# Blind Image Quality Assessment Based on Multi-Window Method and HSV Color Space
## Proposed Method
### Distribution Statistics within Different Receptive Fields  
It has been proved that the empirical distribution of the normalized image can be modeled by a zero mean GGD model [15]. For the \(i\)th NFM, the probability density function associated with the GGD is defined as  
\[f(x;\alpha_{i},\sigma_{i}^{2})=\frac{\alpha_{i}}{2\beta_{i}\Gamma(1/\alpha_{i} )}\text{exp}\left(-\left(\frac{|x|}{\beta_{i}}\right)^{2}\right) \tag{4}\]  
where \(\beta_{i}=\sigma_{i}\sqrt{\frac{\Gamma(1/\alpha_{i})}{\Gamma(3/\alpha_{i})}}\), \(\alpha_{i}\) represents the shape parameter of the distribution, \(\sigma_{i}^{2}\) is the distribution variance, and \(\Gamma(x)=\int_{0}^{\infty}t^{x-1}e^{-t}dt,x>0\) is a Gamma function. Gamma function is an infinite generalized integral, where \(t\) is the integral variable of this infinite generalized integral.  
Distortions will also affect the distributions of pairwise products of neighboring normalized coefficients along horizontal, vertical, main-diagonal and secondary-diagonal orientations [15]:\(H_{i}(i,j)=T_{i}(i,j)T_{i}(i,j+1)\), \(V_{i}(i,j)=T_{i}(i,j)T_{i}(i+1,j)\), \(MD_{i}(i,j)=T_{i}(i,j)T_{i}(i+1,j+1)\), and \(SD_{i}(i,j)=T_{i}(i,j)T(i+1,j-1)\). The distributions of these pairwise products exhibit regular structure and can be modeled by the AGGD model [15], which is defined by  
\[f(x;\gamma_{i},\sigma_{i,l}^{2},\sigma_{i,r}^{2})=\left\{\begin{array}{l} \frac{\gamma_{i}}{(\beta_{i,l}+\beta_{i,r})\Gamma(1/\gamma_{i})}\exp\left(- \left(\frac{-x}{\beta_{i,l}}\right)^{\gamma_{i}}\right),x<0\\ \frac{\gamma_{i}}{(\beta_{i,l}+\beta_{i,r})\Gamma(1/\gamma_{i})}\exp\left(- \left(\frac{x}{\beta_{i,r}}\right)^{\gamma_{i}}\right),x\geq 0\end{array}\right. \tag{5}\]  
where \(\gamma_{i}\) is the shape parameter that adjusts the shape of the distribution, \(\sigma_{i,r}^{2}\) and \(\sigma_{i,l}^{2}\) are scale parameters controlling the spread on right and left sides of the distribution, \(\beta_{i,r}=\sigma_{i,r}\sqrt{\Gamma(1/\gamma_{i})/\Gamma(3/\gamma_{i})}\), \(\beta_{i,l}=\sigma_{i,l}\sqrt{\Gamma(1/\gamma_{i})/\Gamma(3/\gamma_{i})}\), and \(\Gamma(x)=\int_{0}^{\infty}t^{x-1}e^{-t}dt,x>0\) is a Gamma function. We estimate the parameters \(\alpha_{i}\) and \(\sigma_{i}^{2}\) from the GGD fit of the three NFMs, and estimate the parameters \(\gamma_{i},\sigma_{i,r}^{2},and\sigma_{i,l}^{2}\) from the AGGD fit of pairwise products of neighboring pixels in the three NFMs along four orientations.  
To show how the GGD and AGGD parameters of different NFMs distribute in the parameter space, we randomly select 300 distorted images from three different quality ranges in the LIVE database [28]. The DMOS value of LIVE database is in the range [0, 100], where higher scores represent lower quality. It can be seen in Figure 1 that GGD parameters extracted from the distorted images of different quality regions occupy different regions of the parameter space. Relatively speaking, the distribution statistics of each of the three NFMs have their own value ranges in the parameter space. Meanwhile, it can be seen in Figure 2 that AGGD parameters of the three quality regions are also separated well in the parameter space. Therefore, we employ the GGD and AGGD parameters as perceptual features to reflect the luminance intensity changes in the distorted images.  
Figure 1: 2D scatter plots between GGD parameters \(\alpha\) and \(\sigma^{2}\) of the three NFMs, where each point in the scatter plots represents 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.