# Research on a Point Cloud Registration Method Based on Dynamic Neighborhood Features
## 2 Methods
### Dynamic Neighborhood Calculation  
Following the selection of feature points, it is necessary to determine a dynamic neighborhood for each feature point to characterize its local geometric information [19]. To define the size of this dynamic neighborhood, we introduce three parameters: local point density, local mean curvature, and wavelet transform detail coefficients based on the curvature. Point cloud density, representing the degree of sparseness or denseness of point cloud data in space, is a crucial parameter for determining the size of the dynamic neighborhood [20]. In regions with high point cloud density a larger number of points are contained within a unit volume, indicating richer point cloud information. In such cases, if the neighborhood size is excessively large it may encompass too many points, leading to a smoothing effect on the computed local features and a loss of critical detail information. Therefore, the dynamic neighborhood in dense point cloud regions should be appropriately reduced to ensure that the calculation of local features can describe finer geometric structures and avoid feature generalization. Smaller neighborhoods can better capture subtle variations in regions with rich surface details (e.g., textures, folds). Conversely, in regions with a sparse point cloud distribution the number of points contained within a unit volume is limited, resulting in relatively insufficient point cloud information. If the neighborhood is too small it may lead to an insufficient number of points to support the calculation of local features, introducing noise or instability [21]. Thus, in sparse regions, the dynamic neighborhood should be appropriately enlarged to ensure that there are enough points within the neighborhood to compute local features. In spacious background areas or regions with missing point clouds a larger neighborhood can compensate for the lack of information caused by point cloud sparsity. In summary, point cloud density indirectly determines the size of the dynamic neighborhood by influencing the number of points within it: dense regions require smaller dynamic neighborhoods to preserve details while sparse regions require larger dynamic neighborhoods to ensure computational stability. Local mean curvature is an important metric for describing the geometric characteristics of point cloud surfaces, reflecting the average bending of the point cloud surface in the vicinity of a given point. Compared to single curvature measures, mean curvature provides a more comprehensive description of local surface geometry. In regions with high mean curvature (e.g., edges, corners, sharp features), the geometric variations in the point cloud surface are significant, resulting in larger mean curvature values. These regions typically contain rich geometric detail information, such as object contours and sharp edges, which play a crucial role in tasks like point cloud registration, segmentation, and recognition [22; 23]. To preserve these detailed features, the dynamic neighborhood should be appropriately reduced to avoid feature smoothing caused by an excessively large neighborhood, preventing the loss of important geometric information. Conversely, in regions with low mean curvature (e.g., planar surfaces, smooth surfaces) the geometric variations in the point cloud surface are gradual, resulting in smaller mean curvature values. The geometric features in these regions are relatively uniform, without significant detail variations. In such cases, the dynamic neighborhood can be appropriately enlarged to capture more local geometric information while enhancing the robustness of feature computation. Curvature-based wavelet transform detail coefficients provide a further extension of local curvature information, capturing local geometric details and curvature variations in point cloud data through multi-scale analysis.