## 5 Conclusions and Future Work  
In this paper, a hybrid optimization algorithm based on the Improved Whale Optimization Algorithm and improved ICP was proposed to achieve point cloud registration in response to the problems and shortcomings of existing point cloud registration methods. In the initial registration stage of this paper, an improved whale optimization algorithm based on nonlinear convergence factor and adaptive weight coefficients was proposed because the number of point clouds is usually substantial, and the standard whale optimization  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Point Cloud**} & \multirow{2}{*}{**Error**} & \multicolumn{4}{c}{\(\sigma_{MSE}\) (mm)} \\ \cline{3-6}  & & **ICP** & **RANSAC** & **Depth Filtering-ICP** & **Algorithm of This Paper** \\ \hline \multirow{4}{*}{A} & x & 2.49386 & 2.38141 & 3.245254 & 1.145785 \\  & y & 0.885543 & 0.507815 & 1.251014 & 0.751423 \\  & z & 0.307292 & 0.65359 & 1.321525 & 0.895243 \\ \hline \multirow{4}{*}{B} & x & 1.215468 & 0.856487 & 1.321587 & 0.786325 \\  & y & 0.569874 & 1.325469 & 0.514524 & 0.684751 \\ \cline{1-1}  & z & 0.965124 & 0.956787 & 1.025410 & 0.884265 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of mean square error of the 4 algorithms.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Point Cloud** & **ICP** & **RANSAC** & **Depth Filtering-ICP** & **Algorithm of This Paper** \\ \hline A & 961,357 & 13,252,610 & 2,512,542 & 989,790 \\ B & 150,330 & 261,587 & 452,535 & 368,283 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Registration time of surface workpiece point cloud (ms).  
algorithm is easy to suffer premature convergence that causes it to trap in local optimum as the search proceeds. The algorithm uses smaller weights to search in the neighborhood of the optimal solution in a spiral manner to prevent falling into the local optimum. In the second step of accurate registration, since the standard ICP algorithm is sensitive to noise and outliers, it is prone to misregistration. We proposed an improved ICP algorithm with weighted constraints on the normal vectors of key points to avoid the algorithm from falling into local optimum and further improve the performance of the ICP algorithm in point cloud accurate registration. The experimental results show that the proposed algorithm has lower error compared with other registration algorithms, higher registration accuracy, and faster convergence speed and can meet the needs of subsequent work.  
With the increasing accuracy and resolution of visual systems, the obtained point cloud data are becoming more and more informative, and further research is still needed for point cloud denoising strategies while keeping the main cloud point data features and information intact. For the registration of a large amount of point cloud data, there are still limitations in the existing algorithms, and further research is needed to improve the accuracy and efficiency of the registration algorithm.  
Formal analysis, L.M.; Funding acquisition, L.W.; Investigation, Y.C.; Methodology, G.L. All authors have read and agreed to the published version of the manuscript.  
This paper is supported by the 2021 Jiangsu Higher Education Teaching Reform Research Key Project (No. 2021 JSJG156) and Shaanxi Key Laboratory of Machinery Manufacturing Equipment Construction Project.  
Written informed consent has been obtained from the patient(s) to publish this paper.  
The authors declare no conflict of interest.