## 4 Proposed Approach  
The idea of the combination of various features is partially utilized in many metrics discussed in Section 2, starting from the Structural Similarity, being in fact a combination of three components, representing the luminance, contrast, and structure. Nevertheless, such combination may also be applied for individual (elementary) metrics instead of features, leading to a significant increase in the correlation with subjective quality evaluations. The most advantageous results may be obtained for the combination of metrics utilizing various kinds of features or different domains, which are somewhat complementary to each other. The first such attempt for the general-purpose IQA, based on the nonlinear combination of three metrics, similarly as in the construction of the SSIM or FSIM formulas, has been proposed in  
Figure 1: Sample images from the developed database with their average subjective quality scores sorted from the highest to lowest: (**a**) high quality salmon pink sample (MOS = 4.7253), (**b**) high quality pink sample (MOS = 4.6923), (**c**) high quality brown sample (MOS = 4.1333). (**d**) moderately high quality red sample (MOS = 2.4130), (**e**) moderately low quality yellow sample (MOS = 1.4130), (**f**) low quality dark green sample (MOS = 1.1868), (**g**) low quality black sample (MOS = 1.0978), (**h**) low quality fluorescent pink sample (MOS = 1.0110), (**i**) low quality blue sample (MOS = 1.0000). the paper [45], where the weighted product of MS-SSIM [30], Visual Information Fidelity (VIF) [46] and R-SVD metric [47] has been used. A modified metric referred to as Combined Image Similarity Index (CISI) [48] has been presented assuming the replacement of the R-SVD metric with FSIMc. According to one of the recent papers [49], presenting a comprehensive overview and comparison of many IQA methods, this metric (actually based on two similarity-based formulas) seems to be still competitive with many recently proposed more sophisticated FR IQA approaches, also for multiply distorted image databases, confirming the validity of the assumptions made in this work as well. Hence, the idea of combination of similarity-based metrics is considered as worth investigating also for the 3D printed surfaces. Some other approaches to multi-method fusion have also been proposed by some other researchers, e.g., based on the regression approach [50], also with the use of machine learning [51], application of neural networks [52], also for remote sensing images [44], or genetic algorithms [53]. Nevertheless, considering the assumed application for the quality assessment of the 3D printed surfaces during the manufacturing process, the use of a limited number of metrics combined using their weighted product is assumed according to the general formula:  
\[\mathcal{Q}_{\text{combined}}=\prod_{n=1}^{N}\text{Metric}_{n}^{\text{ weight}_{n}}\, \tag{6}\]  
where \(N\) is the number of the weighted elementary metrics. As the original similarity-based metrics, starting from UIQI and SSIM, belong to the group of full-reference IQA methods, their direct application for the considered tasks would require the knowledge of the reference image. In practical applications, it is usually impossible and even the use of the rendered model of the 3D printed object would require a precise image registering and phase adjustment to compare two images in the same way as for the general-purpose IQA. An additional problem might be related fo different colors and luminance of the acquired images and those rendered from the 3D models. Hence, the idea of the calculation of the average mutual similarity is proposed for the images of the 3D printed surfaces assuming the side location of cameras, initially investigated in the papers [54; 55] exclusively for classification purposes.