# An Automatic 3D Point Cloud Registration Method Based on Biological Vision
## 7 Conclusions  
In order to solve the problem of surface deformation measurement during ablation tests in an arc-heated wind tunnel, in this study, we proposed an automatic point cloud registration method. As compared with other registration methods, we provided a complete solution, including two parts: (1) Guarantee high-quality initial values and overlaps for aligning point clouds which have deformed much. (2) A strategy to automatically compute rigid transformations between point clouds. Inspired by 2D artificial targets used to improve precision of camera calibration or photogrammetry, we introduced 3D artificial targets to obtain accurate registration results, which was the key idea for solving the problem of surface deformation measurement; most state-of-art approaches only considered how to align point clouds more accurately and robustly using a big enough overlap. Simulations and experiments were conducted, and the research results indicated the following: (1) The proposed method performed well under Gaussian noise with an intensity ranging from 0 to 1 mr. When \(\sigma_{GN}\) = 1 mr, rotation and translation error were smaller than 0.025\({}^{\circ}\) and 1 mr, respectively. (2) The error of surface deformation measurement was smaller than 0.05 mm when deformation was no more than 4 mm. In addition to surface deformation measurement, the proposed method can also be applied for experimental studying of soft matter. However, there are still some aspects that need to be studied: (1) The procedure of cone vertex detection should be more efficient. As compared with the Harris operator used in cone vertex detection, Radon or Hough transform may be more simplified [22; 23], but the robustness needs to be evaluated. (2) The 3D artificial target should be more multiple. An artificial neutral network (ANN) can be adopted to train a classifier. And rotational projection statistics (RoPS) can be taken as the inputs of the classifier [6]. The classifier can be used to recognize different geometric features and delete fake features, which can improve the efficiency of data fusion and decrease the time cost. Conceptualization, J.L. ; Data curation, P.G. ; Formal analysis, J.L. and X.S. ; Funding acquisition, J.L. ; Investigation, J.L. and P.G. ; Methodology, J.L. ; Supervision, X.S. ; Validation, X.S. ; Writing--original draft, J.L. ; Writing--review and editing, P.G. and X.S. All authors have read and agreed to the published version of the manuscript. This work was funded by the National Natural Science Foundation of China with grant no. 11802321. The authors declare no conflict of interest. The quadratic form of the conic surface can be written as:  
\[P^{\mathrm{T}}AP=0,\] (A1)and:_  
\[A=\left( \begin{array}{ccccc}a_{1}&a_{4}/2&a_{5}/2&a_{7}/2\\ a_{4}/2&a_{2}&a_{6}/2&a_{8}/2\\ a_{5}/2&a_{6}/2&a_{3}&a_{9}/2\\ a_{7}/2&a_{8}/2&a_{9}/2&a_{10}\end{array} \right),P=\left[ \begin{array}{ccccc}x&y&z&1 \end{array} \right]^{\rm T}.\]  
_A can be decomposed using SVD._  
\[A=U_{A}D_{A}V_{A}^{\rm T}.\] (A2)  
_Then, the last column of \(V_{A}\) represents the homogeneous coordinate of the cone vertex._  
**Proof. ** Matrix \(A\) can be diagonalized on the basis of eigenvalues and eigenvectors. \[A=RDR^{\rm T},\] (A3)  
where \(D\) is a diagonal matrix and \(R\) is a transformation matrix. Substituting Equation (A3) into Equation (34) yields:  
\[P^{\rm T}AP=\Big{(}P^{\rm T}R\Big{)}D\Big{(}P^{\rm T}R\Big{)}^{\rm T}=\big{(} P^{\prime}\big{)}^{\rm T}DP^{\prime}=0,\] (A4)  
where \((P^{\prime})^{\rm T}DP^{\prime}=0\) is the standard quadratic form of the conic surface. Equation (A4) is essentially a transformation between coordinate systems. Through this transformation, the cone vertex can be shifted to the origin of the new coordinate system, and the axis of the cone can be made parallel to the Z-axis of new coordinate system. The homogeneous coordinates of the cone vertex in the new coordinate system can be notated as:  
\[P^{\prime}_{v}=\big{[} \begin{array}{ccccc}0&0&0&1\end{array}