# Two Low-Level Feature Distributions Based No Reference Image Quality Assessment
## 3 TLLFD for NR IQA
### Low-Level Feature Distribution  
#### 3.2.1 Local Binary Pattern  
The traditional rotation invariant uniform local binary pattern (LBP) operator [9; 10; 11] can be defined as:  
\[LBP_{P,R}^{riu2}=\left\{\begin{array}{l}\sum\limits_{i=0}^{P-1}S(g_{i}-g_{c }),U(LBP_{P,R})\leq 2\\ P+1,\text{others}\end{array}\right. \tag{4}\]  
\[U(LBP_{P,R})=|S(g_{P-1}-g_{c})-S(g_{0}-g_{c})|+\sum\limits_{i=1}^{P-1}|S(g_{i} -g_{c})-S(g_{i-1}-g_{c})| \tag{5}\]  
\[S(x)=\left\{\begin{array}{l}1,x\geq 0\\ 0,x<0\end{array}\right. \tag{6}\]  
where LBP superscript \"riu2\" denotes the rotation invariant \"uniform\" patterns, and \(U\) value represents the number of transitions from 0 to 1 or from 1 to 0 with \(U\) value less than or equal to 2. \(R\) is the neighborhood radius, \(g_{c}\) is the gray value of the central pixel point, \(P\) represents the number of neighborhood pixels around the central pixel point \((x_{c},y_{c})\), and \(g_{i}\) represents the gray value of the neighborhood pixel point \(i\),\(i=0,1,\ldots,P-1\).  
The rotation invariant uniform LBP pattern eventually generates only \(P+2\) dimensional texture features, which include \(p+1\) uniform pattern and 1 non-uniform pattern. So, the dimension is significantly lower than traditional LBP. In the specific application, the rotation invariant uniform LBP method still has some limitations in scale size and image noise. Different from the traditional LBP, the preprocessing method of formula (2) is used to extract the LBP features of different scales, which is more expressive and discriminative. For solving the sensitivity of LBP to image noise, [PERSON] et al. [23] investigated completed LBP (CLBP). This method analyzes the LBP algorithm from the perspective of local difference sign-magnitude transform. Therefore, the CLBP method will be explored at each position in the texture image to extract texture features, which is defined as [23]:  
\[CLBP_{P,R}^{riu2}=\left\{\begin{array}{l}\sum\limits_{i=0}^{P-1}S(g_{i}-g_{c },T),U(CLBP_{P,R})\leq 2\\ P+1,\text{others}\end{array}\right. \tag{7}\]  
\[S^{\prime}(x,T)=\left\{\begin{array}{l}1,x\geq T\\ 0,x<T\end{array}\right. \tag{8}\]  
where \(T\) is a threshold parameter to be determined adaptively. If the \(T\) value is large, CLBP tends to describe the characteristics of image texture which changes dramatically. Conversely, if the \(T\) value is small, CLBP tends to describe the details of image texture information. When \(T=0\), namely \(CLBP-S_{P,R}^{riu2}\), similar to \(LBP_{P,R}^{riu2}\). When \(T\
eq 0\), namely \(CLBP-M_{P,R}^{riu2}\). Here, \(T\) in the image is set to \(\frac{1}{P}\sum\limits_{l=1}^{P-1}|g_{i}-g_{c}|\).  
After applying CLBP operator, local \(CLBP-S\) and \(CLBP-M\) map can be obtained. Then, the global structural features are extracted from \(CLBP-S\) and \(CLBP-M\) map as the visibility weighted \(H_{GTLBP-S}\) and \(H_{GTLBP-M}\) histogram, which are presented as following:  
\[\begin{array}{c}H_{GTLBP-S_{P,R,T}}(k)=\sum\limits_{i=1}^{M}\sum\limits_{j=1 }^{N}\left|\hat{I}(i,j)\right|f\left(CLBP{S_{P,R}^{tri2}}(i,j),k\right)\\ H_{GTLBP-M_{P,R,T}}(k)=\sum\limits_{i=1}^{M}\sum\limits_{j=1}^{N}\left|\hat{I}( i,j)\right|f\left(CLBPM_{P,R}^{tri2}(i,j),k\right)\end{array} \tag{9}\]  
Here  
\[f(x,y)=\left\{\begin{array}{c}1,x=y\\ 0.\text{others}\end{array}\right. \tag{10}\]  
where \(k\in[0,K],K=9\) is the maximum value of \(GTLBP\) model, \(M\times N\) denotes the image size, and \(\hat{I}(i,j)\) is MSCN coefficients.  
Although LBP method is widely used in many fields, it still needs further research and improvement. Some researchers have begun to study multi-feature fusion, which combines LBP with other features more effectively. Generally, features should be complementary to each other for different types of image databases and different fields. Compared with LBP, the gradient has better ability to describe the edge information of the image.