# Blind Image Quality Assessment Based on Multi-Window Method and HSV Color Space
## Proposed Method
### Correlation Coefficient between Adjacent Pixels in NFMs  
There are strong structural correlations among neighboring pixels [15]. By examining the relationship between neighboring pixels in the NFMs, we found that the presence of distortions will alter the global correlation between spatially adjacent pairs in natural images. PLCC is employed to quantify the correlation changes between adjacent pairs in the NFMs. The four PLCC values along horizontal (\(p_{\text{H}}\)), vertical (\(p_{\text{V}}\)), main-diagonal (\(p_{\text{MD}}\)) and secondary-diagonal (\(p_{\text{SD}}\)) orientations are calculated by  
\[p_{i,\text{H}}=P(T_{i}(1:M,1:N-1),T_{i}(1:M,2:N)) \tag{6}\]  
\[p_{i,\text{V}}=P(T_{i}(1:M-1,1:N),T_{i}(2:M,1:N)) \tag{7}\]  
\[p_{i,\text{MD}}=P(T_{i}(1:M-1,1:N-1),T_{i}(2:M,2:N)) \tag{8}\]  
\[p_{i,\text{SD}}=P(T_{i}(2:M,1:N-1),T_{i}(1:M,2:N)) \tag{9}\]  
where \(T_{i}\) is the \(i\)th NFMs, \(i\in{1,2,3}\) is the NFM index, \(M\) and \(N\) are the height and the width of NFMs, respectively, and  
\[P(X,Y)=\frac{\sum\limits_{m=1}^{M}\sum\limits_{n=1}^{N}(x_{m,n}-\overline{X}) (y_{m,n}-\overline{Y})}{\sqrt{\sum\limits_{m=1}^{M}\sum\limits_{n=1}^{N}(x_{m, n}-\overline{X})^{2}\sum\limits_{m=1}^{M}\sum\limits_{n=1}^{N}(y_{m,n}- \overline{Y})^{2}}} \tag{10}\]  
where \(X\) and \(Y\) are two non-overlapping blocks with equal size of the NFM, \(\overline{X}\) and \(\overline{Y}\) are the mean values of \(X\) and \(Y\), \(m\in{1,2,\ldots,M}\) and \(n\in{1,2,\ldots,N}\) are the pixels indices, and \(M\) and \(N\) are the blocks height and width, respectively. To illustrate how distortion types and distortion levels will affect the PLCC values between adjacent pairs, we take images in CSIQ database [29] as an example. Figure 3 plots the PLCC values between neighboring pixels of the first NFM along four orientations for six types of distorted images in CSIQ database. The six distortion types are additive Gaussian white noise (WN), JPEG2000 compression (JP2K), JPEG compression (JPEG), pink Gaussian noise (PGN), Gaussian blur (GB), and global contrast decrements (GCD). Each distortion type contains four distorted images with different difference mean opinion scores (DMOS) values. The DMOS value of CSIQ database is in the range [0, 1], where higher scores represent lower quality. In Figure 3, we plot the curve of PLCC values varying with DMOS values for the first NFM for each type of distorted images and for the reference images, where DMOS = 0 corresponding to PLCC values of the reference images. It is clear that the PLCC values of WN and PGN images decrease gradually as the DMOS value increases, while the PLCC  
Figure 2: 3D scatter plots between AGGD parameters \(\alpha\), \(\sigma_{T}^{2}\) and \(\sigma_{T}^{2}\) in horizontal orientation of the three NFMs, where each point in the scatter plots represent one distorted image in LIVE [28] database: (**a**) scatter plots for the first NFM; (**b**) scatter plots for the second NFM; and (**c**) scatter plots for the third NFM. values of JPEG, JP2K and GB images increase significantly as the DMOS value increases. This implies that the PLCC values between spatially adjacent pixels can well characterize the presence of distortions. Furthermore, we measure the PLCC values along four orientations for all the reference and distorted images in CSIQ database to more precisely describe the effect of the presence of distortions. Table 1 lists the average values of PLCC values along four orientations for each distortion type and the reference images. It is clear that the average PLCC values of different distortion types are quite different with the average PLCC values of the reference images. The average PLCC values of WN and PGN images are smaller than the average PLCC values of the reference images. The main reason is that there are many random signals in WN and PGN images, which will increase the differences between neighboring pixels and will also reduce the correlation between neighboring pairs.