## 5 Conclusions  
In this paper, we propose a feature descriptor based on a multi-scale covariance matrix that describes the geometrical relationship, the eigenvalue variation gradient, and the surface variation gradient, and we use it to extract local features of keypoints detected by our keypoint detection method. We, thereafter, present an accurate transformation estimation method by multi-level estimating point cloud transformations to obtain the best optimal transformation between a pair of point clouds. Experiment findings reveal that our proposed feature descriptor is more resistant to noise than PFH, 3 DSC, spin image, etc., our accurate transformation estimation outperforms state-of-the-art transformation estimation \begin{table}
\begin{tabular}{l c} \hline \hline
**Method** & **Registration Time (ms)** \\ \hline Based on our proposed transformation estimation & 4085 \\ Based on feature matching & 1422 \\ Based on clustering & 3448 \\ Based on ICP & 3252 \\ Based on feature matching + clustering & 6066 \\ Based on feature matching + ICP & 5247 \\ Based on RANSAC & 5395 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average registration time for point cloud registration based on different transformation estimations. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Method** & **Dimension** & **Registration Time (ms)** \\ \hline Based on our proposed feature descriptor & 49 & 4085 \\ Based on 3 DSC & 1980 & 14,530 \\ Based on spin image & 400 & 7004 \\ Based on PFH & 125 & 3153 \\ Based on RoPS & 135 & 8606 \\ Based on FPFH & 33 & 2257 \\ Based on BRoPH & 256 & 9905 \\ Based on KDD & 128 & 5714 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Average registration time for point cloud registration based on different feature descriptors. such as feature matching, clustering, ICP, RANSAC, etc., and our registration effectiveness is extremely successful in the Kinect dataset with noisy data. Of course, the approach we propose has certain limitations, which are as follows. (1) Too many parameters and thresholds must be supplied in our proposed approach. For example, \(r\) (the support radius is used to detect keypoints), \(e_{\theta}\) (a threshold for a surface variation index), \(L_{th}\) (a threshold for the maximum difference between adjacent included angles), \(d_{min}\) (a threshold for the nearest distance between a keypoint and a boundary point), et al., must be provided. Setting these parameter values/thresholds is a hard and time-consuming operation, and the quality of the settings will influence the registration outcomes. As a result, the next phase of work should concentrate on research in this area, such as establishing multiple parameter values/threshold acquisition standards and adaptively choosing parameter values/thresholds for 3D point cloud registration. (2) The rigid point cloud registration approach assumes that objects do not undergo deformation during the registration process, while the non-rigid point cloud registration involves objects that undergo deformation, that is, objects may undergo shape or size changes during the registration process due to various factors such as pressure, temperature, etc. Therefore, the method used in this paper cannot be directly applied to non-rigid body registration due to its inherent assumptions and limitations. But if non-rigid bodies are decomposed into multiple small rigid bodies, non-rigid body registration can be defined as a non-uniform Euclidean transformation between multiple small rigid bodies and the approach proposed in this paper also have practical applications. Therefore, future work needs to research how to decompose non-rigid point cloud registrations into multiple local rigid point cloud registrations and apply the method proposed in this paper to the non-rigid point cloud registrations. (3) Apply our proposed point cloud registration approach in this paper to the registration of indoor and outdoor scenes.