used the threshold of $60\%$), no improvement can be found and the RANSAC process of R1PP$n$P could be terminated. Accuracy evaluation results in this paper have testified the rationality of this assumption.

\(2) *Termination Conditions for R1PPnP Iterations*

As shown in Fig. \[fig\_algorithmstep\], we first detect as many inliers as possible and the related *termination condition A* is satisfied when the detected number of inliers becomes stable, that is,

$$\label{eq_terminationA}
N_{\rm{inlier}}^{(k)} - N_{\rm{inlier}}^{(k-20)} \le 0 \text{  and  } k>20,$$

where $k$ is the index of iterations, $N_{\rm{inlier}}$ is the number of detected inliers. According to our experience, in most cases no more inliers would be detected if $N_{\rm{inlier}}$ has not increased in 20 iterations.

\[htp\] ![Experiments with synthetic data (ordinary 3D case, $50\%$ of outliers) to demonstrate the iteration process of R1PP$n$P when the control point $o$ is an outlier. Randomly colored lines are results with different control points. (a) The changes of estimated camera pose between frames $k$ and $k-1$ are complex during the iteration process, based on which it is difficult to decide when to stop the process. (b) It is more robust and efficient to stop the process when no more inliers can be detected.[]{data-label="fig_testTerminationA"}](figures/testTerminationA1.pdf "fig:"){width=".24\textwidth"} ![Experiments 