# A Point Cloud Registration Algorithm Based on Weighting Strategy for 3D Indoor Spaces
## 6 Conclusions  
Many millimeter-wave radar applications, including autonomous driving, robotic navigation, and augmented reality, widely use point cloud registration. During the registration process, accuracy and effectiveness are two key factors that will have a direct impact on performance. This paper proposes a novel algorithm for point cloud registration. First, PointNet uses different category labels in the 3D indoor spaces to semantically segment the point cloud for registration. We introduce a statistical weighting strategy that assigns varying weights to the point cloud corresponding to the category labels. Then, during the registration process, we propose a new method to calculate the closed form of ICP iterative optimal solutions in three-dimensional spaces. This method addresses the issue in traditional registration algorithms where the linear approximation of the objective function reduces accuracy. We successfully calculate the closed-form solutions by applying the weights of the point cloud to the objective function solving process. We validate the accuracy and efficiency of the proposed algorithm on point cloud datasets of 3D indoor spaces, and the registration experiments reveal significant improvements in both accuracy and efficiency after incorporating the weighting strategy into the ICP algorithm. The technique may swiftly iterate to the ideal solution by breaking hard transformations into numerous tiny transformations, each with an infinitesimal angle. Furthermore, the approach to finding closed-form solutions presented in Section 4 may significantly improve the registration's accuracy.  
The dataset tests show that the RMS of different types of rigid transformation become much smaller compared to ICP, the NDT, and PointNetLK. On the other hand, compared to the original ICP, the algorithm's runtime and usage of both CPU and memory improve. Overall, this paper's proposed weighting-strategy-based point cloud registration algorithm demonstrates improved accuracy and increased efficiency in large-scale 3D indoor spaces.  
While the novel algorithm in this paper, based on a weighting strategy, significantly improves the accuracy and efficiency of point cloud registration in 3D indoor spaces, it still falls short in terms of hardware resource utilization when compared to other registration algorithms like the NDT. Future work will focus on further optimizing the ICP iterative process to reduce computation costs, as well as exploring the integration of other more efficient registration algorithms with the proposed weighting strategy.  
Methodology, W.L., H.Z. and S.S.; Software, W.C. and S.S.; Formal analysis, W.L., H.Z. and X.L.; Writing--original draft, W.L.; Writing--review & editing, H.Z., W.C., X.L. and S.S.; Visualization, W.C. All authors have read and agreed to the published version of the manuscript. This research was funded by Heilongjiang Province's Key Research and Development Project: 'open competition mechanism to select the best candidates', grant number 2023 ZXJ03C02; and National Science Foundation of China, grant number 52075117. The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author. The authors declare no conflict of interest.