# Blind Image Quality Assessment Based on Multi-Window Method and HSV Color Space
## Proposed Method
### Difference between NFMs  
Since different NFMs contain different information from receptive fields of different sizes, we calculate the differential feature map (DFM) between NFMs to measure more detailed information of image degradation. The DFM between two NFMs is calculated by  
\[D_{i}(m,n)=\left|\left(T_{i}(m,n)\right)^{2}-\left(T_{i+1}(m,n)\right)^{2}\right| \tag{11}\]  
where \(D_{i}\) are the \(i\)th DFMs, \(T_{i}\) and \(T_{i+1}\) are two different NFMs, \(m\in 1,2,\ldots,M\) and \(n\in 1,2,\ldots,N\) are the pixels indices, \(M\) and \(N\) are the image height and width, respectively, and \(i\in 1,2\) is the index of the DFMs.  
Our hypothesis is that the presence of distortions may affect the distribution properties of the DFMs, and measuring the distribution statistics in DFMs may better characterize image degradation. To visualize how the presence of distortions will affect the distributions of DFMs, we use five distorted images of different mean opinion score (MOS) values in the LIVE In the Wild Image Quality Challenge Database (WIQCD) [30] as an example. The MOS value of WIQCD database is in the range [0, 100], where higher scores represent higher quality. Figure 4 gives the five images in WIQCD database. Figure 5a visualizes the distributions of the DFMs between \(T_{1}\) and \(T_{2}\) for the five distorted images showed in Figure 4. It can be seen in Figure 5a that histograms of these DFMs follow the Weibull distribution, while the peak and tails of the five histograms are different. Therefore, we use Weibull model to fit the distribution of the DFMs. The probability density function associated with Weibull model is defined as  
\[f(x_{i};a_{i},b_{i})=\frac{b_{i}}{a_{i}}\left(\frac{x_{i}}{a_{i}}\right)^{b_{i }-1}\exp\bigg{(}-\left(\frac{x_{i}}{a_{i}}\right)^{b_{i}}\bigg{)},x_{i}>0 \tag{12}\]  
where \(a_{i}\) and \(b_{i}\) are the scale parameter and shape parameter of the \(i\)th DFM, respectively, and \(i\in 1,2\) is the index of DFMs.  
Figure 5b gives bar plots of \(a_{1}\) and \(b_{1}\) of the five histograms shown in Figure 5a. It is clear that \(a_{1}\) and \(b_{1}\) increase as the MOS value grows. This indicates that the distribution statistics of the DFMs can measure the quality variation and can be adopted as perceptual features.  
\begin{table}
\begin{tabular}{l c c c c} \hline
**Distortion** & \(\mathbf{p_{1,\text{H}}}\) & \(\mathbf{p_{1,\text{V}}}\) & \(\mathbf{p_{1,\text{MD}}}\) & \(\mathbf{p_{1,\text{SD}}}\) \\ \hline Reference & 0.3238 & 0.2689 & 0.0595 & 0.0600 \\ WN & 0.0902 & 0.0650 & 0.0086 & 0.0122 \\ JPEG & 0.4698 & 0.3991 & 0.1049 & 0.1041 \\ JP2K & 0.5367 & 0.4695 & 0.2773 & 0.2746 \\ PGN & 0.2821 & 0.2437 & 0.0430 & 0.0407 \\ GB & 0.5495 & 0.4930 & 0.3401 & 0.3359 \\ GCD & 0.3366 & 0.2781 & 0.0693 & 0.0705 \\ \hline \end{tabular}
\end{table}
Table 1: The average PLCC values along four orientations for the reference images and each type of distorted images in CSIQ database [29].  
Figure 4: The five distorted images in the WIQCD database [30]: (**a**) MOS = 25.33; (**b**) MOS = 35.89; (**c**) MOS = 48.94; (**d**) MOS = 54.58; and (**e**) MOS = 66.51.