# A Multivariate Local Descriptor Registration Method for Surface Topography Evaluation
## 7 Conclusions  
This study presents a multi-component local descriptor method to optimize coarse registration precision. First, they obtain the measurement and digital model point cloud, further divided by the multi-scale RSCS. Then, multivariate descriptors were integrated to generate feature vectors, and the SAC-IA algorithm was applied to find the corresponding points, followed by the matching score to get the final position of the related points, and an ICP-based fine point cloud registration was carried out. Finally, the STEP file is applied to guide the measurement point cloud segmentation to complete the automatic error analysis of specific functional surfaces. In the experiment, this study selects the rear beam parts of an automobile for error analysis. One of the results is that the r-angle cylindricity is 0.881 mm, the roughness sq parameter is 0.219 mm, and the flatness of its plane is 1.037 mm. Compared with a micrometer, CMM and profilometer, the measurement results differ slightly; the results show that the proposed method can solve the challenging problem of automating error analysis based on optical measurement data. The major contribution of this study is the development of a multivariate local descriptor registration method and segmentation method, which can be applied in a 3D structured light measurement system. The developed methods consider 3D surface topography measurement and improve registration accuracy compared to existing methods. Further, the methods are suitable for automatic error evaluation in the automobile industry when measurement for vehicle parts needs cost consideration. The STEP file contains geometric information, which can not only serve as the guidance of point cloud segmentation but also complete some feature recognition and the mid-surface generation algorithm of CAE. However, although the proposed descriptors can improve registration precision, there are still registration failures for minimal shapes. Therefore, deep learning-based descriptors will be considered in the registration positioning stage to improve the registration robustness further in future work. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Features** & **Micrometer** & **CMM** & **Profilometer** & **Proposed Method** \\ \hline a\_S1 & 0.216 & 0.301 & 0.203 & 0.219 \\ a\_S2 & 1.354 & 1.326 & 1.276 & 1.298 \\ a\_S3 & 0.235 & 0.244 & 0.198 & 0.207 \\ b\_S1 & 0.873 & 0.854 & 0.801 & 0.813 \\ b\_S2 & 0.852 & 0.832 & 0.732 & 0.762 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of comparison with existing methods for roughness (mm). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Features** & **Micrometer** & **CMM** & **Profilometer** & **Proposed Method** \\ \hline a\_S2 & 1.067 & 1.011 & 1.103 & 1.037 \\ b\_S1 & 0.842 & 0.702 & 0.801 & 0.713 \\ b\_S2 & 0.539 & 0.578 & 0.612 & 0.545 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of comparison with existing methods for flatness (mm). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Features** & **Micrometer** & **CMM** & **Profilometer** & **Proposed Method** \\ \hline a\_S1 & 0.892 & 0.856 & 1.020 & 0.881 \\ a\_S3 & 1.035 & 0.921 & 1.142 & 0.945 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of comparison with existing methods for cylindricity (mm). **Author Contributions:** Conceptualization, C.K., Y.X. and Z.L. ; Software, J.L. ; Validation, Z.L., J.L. and I.M. ; Investigation, C.K. and C.Z. ; Resources, I.M. and Y.X. ; Writing--original draft, C.K. and Z.L. ; Writing--review & editing, Y.X. and T.L. ; Visualization, C.K. and D.T. ; Supervision, Y.X. and X.J. ; Funding acquisition, Y.X. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (NSFC) (61203172); the Sichuan Science and Technology Programs (2023 NSFSC0361, 2022002). **Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.