## 2 Materials and Methods
### Moving Object Detection Based on Robust Feature Threshold Segmentation
Because the background region of the previous frame image can be transformed into the background region of the next frame image by the affine transformation, the homography matrix \(M\) of the affine transformation of the background model at the time of \(t\to t+1\) should satisfy the following equation:  
\[M_{t\to t+1}*{{I_{t}}^{B}}={{I_{t+1}^{B}}} \tag{11}\]  
where \({{I_{t}}^{B}}={{(ij1)}^{T}}\) represents each pixel in the image background area at time \(t\); \({{I_{t+1}^{B}}}\) represents each pixel in the image background area at time \(t+1\); and \(M_{t\to t+1}\) represents the background model affine transformation matrix calculated from time \(t\) to \(t+1\). According to the optical flow estimation, the corresponding points in the next frame image \({{I_{t+1}}^{B}}\) can be determined by adding each pixel \({{(ij1)}^{T}}\) in \({{I_{t}}^{B}}\) into its estimated optical flow value \(\omega={{(uv0)}^{T}}\) and is expressed as follows:  
\[{{I_{t+1}}^{B}}={{I_{t}}^{B}}+\omega \tag{12}\]  
Because the affine transformation of the background region and the optical flow estimation of the same image are equal to the corresponding points in the next frame image \({{I_{t+1}}^{B}}\) (combining Equations (11) and (12)), the affine transformation matrix calculation with a background model of size \(3\times 3\) can be determined as follows:  
\[M_{t\to t+1}*{{I_{t}}^{B}}={{I_{t}}^{B}}+\omega \tag{13}\]  
The MSAC algorithm was used to solve and optimize Equation (13) to exclude the feature points that do not belong to the background model because of the uncertainty of the location of the extracted feature points which may be located in the background area or the foreground area. To increase the computational efficiency, feature points and the corresponding optical flow estimation were calculated to calculate the affine transformation matrix on the optical flow of feature points. This process finally filters out the stable feature points in the background model area, known as robust feature points. Figure 4 shows the outcomes of robust feature point extraction, wherein Figure 4a,b depict the current and the next frames, respectively. Figure 4c shows the feature points extracted by the features from the accelerated segment test (FAST) feature extraction algorithm [34] in the previous image. Figure 4d presents the FAST robust background feature points, which are selected from the FAST feature points by background model affine transformation matrix calculation and MSAC methods with their optical flow values. Figure 4e,f illustrate the speeded-up robust features (SURF) feature points [35] and the SURF robust background feature points, respectively. Figure 4g,h show the Harris feature [36] points and the Harris robust background feature points, respectively. The results demonstrate less feature information extracted by the FAST algorithm in Figure 4c. The final selected background robust feature points are concentrated in one area, which easily causes estimation errors in the calculated background model affine transformation matrix. It is difficult to screen out the correct background feature points. The SURF feature points in the moving target area are misinterpreted as the background feature points in Figure 4d. Figure 4e shows that the number of feature points extracted by SURF is too much, which increases the computational complexity of the background model matrix. The final extracted robust feature points also constitute the feature points in the moving target area (Figure 4f). Figure 4g,h demonstrate that the Harris feature extracts the feature points at the strong inflection points, which are more robust. The Harris feature points are quantity reasonable and distribution balanced. The screened robust feature points were shown in Figure 4h with no mistakes. The results revealed that the Harris robust background feature points are more accurate than FAST and SURF and are more suitable for estimating the background change model. All the robust background feature points screened exhibit the highest accuracy.