## 3 Experiment and Results  
### Experimental Environment and Evaluation Indicators  
(1) Experimental environment  
To verify the algorithm's effectiveness, the Max Planck Institute Sintel Flow Dataset [37], a commonly used public dataset for image optical flow estimation, was applied to verify the accuracy of the proposed enhanced optical flow field estimation and moving object detection based on robust feature points. To reflect the algorithm's accuracy, the optical flow estimation and comparison algorithms are LK [38], HS pyramid [39], Black & Anandan (B&A) [40], and Brox [41], among others. These are frequently used optical flow estimation methods. The optical flow threshold segmentation comparison algorithm is Otsu, which is the most commonly used algorithm for moving target detection based on optical flow.  
(2) Evaluation indicators  
In this paper, the accuracy of optical flow estimation [32] is evaluated by endpoint error (EPE) and average angular error (AAE), where EPE represents the Euclidean distance between the estimated optical flow value \((u,v)\) and the real optical flow value \((U,V)\). AEE represents the average angle between the estimated optical flow vector \(\omega=(u,v)^{T}\) and the real optical flow vector \(W=\left(U,V\right)^{T}\). The calculation formulas of the two indexes are presented as follows:  
\[\text{EPE}=\frac{1}{N}\underset{i=1}{\overset{N}{\sum}}\sqrt{\left(u_{i}-U_{i} \right)^{2}+\left(v_{i}-V_{i}\right)^{2}} \tag{14}\]  
\[\text{AAE}=\frac{1}{N}\underset{i=1}{\overset{N}{\sum}}\arccos\left(\frac{u_{ i}U_{i}+v_{i}V_{i}+k^{2}}{\sqrt{u_{i}^{2}+v_{i}^{2}+k^{2}}\sqrt{U_{i}^{2}+V_{i}^{2} +k^{2}}}\right) \tag{15}\]  
Figure 5: The normalization of the image optical flow field and extraction of moving object foreground region. (**a**) Grey image of the optical flow, (**b**) binary image of robust Harris feature points thresholding, (**c**) binary image after morphological processing, and (**d**) mask of the target area.  
where \(N\) represents the total number of image pixels; \((u_{i},v_{i})\) is the optical flow vector estimation value; \((U_{i},V_{i})\) is the real optical flow vector; and \(k\) is the number of frames between the two frames used to calculate the optical flow. Because the true optical flow values provided by the public dataset are between the adjacent frames, the datasets used for validation in this paper are all calculated as the optical flow values between two adjacent frames; hence, in this paper, \(k=1\).  
In this paper, the performance test of the moving target detection algorithm primarily includes three indicators [42]: \(E_{Pre}\) represents precision, \(E_{Rec}\) represents recall, and \(E_{FM}\) represents the \(F\)-measure. The calculation formulas of the three evaluation indexes are expressed as follows:  
\[E_{Pre}=\frac{TP}{TP+FP} \tag{16}\]  
\[E_{Rec}=\frac{TP}{TP+FN} \tag{17}\]  
\[E_{FM}=\frac{2*E_{pre}*E_{rec}}{E_{pre}+E_{rec}} \tag{18}\]  
\(TP\) represents true positive, which is the number of correctly detected foreground pixels of the moving object detection results. \(FP\) represents false positive, which is the number of pixels that mistakenly identify the background area as the moving object foreground area. Therefore, \(TP+FP\) in Equation (16) represents the number of targets' foreground pixels detected by the algorithm, and \(FN\) (false negative) represents the number of pixels in the moving object foreground that is not seen in the detection result and is marked as the background area. \(TP+FN\) in Equation (17) represents the real number of pixels in the moving object foreground area.