# Point Cloud Registration Algorithm Based on Adaptive Neighborhood Eigenvalue Loading Ratio
## 4 Discussion  
To address the issue that traditional ICP registration algorithms often converge to locally optimal solutions, leading to global point cloud registration failure, in this study, a point cloud registration scheme was introduced based on the adaptive neighborhood eigenvalue loading ratio. The scheme employs a dual-registration strategy consisting of coarse registration followed by fine registration, which enhances the registration results in terms of accuracy and time efficiency compared with traditional methods. The scheme first takes advantage of the uniqueness of the point cloud data to calculate the point cloud resolution of the source point cloud and the target point cloud and determine the average grid density in the adaptive grid filtering algorithm, thereby eliminating the point cloud noise. Then, using the rigid body in the transformation, the relative position between its internal points to maintain a constant change in this property, and the above point cloud resolution as the basis of adaptive spherical field radius, the covariance matrix eigenvalues of the point and the neighborhood are calculated. This eigenvalue loading ratio is used to extract the point cloud feature points. For the incorrect matching pairs, the matching pair group is optimized with an angular threshold. The initial change matrix is then calculated by using the sampling consistency initial registration SAC-IA to complete the coarse registration of the point cloud, followed by KD-tree-accelerated ICP fine registration to obtain the final transformation matrix to complete the whole registration process.  
Compared with traditional ICP, this method overcomes the problem that ICP may easily fall into local optima. By using adaptive grid filtering and eigenvalue load ratio feature extraction, it effectively removes noise points, ensuring registration accuracy and  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Original Data**} & \multicolumn{2}{c}{**ICP**} & \multicolumn{2}{c}{**ColorICP**} & \multicolumn{2}{c}{**FPFH+ICP**} & \multicolumn{2}{c}{**Ours**} \\ \cline{2-9}  & **RMSE/mm** & **Time/s** & **RMSE/mm** & **Time/s** & **RMSE/mm** & **Time/s** & **RMSE/mm** & **Time/s** \\ \hline Bunny & 10.739 & 8.943 & 9.457 & 10.112 & 0.764 & 7.987 & **0.103** & **4.223** \\ Dragon & 12.568 & 9.843 & 10.524 & 10.946 & 1.918 & 8.345 & **0.113** & **5.185** \\ Bear doll & 5.124 & 6.578 & 3.152 & 7.027 & 0.509 & 5.231 & **0.092** & **2.569** \\ Tree stool & 25.891 & 14.999 & 2.776 & 17.736 & 0.427 & 12.867 & **0.147** & **6.037** \\ Chamber & 4.615 & 48.693 & 2.203 & 53.234 & 1.031 & 36.378 & **0.065** & **13.846** \\ Office & 4.387 & 53.902 & 1.698 & 65.049 & 0.885 & 39.679 & **0.081** & **14.601** \\ \hline \hline \end{tabular}  
* The best performance figures are highlighted in bold font.  
\end{table}
Table 3: Performance comparison of different registration methods on six sample point clouds: RMSE (mm) and computation time (s).  
stability. Meanwhile, compared with ColorICP and FPFH, this method can more effectively extract the internal structural features of the point cloud, improving the speed and accuracy of feature point extraction. Although the feature point extraction phase is time-consuming, accounting for about 80% of the total cost, future research can address this issue by optimizing the algorithm or using parallel computing technology.