# Blind Quality Evaluation for Screen Content Images Based on Regionalized Structural Features
## 2 Proposed Method
### Feature Extraction of Textual Regions
The magnitude \(M^{1}(x,y)\) and orientation \(O^{1}(x,y)\) of the first-order derivative are calculated as  
\[M^{1}(x,y)=\sqrt{d_{h}^{1}(x,y)^{2}+d_{v}^{1}(x,y)^{2}} \tag{3}\]  
\[O^{1}(x,y)=arctan\frac{d_{v}^{1}(x,y)}{d_{h}^{1}(x,y)} \tag{4}\]  
Similarly, to compute the magnitude and orientation of the second-order derivative, the Prewitt filter is employed based on the results of the first-order derivative. In the same manner, the \(n\)th-order derivative can be calculated based on the results of the \((n-1)\)th-order derivative. Secondly, the IHOG features of textual regions of the SCI are computed. Textual regions are split into non-overlapping blocks; each block includes four neighboring cells and each cell comprises \(8\times 8\) pixels. For each cell, we calculate the statistical histogram of the orientation of the first-order derivative. In this histogram, the horizontal coordinate denotes the orientation of the first-order derivative, which is divided into nine intervals. Each orientation interval is \(40^{\circ}\). If the orientation of the first-order derivative of one pixel belongs to an interval, the magnitude of the first-order derivative of this pixel is accumulated onto the corresponding ordinate value of this interval. Since each orientation interval corresponds to one HOG feature, each cell generates nine HOG features and each block produces 36 HOG features. To compress the strength of the HOG features in a block, the normalization operation is conducted by employing the \(L_{2}\) norm, which is given as  
\[h_{N,m,j}=\frac{h_{m,j}}{\left\|\overrightarrow{h_{m}}\right\|_{2}+\varepsilon},\ \overrightarrow{h_{m}}=[h_{m,1},h_{m,2},\ldots,h_{m,36}] \tag{5}\]  
where \(h_{m,j}\) and \(h_{N,m,j}\) denote the \(j\)th HOG feature of the \(m\)th block before and after the normalization operation, respectively; the symbol \(\left\|\cdot\right\|_{2}\) represents the operation of the \(L_{2}\) norm; \(\overrightarrow{h_{m}}\) denotes the vector, which is comprised of 36 HOG features in the \(m\)th block; and \(\varepsilon\)stands for a small constant and is set to 0.1. The HOG features of the zero-order derivative of textual regions are calculated by the average values of overall blocks in textual regions, which are given as  
\[h_{a,j}^{0}=\frac{1}{N_{B}}\sum_{m=1}^{N_{B}}h_{N,m,\ j}\quad(j=1,2,\ldots,36) \tag{6}\]  
where \(h_{a,j}^{0}\) denotes the \(j\)th HOG feature of the zero-order derivative of textual regions and \(N_{B}\) represents the number of the blocks in textual regions. As a result, the zero-order derivative of textual regions produces 36 HOG features. Similarly, we calculate the HOG features of other-order derivatives. In this paper, HOG features of only zero-, first- and second-order derivatives are adopted and HOG features of higher-order derivatives whose orders are greater than two are not adopted. Figure 5 shows the examples of the IHOG features of textual regions. Seven distortion types of distorted SCIs in Figure 5 include Gaussian noise (GN), Gaussian blur (GB), motion blur (MB), contrast change (CC), JPEG compression (JPEG), JPEG2000 compression (JP2K) and layer-segmentation based compression (LSC). In Figure 5, (b1-b8)are the HOG features of the first-order derivative of textual regions contained in corresponding (a1-a8). From (b1-b8) of Figure 5, we can see that textual regions of distorted SCIs with different distortion types result in different IHOG features. Thus, the IHOG features have the discriminative ability for different distortion types. In this paper, the total IHOG features \(F_{T}\) of textual regions of an SCI are derived as  
\[F_{T}=\left[h_{a,j}^{0},h_{a,j}^{1},h_{a,j}^{2};\ j=1,2,\ldots,36\right] \tag{7}\]  
where \(h_{a,j}^{0}\), \(h_{a,j}^{1}\) and \(h_{a,j}^{2}\) denote the \(j\)th HOG features of zero-, first- and second-order derivatives, respectively.