## 3 Results and Analysis
### Overlapping-Droplet-Segmentation-Test Validation and Analysis
As shown in Figure 14, by comparing and verifying the segmentation results of manual calibration, the method in this paper is highly consistent with the manual calibration results in terms of the segmentation accuracy of overlapping droplets and the generation effect of segmentation lines, which indicates that the method has an excellent and accurate segmentation capability for overlapping water droplet images. Specifically, the method in this paper is able to accurately segment overlapping droplets into independent units, and its segmentation boundaries are almost completely consistent with the manual calibration results. This high degree of consistency is not only reflected in the number of segmented droplets, but also in the accuracy of the segmentation line. In order to quantitatively assess the performance of overlapping-droplet separation, we used the following four key metrics: segmentation error rate S1 and segmentation accuracy S2 for specific overlap types, overall average segmentation accuracy, and average  
Figure 14: Single WSP overlapping-droplet segmentation results. Where (**a**) is the original overlapping-droplet layer extracted from the sample and (**b**) shows the segmentation results of the manual calibration. segmentation time for a single WSP image. These metrics are used to construct a complete segmentation algorithm performance evaluation system from three dimensions: segmentation accuracy, global performance, and computational efficiency. The calculation formula is as follows. \[S_{1}=\frac{T_{ti}+T_{ei}}{T_{0i}}\times 100\% \tag{4}\]  
\[S_{2}=\frac{T_{\text{ci}}}{T_{0i}}\times 100\% \tag{5}\]  
\[\overline{S_{2}}=\frac{T_{\text{c}}}{T_{0}}\times 100\% \tag{6}\]  
\(T_{0i}\)--Number of actual overlapping fog droplets of a certain type in the image. \(T_{ut}\)--Number of overlapping droplets of a type not adequately segmented in the image. \(T_{ei}\)--Number of over-segmented and mis-segmented overlapping fog droplets of a certain type in the image. \(T_{ei}\)--Number of overlapping fog droplets of a certain type correctly segmented in the image. \(T_{0}\)--Total number of actual overlapping droplets in the image. \(T_{e}\)--Total number of correctly segmented overlapping fog droplets in the image. Based on different segmentation methods, the segmentation performance of different types of overlapping fog droplet images was comprehensively evaluated, including the segmentation error rate (S1), the segmentation accuracy rate (S2), the overall average segmentation accuracy rate (\(\overline{S_{2}}\)), and the average segmentation time of a single WSP image. The statistical results of the performance metrics of each method are detailed in Table 6.  
As can be seen from Table 6, the method in this paper shows significant advantages in the task of single-concave-point strongly overlapping-fog-droplet segmentation. Specifically, the segmentation error rate of this paper's method is only 7.32%, which is 30.13 percentage points lower than that of the contour-fixation and watershed-based algorithm, while the segmentation error rate of the existing improved-concave-point segmentation method is up to 95% or more, which indicates that it is the worst for this type of overlapping-droplet segmentation. In terms of segmentation accuracy, the method in this paper also performs well. For single-concave-point strongly overlapping droplets, its segmentation accuracy is more than 90%, while in the segmentation task of non-parallel overlapping droplets, which accounts for a larger proportion of overlapping droplets, the segmentation error rate is only 8.57%, which is significantly lower than the other two methods. In addition, the segmentation accuracy of this paper's method is more than 91%, while the segmentation accuracy based on the contour solidity and watershed algorithm and the improved-concave-point segmentation method are 89.83% and 76.19%, respectively. Even