# On-Board Flickering Pixel Dynamic Suppression Method Based on Multi-Feature Fusion
## 2 Methodology
### Motion Feature Extraction  
In this paper, the IRPTs are divided into two categories: space target and aircraft. The movement of the space target is restricted to a specific orbit. Meanwhile, the movement of aircraft is also constrained by specific flight envelop [23]. Therefore, the moving path of IRPT can be treated as smooth curvilinear motion within a short time. In terms of blind pixel, although blind pixels cannot move, the inter-frame correlation may cause an error path formed by adjacent blind pixels. Therefore, the blind pixels appear as static points or winding paths. According to the above analysis, we set up two kinds of motion feature models of blind pixels (MFBP model) to extract the motion feature of blind pixels. The static MFBP model with IRPT detection results as input is used to detect isolated blind pixels. Meanwhile, the dynamic MFBP model with IRPT tracking results as input detects adjacent blind pixels by evaluating the curvature degree of the path. The static MFBP model firstly calculates the frequency that a pixel is detected as the blind pixel. Then, compare this frequency with the threshold to detect isolated blind pixels, as shown in Equation (8). \[X_{MOst}(i,j)=\left\{ \begin{array}{ll}0,&\sum_{f=F-F_{length}+1}^{F}X_{d}(f,i,j)/F_{length}<\text{Th}_{MOost}\\ 1,&\sum_{f=F-F_{length}+1}^{F}X_{d}(f,i,j)/F_{length}\geq\text{Th}_{MOost}\end{array} \right., \tag{8}\]  
where \(X_{d}(f,i,j)\) is the result of IRPT detection. If \(X_{d}(f,i,j)\) is 1, it means that pixel \((i,j)\) is detected as potential blind pixel in \(f\)th frame. \(F\) presents current frame number while \(F_{length}\) presents the frame range of testing. Finally, \(X_{MOst}(i,j)\) is the result of static MFBP model matching. If \(X_{MOst}(i,j)\) equals to 1, it means that pixel \((i,j)\) may be blind pixel. Conversely, if \(X_{MOst}(i,j)\) equals to 0, this pixel may be normal. In terms of parameter selection, the threshold of static MFBP model (\(\text{Th}_{MOost}\)) is set to 0.3. However, this threshold needs to be adjusted according to frame frequency and moving state of IRPT. It is necessary to point out that, considering computational complexity and reliability, \(F_{length}\) is set to 10 to 20 in this paper. Dynamic FPMF model also evaluates within \(F_{length}\) frames and takes the path of IRPT tracking as input. Suppose that \((i_{fn},j_{fn})\) denotes the path points forms a certain path, and the subscript fn means the frame number. Using the result of IRPT tracking as input, pick up direction vectors from the path, we now describe the procedure as follows. Firstly, traverse all path points in frame order as the starting point of each direction vector. Then, traverse the path points whose distance to the starting point is greater than \(\sqrt{2}\) and the frame number is greater than the starting point, and choose the path point with the smallest frame number among them as the end point of the corresponding direction vector. Let \(\overset{\rightarrow}{D_{n}}\) be direction vectors and the subscript \(n\) means order number of direction vectors. Finally, the threshold of the dynamic MFBP model (Th\({}_{\text{MOdy}}\)) was introduced to evaluate the winding degree of a path, as shown in Equation (9). \[X_{MOdy}(i_{fn},j_{fn})=\left\{ \begin{array}{ll}0,&\frac{1}{n-1}\sum_{j=1}^{ n-1}\frac{\overset{\rightarrow}{D_{j+1}}\overset{\rightarrow}{D_{j}}}{ \left|\overset{\rightarrow}{D_{j+1}}\right|}<\text{Th}_{\text{MOdy}}\\ 1,&\frac{1}{n-1}\sum_{j=1}^{n-1}\frac{\overset{\rightarrow}{D_{j+1}}\overset{ \rightarrow}{D_{j}}}{\left|\overset{\rightarrow}{D_{j+1}}\right|}\geq\text{ Th}_{\text{MOdy}}\text{ }or\text{ }n\leq 3\end{array} \right., \tag{9}\]  
where \(X_{MOdy}(i_{fn},j_{fn})\) presents the matching result of the dynamic MFBP model. The left side of the inequality denotes the mean value of the angle transformation of the path direction vector.