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\[htp\]

To select different points as the control point $o$ may result in different convergence rates. Without taking into account noise, the correct value of rotation $\bf{R}$ should be the same for any control point $o$ in a P$n$P task. Hence, larger rotation updating steps in the iteration process suggest that less number of iterations are required to converge to the correct value when starting from the same initial value. In R1PP$n$P, $\bf{R}$ is updated according to the differences between points ${\bf{p}}_i$ and ${\bf{q}}_i$, $i=1,...,N, i \neq o$. When point $o$ is close to ${\bf{p}}_i$, the rotation updating steps are more likely to be large, as shown in Fig.\[fig\_convergencerate\](a). The updating rates of $\mu$ also follow this analysis. Therefore, we are prone to select the control point $o$ from the center of the point cloud, which has better odds of having smaller distances to the rest of the point cloud to achieve faster convergence rate, as shown in Fig.\[fig\_convergencerate\](b).

Outliers Handling Mechanism
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The robust and fast capability of handling outliers is the main contribution of the proposed R1PP$n$P algorithm. Our outliers handling mechanism combines a soft weight assignment method and the 1-point RANSAC scheme.

Soft Re-weighting
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R1PP$n$P 