# Research on a Convolution Kernel Initialization Method for Speeding Up the Convergence of CNN
## 2 Materials and Methods
### Local Binary Patterns  
Local binary patterns (LBP) is an operator that is used to describe local texture features. It was proposed by [PERSON], [PERSON], and [PERSON] in 1994 [18]. The algorithm calculates the gray value of the local area of the image point by point and respectively counts the times that different LBP values appear to describe the texture features of the image in the area. The characteristics of the algorithm are simple calculation, low complexity, and strong gray and rotation invariance. The algorithm is used to extract local texture features of images and is widely used in image retrieval, face recognition, and military fields. It is highly respected by researchers. The original LBP operator is defined in the window whose size is \(3\times 3\). The central pixel of the window is the threshold that is compared with the gray value of the adjacent 8 pixels. If the surrounding pixel value is bigger than the central pixel value, the surrounding pixel value is marked as 1; otherwise, it is 0. The 8-bit binary number is obtained after comparing, which is the LBP operator. Because it is an 8-bit binary number, there are 256 values in total. The values are used to represent the texture information of the area. The whole process is shown in Figure 3, and the formula is shown in (6). \[\text{LBP}(x_{c},y_{c})=\sum_{n=0}^{N-1}2^{n}s(i_{n}-i_{c}) \tag{6}\]  
where \(N=8\), \((x_{c},y_{c})\) is the central pixel, \(i_{c}\) is the gray value of the central pixel, \(i_{n}\) is the gray value which is adjacent to the center pixel, and \(s\) is a symbolic function:  
\[s(x)=\left\{ \begin{array}{ll}1&x\geq 0\\ 0&x<0\end{array} \right. \tag{7}\]The pixel value of the eight-neighborhood is bigger than the central point value; the pixel value is marked as 1; otherwise, it is marked as 0 in Formula (7). Then the 8-bit binary number is obtained by reading clockwise. As shown in the above figure, the 8-bit binary number is 11100001, which is converted to a decimal number, 225. There is no requirement for the reading order of binary numbers if only the same order is kept in the processing. The original LBP operator only covers a small area within a fixed radius, which is the biggest drawback. Therefore, it is not suitable for different sizes and frequency textures. [PERSON] et al. improved the LBP operator [19]. The 3 \(\times\) 3 neighborhood is extended to any neighborhood, and the square neighborhood is replaced by a circular neighborhood. The improved algorithm has any number of pixels in a circular neighborhood whose radius is R, so the LBP operator of P sample points is obtained. LBP\({}_{R}^{P}\) means to take P sample points in a circular area whose radius is R. It is shown in Figure 4.  
Because R is the radius of the neighborhood and P is the number of sample points, the number of sample points may not be an integer. In order to solve this problem, double-line interpolation is used to determine the pixel value of the point. The linear combination of the four-pixel values around the point is used to represent the value of the point [20; 21]. The LBP operator has gray invariance from the definition of LBP. Gray invariance means that the illumination change has little impact on the description. As a result, it has strong robustness to illumination [22]. The 8-neighborhood is taken as an example. When the illumination changes, it is difficult to change the relationship between the center pixel and the surrounding 8 pixels. Because the illumination change is not a single pixel  
Figure 4: The improved LBP operator. Figure 3: Local binary patterns (LBP) operator. change but a regional change. When there is strong light on the 9 pixels, the 9-pixel values will increase at the same time, but the relative relationship of the size remains unchanged. Although the original LBP has gray invariance, it does not have rotation invariance. The different LBP operators will be obtained after the image is rotated, by which, [PERSON] et al. improved the LBP algorithm. They proposed LBP operators with rotation invariance [11].