camera working in the 2D space, as shown in Fig. \[fig\_iterprocess\]. In this demonstration, an object with four points ${\bf{P}}_i$, $i=1,...,4$ are projected to the camera image plane and their image points ${\bf{x}}_i$ are obtained. ${\bf{P}}_1$ is selected as the control point, which means $o=1$. Different initial values may result in different convergence results.

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Fig. \[fig\_iterprocess\](a) demonstrates a process that is approaching the correct global optimal results. Beginning with points ${\bf{p}}^{(k)}$, the algorithm projects ${\bf{p}}^{(k)}$ to their related lines of sight and obtains points ${\bf{q}}^{(k+1)}$. Then, according to ${\bf{q}}^{(k+1)}$, the algorithm updates the rotation $\bf{R}$ and scale factor $\mu$ to generate points ${\bf{p}}^{(k+1)}$. In this process, the rotation and scale factor related to ${\bf{p}}^{(k+1)}$ are closer to the truth compared to that related to ${\bf{p}}^{(k)}$, and finally the algorithm will reach the correct solution.

However, as the progress shown in Fig. \[fig\_iterprocess\](b) indicates, ${\bf{p}}^{(k+1)}$ has a larger pose error than ${\bf{p}}^{(k)}$, and the algorithm will finally get stuck in local minima. The reconstructed points ${\bf{p}}^{(k)}$ or ${\bf{p}}^{(k+1)}$ come in mirror-image forms of the real object points ${\bf{P}}$. Without loss of generality, in either 2D or 3D space, a mirror-image form suggests that the left-right-handed shape of the point cloud 