# A No Reference Image Quality Assessment Metric Based on Visual Perception +
## 3 Extraction Model of Visual Region of Interest
### Algorithm Improvement
#### 3.2.1 Texture Feature Extraction  
Texture is an important visual cue, which is a common and difficult feature in the image. The texture feature is consistent with human visual perception process and plays an important role in the region of interest. There are many methods to extract texture features of images currently, such as wavelet extraction methods, gray level co-occurrence matrix (GLCM) extraction methods and so on. In recent years, the wavelet methods have been widely used in many fields. In literatures [39; 40], the authors introduced the wavelet method into the medical field and had achieved considerable success. In the former article, the authors used the discrete wavelet packet transform (DWPT) to extract wavelet packet coefficients from MR brain images. In the latter article, to help improve the directional selectivity impaired by discrete wavelet transform, they proposed a dual-tree complex wavelet transform (DTCWT), which was implemented by two separate two-channel filter banks. DTCWT obtained directional selectivity by using approximately analytic wavelets. At each scale of a two dimensions DTCWT, it produces in total six directionally selective sub-bands (\(\pm 15^{\circ}\), \(\pm 45^{\circ}\), \(\pm 75^{\circ}\)) for both real and imaginary parts. The method can obtain more information about the direction of the images. However, Gabor wavelet is an important method of texture feature extraction. It not only can extract texture features effectively, but also eliminate redundant information. In addition, the frequency and direction of Gabor filter that close to the human visual system for frequency and direction, and they were used for texture representation and description. A series of filtered images can be obtained by convolution of the image with the Gabor filter, and the information of each image on the scale and direction is described in each image [41]. In this paper, we use Gabor wavelet to extract texture features of each filter image. Two dimensional Gabor function \(g(x,y)\) can be expressed as:  
\[g(x,y)=\left[\frac{1}{2\pi\sigma_{x}\sigma_{y}}\right]\exp\left[-\frac{1}{2} \left(\frac{x^{2}}{\sigma_{x}^{2}}+\frac{y^{2}}{\sigma_{y}^{2}}\right)+2\pi iWx\right] \tag{1}\]  
where \(W\) is Gaussian function of polyphonic system frequency. According to the accordance with human visual system, \(W\) = 0.5. The Fourier transform of \(g(x,y)\) can be expressed as:  
\[G(u,v)=\exp\left\{-\frac{1}{2}\left[\frac{(u-W)^{2}}{\sigma_{x}^{2}}+\frac{v^{ 2}}{\sigma_{y}^{2}}\right]\right\} \tag{2}\]  
where \(\sigma_{x}=\frac{(a+1)\sqrt{2\ln 2}}{2\pi a^{\eta}(a-1)U_{M}},\sigma_{y}= 1\left/\left[2\pi\tan(\frac{\pi}{2N})\sqrt{\frac{U_{h}^{2}}{2\ln 2}-\left( \frac{1}{2\pi\sigma_{x}}\right)^{2}}\right].\) The frequency spectrum is shown in Figure 3.  
Figure 3: Frequency component of Gabor filter. In order to get a set of self-similar filters, we use \(g(x,y)\) as the generating function, and do moderate scale expansion and rotation transformation on it. That is, Gabor wavelet:  
\[g_{mn}(x,y)=a^{-m}g(x^{\prime},y^{\prime}) \tag{3}\]  
where \(a>1,\ m,\ n\) are integer. \(x^{\prime}=a^{-m}(x\cos\theta+y\sin\theta)\), \(y^{\prime}=a^{-m}(-x\sin\theta+y\cos\theta)\), \(a=(U_{k}/U_{M})^{\frac{1}{M-1}}\), where \(\theta=n\pi/k\), and k is the number of direction. \(m\), \(n\) are scale and direction respectively, \(n\in[0,\) k\(]\). Figure 4 are four different directions of the Gabor wavelet. Then we use the Gabor wavelet transform to extract the texture features of the image. For an image \(I(x,y)\), its Gabor wavelet transform can be defined as:  
\[T_{m,n}(x,y)=\sum_{x_{1}}\sum_{y_{1}}I(x,y)g_{mn}*(x-x_{1},y-y_{1}) \tag{4}\]  
where, \(*\) represents the conjugate complex, and the texture features are calculated as shown in Formula (5). In the model, the center-surround is implemented as the difference between fine and coarse scales. The center represent a pixel at scale \(c\in\{2,\) 3, 4\(\}\), and the surround represent the corresponding pixel at scale \(s=c+\delta\), \(\delta\in\{3,\) 4\(\}\).