## 1 Introduction
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Methods** & **Key Instruments** & **Advantages** & **Limitations** & **Samples** & **Accuracy** \\ \hline \multirow{4}{*}{Morphology} & Morphological & Simple, quick and able to manage mild or moderate overlap & Unable to segment severely overlap & Cell images & 92.4\% \\ \cline{2-6}  & morphological & Split times have improved & Wide variation in segmentation across structures & Cluster Images & – \\ \hline \multirow{4}{*}{watershed} & distance transformation, watershed algorithm & Accuracy, stability and resistance to interference & For large size differences and large target errors & Blood Cell Images & 94.80 \\ \cline{2-6}  & Contour solidity, watershed algorithm & Robust and better at overcoming over-segmentation & Vulnerable to changes in border saturation and brightness & overlapping fog droplets & 94.74 \\ \hline \multirow{4}{*}{concave point matching} & multi-scale opening and closing reconstruction, concave points matching & Better contour edge information, lower over-segmentation rate & For images with light overlap & Goji Berry Images & 96\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of different overlapping target detection methods. blood cells in a blood smear through phased processing. The method has high accuracy, stability, and anti-interference, but there are precision errors when dealing with targets with significant size differences. [PERSON] et al. (2014) proposed an improved watershed-image-segmentation algorithm, which effectively overcomes the over-segmentation problem of overlapping targets through the droplet-type-discrimination method based on the solidity of the contour and the overlapping-droplet iterative opening operation, but it is greatly affected by the saturation of the boundaries and the change in the brightness, and the stability needs to be improved. A concave point is a characteristic point formed at the edge of an object by two or more targets due to mutual contact or overlap. Most of the overlapping objects are convex polygons, and, if overlapping occurs, concave dots are usually formed at the overlap, and the degree of overlap varies among different sizes of objects ([PERSON] et al., 2015). The concave-point method utilises the edge feature points formed by the overlapping of objects for segmentation. [PERSON] et al. (2016) proposed a method combining concave-point matching and morphological multi-scale open and closed reconstruction to achieve the segmentation of overlapping objects, which is able to extract the contour edge information better, and the over-segmentation rate of overlapping Goji berry images is lower, but it is only applicable to the targets with a shallow overlapping degree. [PERSON] et al. (2017) proposed a concave-point-based detection of contact pearls segmentation method, which involves establishing the mathematical model of the edge-contour-point pinch angle, introducing the concave-point-matching algorithm, and using the Euclidean distance as the metric function to achieve the segmentation of tangent pearls. The method has a good segmentation accuracy, but has not yet solved the single-concave-point-segmentation problem. This study addresses the key issues in overlapping-droplet segmentation. When the fog droplets overlap, the boundary of the overlapping region is blurred and the morphology is variable, especially, the irregular overlap will form a complex geometric structure. Overlapping droplets often have similar grey values, texture features, and size parameters, resulting in low feature-space differentiation, and morphological and watershed segmentation methods are prone to over-segmentation or under-segmentation. Segmentation methods based on concave-point detection can determine and match the droplet-overlapping region according to different degrees of edge concavity. This method only extracts data from the image boundary without morphological operations such as dilation and erosion, thus avoiding the loss of image detail information.