation Coefficient (SROCC) marker as \(\rho\) and Kendall Rank Order Correlation Coefficient (KROCC) denoted as \(\tau\). They are defined as  
\[\rho=1-\frac{6\cdot\sum d_{i}^{2}}{n\cdot(n^{2}-1)} \tag{8}\]  
Figure 2: Illustration of the idea of mutual similarity calculation for the division into 4 and 9 regions with necessary respective 6 and 36 computations of the FR metric.