## 2 Overview of Similarity-Based Full-Reference Image Quality Assessment Methods
An interesting fact is that although the contrast has been used in many other metrics, including the original SSIM, in this case, all the calculations are based only on contrast values combined with multi-scale image representation. An interesting attempt to pooling following the measurement of local distortions has been presented in the paper [40], where the analysis of distortion distribution has been used to improve the performance of the Structural Similarity and Gradient Similarity (the modified methods are referred to as ADD-SSIM and ADD-GSIM, respectively). The authors of this approach have utilized the ranking-based weighting, frequency variation based on structural degradation measurement, and additional entropy gain multiplier. Recently, some other metrics being the extensions of the original SSIM have been proposed in the paper [41], which utilizes additional predictability of image blocks. The use of the fourth multiplicative component (block predictability) in the metric referred to as SSIM4 is based on the minimal value of mean squared error between the current block and the neighboring ones. Another modification is related to the use of color components (metrics denoted respectively as CSSIM and CSSIM4) and assumes simultaneous computations of metrics for several image scales in the YCbCr color space. Such obtained partial metrics are then averaged with weights obtained by maximizing the rank-order correlations for three datasets. Two other recent methods utilize contrast combined with visual saliency and Riesz transform with visual contrast. The first one, known as CVSSI (Contrast and Visual Saliency Similarity-Induced Index), has been proposed [42] by the authors of the above mentioned MCSD metric, as the result of the application of the weighted standard deviation of two quality maps obtained for the local contrast and the global visual saliency. The latter approach [43] called Riesz transform and Visual contrast sensitivity-based feature similarity (RVSIM) utilized a Log-Gabor filter for initial image decomposition followed by Riesz transform. Then, the similarity of local amplitude, phase, and direction characteristics is determined forming the similarity matrices subjected to weighting using the visual Contrast Sensitivity Function (CSF), forming a single similarity matrix. It is further combined with gradient magnitude similarity, calculated for the reference and distorted images in the same way as in the FSIM, and subjected to final pooling leading to the overall RVSIM index. Many of these metrics, as well as some others, have been recently combined using the neural networks for the assessment of remote sensing images [44] leading to promising results. Nevertheless, the direct application of such an approach for the quality assessment of the 3D prints would be troublesome due to the time necessary for the calculation of several metrics as well as the necessity of network training. Considering the variety of the proposed similarity-based approaches to image quality assessment, as well as their relatively short computation time (analyzed also in [44]), the above-described metrics have been examined in this paper to verify their usefulness for an automatic quality evaluation of the 3D printed surfaces, as well as the possibility of their combination, additionally converting them into no-reference methods due to potential applications in real-time systems.