## 3 Target Discrimination
### The MLBP Feature Description  
The LBP operator is gray rotation-invariant [29]. However, the LBP method only considers the size relationship between the central and neighboring pixel, with no contrast relationship. Therefore, different contrast distributions have the same LBP value as shown in Figure 8.  
The modified LBP feature (MLBP) is proposed in this paper to solve this problem. The following process is for any pixel (i, j) in the image. Firstly, the local contrast between the central pixel and neighbor pixels is calculated:  
\[g_{p}=I_{p}-I_{(i,j)} \tag{22}\]  
where \(I_{(i,j)}\) denotes the gray value of the i-th row and the j-th column of the image. \(I_{p}\) is the gray value of the neighbor pixel centered in the pixel (i, j), and p = 1, 2,... N. N represents the number of pixels in the neighbor field, and it is set to 8 in this paper. \(g_{p}\) is a contrast value between the central pixel and one neighbor pixel. Figure 7: The regions of interest (ROIs) are extracted by the proposed method. (**a**) Test images. (**b**) Saliency maps generated by our MPQFT in Section 2.2. (**c**) Image segmentation by the method in Section 2.3. Secondly, the maximum (maxC) and minimum (minC) of \(g_{p}\)(p = 1, 2,... N) can be found. The range of values between maxC and minC is then divided into L levels. Therefore, each contrast value corresponds to a certain level. The level of \(g_{p}\) is calculated as follows:  
\[\mathfrak{l}_{p}=\left\lceil\frac{g_{p}-\min C}{(\max C-\min C)/L}\right\rceil \tag{23}\]  
where p = 1, 2,... N. \(\lceil\cdot\rceil\) is a symbol of rounding in the small direction, maxC and minC represent the maximum and minimum contrast values, respectively. L represents the number of levels and is set to 4 based on a large number of experiments. If \(\mathfrak{l}_{p}>L\), then \(\mathfrak{l}_{p}=L\). The contrast level \(l_{p}\) is transformed in to a binary description of 0 or 1:  
\[S_{p}=\left\{ \begin{array}{c}1,l_{p}=\mathrm{L}\\ 0,l_{p}\
eq\mathrm{L}\end{array} \right. \tag{24}\]  
For the pixel (i, j), the binary descriptor MLBP is a series of numbers of 0 and 1 constructed with \(S_{p}\), \(MLBP=\left\{S_{p}\right\}\), and \(p=1,2,\ldots,N\). In order to obtain rotation invariance, the number of exchanges between 0 and 1 is used to describe it again, and the rotation-invariant MLBP proposed in this paper is finally obtained as follows:  
\[MLBP^{rin}=\left\{ \begin{array}{c}\sum\limits_{p=1}^{N}S_{p},if(U(MLBP)<=2) \\ N+1\end{array} \right. \tag{25}\]  
\[U(MLBP)=\sum\limits_{p=2}^{N}\left|f(s_{p}-s_{p-1})\right|+\left|f(s_{N})-f(s_ {1})\right| \tag{26}\]  
\[f(x)=\left\{ \begin{array}{c}1,x\geq 0\\ 0,x<0\end{array} \right. \tag{27}\]  
where \(U(MLBP)\) represents the number of exchanges between 0 and 1 for the series. \(MLBP^{rin}\) is a rotation invariance binary descriptor. One example of the MLBP description process is given in Figure 9. The value of the central pixel is 120, N = 8, L= 4, and the size of the neighbor is 8 pixels, displayed in blue in Figure 9. The surrounding pixel values are compared with the central value to obtain the contrast map as shown in Figure 9b. The level of each neighbor pixel is calculated according to Equation (22) as shown in Figure 9c. The initial binary description of this area is 00000101, according to Equation (23), and the number of exchanges between 0 and 1 is 4. The rotation invariance binary descriptor of this area is 9. Figure 8: Example of local binary pattern (LBP). (**a**) The contrast between the central pixel and neighboring pixels is very small. (**b**) The contrast between the central pixel and neighboring pixels is very high. The square neighbor area is used as an example above. In the actual application, a circular area can be adopted, and the bilinear interpolation method is applied for the estimation of the value that is not at the center of the pixel. According to the method proposed in this paper, the binary description of area (a) and (b) in Figure 8 are 11101111 and 00001111, respectively. The rotation-invariant MLBP is 1 and 2.