# Quality Assessment of 3D Synthesized Images Based on Textural and Structural Distortion Estimation
## 4 Experiments and Results
### Performance Evaluation Parameters  
To evaluate the performance of the proposed method we used different statistical tools, including the Pearson linear correlation coefficient (PLCC), Spearman rank-order correlation coefficient (SROCC), Kendall rank-order correlation coefficient (KROCC), root-mean-square error (RMSE), and mean absolute error (MAE). Before computing these parameters, the scores obtained by objective quality metrics were mapped to subjective deferential mean opinion score (DMOS) values using the nonlinear logistic regression described in [72]:  
\[DMOS_{p}=\beta_{1}\bigg{(}\frac{1}{2}-\frac{1}{1+exp(\beta_{2}(o-\beta_{3}))} \bigg{)}+\beta_{4}o+\beta_{5} \tag{12}\]  
Figure 3: Top row: sample reference images from Balloon (**a**), Dancer (**b**), Love_bird1 (**c**), Poznan_Hall2 (**d**), and Poznan Street (**e**) 3D sequences, from the MCL-3D dataset. Bottom row: top image with AWN (**f**), Gauss (**g**), Sample (**h**), JPEG (**i**), and JP2K (**j**) distortions, respectively.  
where \(o\) is the score obtained by the objective quality metric, \(DMOS_{p}\) is the mapped score, and \(\beta_{1},\ldots,\beta_{5}\) are the regression parameters.  
The Pearson linear correlation coefficient (PLCC) is used to determine the linear correlation between two continuous variables. Since this method is based on covariance computation, it is considered the best method for measuring statistical relationships. The method was used in the prediction accuracy test. Let \(x\) represent the MOS values, \(y\) represent the mapped scores, and \(\bar{x}\) and \(\bar{y}\) represent the mean values of \(x\) and \(y\), respectively. PLCC is computed as  
\[PLCC=\frac{\sum_{i=1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sqrt{\sum_{i=1}^{n}( x_{i}-\bar{x})^{2}}\sqrt{\sum_{i=1}^{n}(y_{i}-\bar{y})^{2}}} \tag{13}\]  
The Pearson correlation coefficient describes how strong the relationship between subjective MOS and evaluated objective scores is. The value lies between \(-1\) and \(1\). Values closer to \(1\) represent a strong relationship.  
The Spearman rank-order correlation coefficient (SROCC) is a nonparametric measure of rank correlation. It assesses how well the relationship between two variables can be described using a monotonic function. The difference between PLCC and SROCC is that the former only assesses linear relationships whereas the latter assesses monotonic relationships that may or may not be linear. For \(n\) observations, the SROCC can be computed as  
\[SROCC=1-\frac{6\sum_{i=1}^{n}(x_{i}-y_{i})^{2}}{n(n^{2}-1)} \tag{14}\]  
The Kendall rank correlation coefficient (KROCC) is another nonparametric measure to determine the relationship between two continuous variables. Like SROCC, it assesses associations based on the ranks of data. It is used to test the similarities in data when they are ranked by quantities.  
\[KROCC=\frac{n_{c}-n_{d}}{\frac{1}{2}n(n-1)} \tag{15}\]  
where \(n\) is the sample size, \(n_{c}\) is the number of concordant pairs and \(n_{d}\) is the number of discordant pairs.  
Root-mean-square error (RMSE) is the most widely used performance evaluation measure and it computes the prediction error [73]. Since the method takes the square of the error before computing the average, it gives a relatively high weight to a large error and that is why it is considered an important method for performance evaluation.  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{n}(x_{i}-y_{i})^{2}}{n}} \tag{16}\]  
Mean absolute error (MAE) is another method to compute the difference between two continuous variables. MAE is a linear score that means that all the individual differences are weighted equally in average.  
\[MAE=\frac{\sum_{i=1}^{n}|y_{i}-x_{i}|}{n} \tag{17}\]  
Since PLCC, SROCC, and KROCC are the correlations and MAE and RMSE are the errors, large values of correlations and small values of errors indicate a better performance of the quality metric.