# An Accurate, Efficient, and Stable Perspective-n-Point Algorithm in 3D Space
## 4 Conclusions and Prospects
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Algorithm**} & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline \multirow{2}{*}{LHM} & \(\begin{matrix}mean_{err}\\ med_{err}\end{matrix}\) & 45 & 136.1 & 25.2 & 134.5 & 53.3 & 29.1 & 51.1 & 34.1 & 30.3 & 22.3 \\  & \(med_{err}\) & 42.4 & 123.6 & 22.4 & 137.1 & 51.9 & 20.2 & 51.0 & 34.6 & 29.7 & 20.9 \\ \hline \multirow{2}{*}{ErnP+GN} & \(\begin{matrix}mean_{err}\\ med_{err}\end{matrix}\) & 14.8 & 10.6 & 10.2 & 19.7 & 8.7 & 19.4 & 6.1 & 9.5 & 18.6 & 15.1 \\  & \(med_{err}\) & 15.1 & 10.5 & 10.4 & 19.7 & 8.9 & 19.5 & 6.1 & 9.6 & 18.8 & 15.1 \\ \hline \multirow{2}{*}{RPnP} & \(\begin{matrix}mean_{err}\\ med_{err}\end{matrix}\) & 14.7 & 10.8 & 12.9 & 20.2 & 10.4 & 18.8 & 6.7 & 10.1 & 18.5 & 15.1 \\  & \(med_{err}\) & 14.7 & 10.8 & 10.9 & 20.2 & 9.1 & 18.8 & 6.2 & 10.1 & 18.6 & 15.1 \\ \hline \multirow{2}{*}{DS} & \(\begin{matrix}mean_{err}\\ med_{err}\end{matrix}\) & 2541.7 & 2542.5 & 2606.1 & 1928.4 & 2156.4 & 2907.1 & 2470.4 & 2118.2 & 1898.5 & 2583.5 \\  & \(med_{err}\) & 2534.5 & 2551.7 & 2602.6 & 1936.5 & 2160.8 & 2913.1 & 2468.3 & 2118.7 & 1901.1 & 2584.3 \\ \hline \multirow{2}{*}{OPnP} & \(\begin{matrix}mean_{err}\\ med_{err}\end{matrix}\) & 14.7 & 10.5 & 10.4 & 20.1 & 8.7 & 18.9 & 6.6 & 9.9 & 32.5 & 14.9 \\  & \(med_{err}\) & 14.9 & 10.5 & 10.4 & 19.8 & 8.8 & 18.9 & 6.1 & 9.8 & 22.8 & 15.1 \\ \hline \multirow{2}{*}{SRPnP} & \(\begin{matrix}mean_{err}\\ med_{err}\end{matrix}\) & 14.8 & 10.5 & 10.2 & 19.8 & 8.6 & 18.9 & 5.8 & 9.6 & 18.5 & 14.8 \\  & \(med_{err}\) & 14.9 & 10.4 & 10.5 & 19.9 & 8.8 & 18.9 & 5.8 & 9.6 & 18.8 & 15.0 \\ \hline \multirow{2}{*}{RDLT} & \(\begin{matrix}mean_{err}\\ med_{err}\end{matrix}\) & 14.8 & 10.6 & 10.1 & 19.8 & 8.7 & 19.6 & 6.1 & 9.6 & 18.6 & 15.1 \\  & \(med_{err}\) & 14.9 & 10.6 & 10.4 & 19.8 & 9.1 & 19.6 & 6.0 & 9.6 & 18.8 & 15.1 \\ \hline \multirow{2}{*}{ASPnP} & \(\begin{matrix}mean_{err}\\ med_{err}\end{matrix}\) & 15.2 & 10.6 & 10.2 & 19.8 & 8.6 & 18.9 & 6.9 & 9.6 & 21.2 & 14.8 \\  & \(med_{err}\) & 14.9 & 10.4 & 10.4 & 19.9 & 8.8 & 18.9 & 5.8 & 9.6 & 18.9 & 15.0 \\ \hline \multirow{2}{*}{Hidden PnP} & \(\begin{matrix}mean_{err}\\ med_{err}\end{matrix}\) & 14.5 & 10.4 & 10.1 & 19.8 & 8.5 & 18.7 & 5.8 & 9.6 & 18.5 & 14.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mean error (\(mean_{err}\)) and median errors (\(med_{err}\)) of reprojection coordinate points in 10 images of the calibration plate at different distances and attitudes (unit: pixel). Figure 13: Ten images of the calibration plate at different distances and attitudes and the reprojection effects. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable. **Conflicts of Interest:** The authors declare no conflict of interest. **Abbreviations**  
P3P Perspective-3-Point  
P4P Perspective-4-Point  
P5P Perspective-5-Point  
PnP Perspective-n-Point  
GN Gauss-Newton iterative method  
CGR Cayley-Gibbs-Rodriguez  
SLAM Simultaneous Localization and Mapping  
DLT Traditional direct liner transformation  
ASPnP Accurate and Scalable Solution to the Perspective-n-Point problem  
RPnP A Robust O(n)Solution to the Perspective-n-Point problem  
OptDLS Optimal DLS Method  
SRPnP A simple, robust and fast method for the Perspective-n-Point problem  
Hidden PnP hidden variable-based PnP algorithm