# Point Cloud Registration Algorithm Based on Adaptive Neighborhood Eigenvalue Loading Ratio
###### Abstract  
Traditional iterative closest point (ICP) registration algorithms are sensitive to initial positions and easily fall into the trap of locally optimal solutions. To address this problem, a point cloud registration algorithm is put forward in this study based on adaptive neighborhood eigenvalue loading ratios. In the algorithm, the resolution of the point cloud is first calculated and used as an adaptive basis to determine the raster widths and radii of spherical neighborhoods in the raster filtering; then, the adaptive raster filtering is implemented to the point cloud for denoising, while the eigenvalue loading ratios of point neighborhoods are calculated to extract and match the contour feature points; subsequently, sample consensus initial alignment (SAC-IA) is used to carry out coarse registration; and finally, a fine registration is delivered with KD-tree-accelerated ICP. The experimental results of this study demonstrate that the feature points extracted with this method are highly representative while consuming only 35.6% of the time consumed by other feature point extraction algorithms. Additionally, in noisy and low-overlap scenarios, the registration error of this method can be controlled at a level of 0.1 mm, with the registration speed improved by 56% on average over that of other algorithms. Taken together, the method in this study cannot only ensure strong robustness in registration but can also deliver high registration accuracy and efficiency. adaptive neighborhood; eigenvalue loading ratio; point cloud registration; point cloud filtering; iterative nearest point method +
Footnote †: journal: Medical  
point (ICP) [8], known for its high accuracy and rapid convergence in aligning point clouds at a high overlap rate. However, the ICP algorithm only considers the Euclidean distance between points and neglects other internal structural features and external color features; moreover, it is susceptible to initial registration positions and prone to converging on local optima, while incurring high computational costs [9]. Therefore, many improvements to the ICP algorithm have been proposed. For example, regarding the selection of neighborhood points, [PERSON] et al. [10] proposed a point method set selection using Gaussian mixture models (GMMs). By modeling the distribution of point sets and selecting points with higher probabilities for registration, the accuracy and robustness of the registration were enhanced. [PERSON] et al. [11] introduced a robust error metric to error functions based on the Welsch function and employed the EM (expectation-maximization) algorithm with [PERSON]'s acceleration to effectively minimize the error metric, finally improving the registration accuracy on a benchmark dataset and greatly enhancing the time efficiency. Regarding neighborhood search, [PERSON] et al. [12] designed a spatial data structure, called \"octree\", to expedite the search for the nearest neighbor points, substantially increasing the ICP algorithm's running speed. To address the issue of local minima, [PERSON] et al. [13] directly identified the optimal correspondence between point clouds by optimizing a global objective function, thus bypassing the step-by-step approximation process and greatly enhancing the ICP algorithm's speed and robustness. Although the four methods mentioned above for optimizing the ICP algorithm can improve registration results, there remains a major error in scenarios with low overlap as well as a strong dependence on the initial positions of point clouds. As mentioned above, it is still limited to improve the ICP algorithm alone. From a bionic point of view, in point cloud registration, people first determine its overall shape before performing point-to-point registration based on representative features. The concepts of feature point detection and feature descriptors can be traced back to the fields of image processing and computer vision. A registration algorithm combining coarse and fine registration has, therefore, been proposed.