## 3 Method of Recognition
### Pseudo-Target Criterion Based on Shape Prior Information  
To distinguish the real underwater targets from the pseudo-targets as previously detected, the prior shape information of underwater targets is used to remove the pseudo-target points that contradict the prior shape information. The homogeneous region at any point is extracted from the local region of \(\rm{d_{F}}\), which can be achieved through methods such as binarization and clustering. The methods of thresholding and clustering can be used to extract homogenous regions. The thresholding method is simple to operate, but its threshold value is difficult to determine. An improper threshold value will affect the accurate extraction of homogeneous regions, resulting in difficulties in the subsequent shape discrimination. Clustering is a common unsupervised method, which divides a group of objects into several categories, with the core concept of maximizing the inter-class distances while minimizing the intra-class distances [21]. The classical clustering algorithms include: partitioning [22], density [23], graph theory [19], and grid-based method [24]. The K-means [25] is a typical partitioned clustering algorithm, which is only applicable to spherical clustering, and the clustering results are easily affected by the initial clustering center. The density-based noise can be found by using the Density-Based Spatial Clustering of Application with Noise (DBSCAN) [26] algorithm, but the clustering results are easily affected by the threshold and neighborhood radius. [PERSON] et al. [27] proposed the Density Peak Clustering (DPC) algorithm, which believes that the density of the cluster center is higher than that of the surrounding data points and is far away from other high-density points. However, the DPC algorithm only calculates the density according to the distance between data points, which is not suitable for datasets with complex shapes and densities. When distributing data points based on distances, the robustness of the algorithm is poor, and the clustering results are sensitive to the value of the cut-off distance. The Local Gravitation Model (LGM) [28] is a method for data clustering. It is different from the traditional gravity clustering model, where the modulus length and direction information of the resultant force of the local gravitation are used in the calculation of the local center measure. Considering the efficiency and accuracy of the algorithm, the local gravity gravitation clustering model [29] is used to extract the homogeneous regions from the measurements. The principle of the LGM clustering algorithm is as follows:  
Inspired by [PERSON]'s law of universal gravitation, the local gravitation of data points in the clustering process can reflect the relationship between data points and their neighbors. Figure 3: The first column including (**a**,**d**,**g**) shows the false-color images corresponding to the hyperspectral images, (**a**) represents the target area where the red box indicates the underwater target region, and (**d**) represents the background area; The second column including (**b**,**e**,**h**) shows the \(\mathrm{d_{F}}\) results, and the third column including (**c**,**f**,**i**) shows the 3D view of \(\mathrm{d_{F}}\). According to the law of universal gravitation, the attraction between two particles can be defined as:  
\[\textbf{F}_{ij}=G\frac{m_{i}m_{j}}{d_{ij}^{2}}\textbf{D}_{ij} \tag{12}\]  
where \(\textbf{F}_{ij}\) represents the gravitation between the points of \(\textbf{X}_{i}\) and \(\textbf{X}_{j}\), \(\text{G}\) represents the coefficient of gravitation, \(\text{m}\) represents the mass of the point \(\textbf{X}_{i}\), \(\text{d}_{ij}\) represents the distance between the points of \(\textbf{X}_{i}\) and \(\textbf{X}_{j}\), the unit vector \(\textbf{D}_{ij}\) is the direction of the line between the two points.