# Registration of Urban Aerial Image and LiDAR Based on Line Vectors
## 4 Discussion  
The registration of aerial images and airborne LiDAR data based on linear features are merely methods based on points or establishing a registration model using line direction. The coplanarity equation of the line vector is established by coplaning two imaging rays and the corresponding control lines. A registration method using line vectors is raised to solve the traditional weak geometric constraint. Experimental results show that both conventional registration and LVR can achieve the correct solution. When handing synthetic data, position error of EOPs from both conventional registration and LVR method is within 0.84 m and an attitude error of EOPs is within 0.00466\({}^{\circ}\). Compared with conventional registration, LVR has 18% higher accuracy in the position parameter and 14% higher accuracy in the attitude parameter. Additionally, the averaged error of check lines by conventional registration is 1.07 pixels, while with the LVR method it is 0.88 pixels. Compared with conventional registration, the LVR method is 18% better in real accuracy. When handling ISPRS test project data, the EOPs are estimated with a \(\sigma_{0}\) value of 2.00 pixels via conventional registration, and the RMSE of the check lines at the image scale is 0.66 pixels. In contrast, a \(\sigma_{0}\) value of 1.75 pixels is achieved for the LVR, with the RMSE of the check line being 0.54 pixels. When handling real aerial images in Calgary, the LVR is about 20% higher and 24% higher than conventional registration in theoretical accuracy and real accuracy, respectively. The proposed adjustment is evaluated by a synthetic, ISPRS test project and real data. Compared with the traditional method, the LVR is theoretically and actually more accurate. This is because conventional registration only uses the direction of the line to set up the registration model, whose essence is still the coplanarity of points. The LVR uses directional and moment vectors to describe feature lines, covering both the direction and position information of the lines. The inaccurate original EOPs before registration has resulted in large deviation in real roof positions and projecting points on the image. The registration of real roof positions and projecting points on an image has been accurately achieved after the registration of aerial images and LiDAR data. It follows that the LVR can achieve an ideal registration accuracy in urban areas with rich linear features. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Line No.**} & \multicolumn{2}{c}{**Simulated Image**} & \multicolumn{2}{c}{**ISPRS Test Project Image**} & \multicolumn{2}{c}{**Real Image**} \\ \cline{2-7}  & **Conventional Registration** & **LVR** & **Conventional Registration** & **LVR** & **Conventional Registration** & **LVR** \\ \hline
1 & 1.16 & 1.02 & 0.17 & 0.08 & 0.92 & 0.49 \\
2 & 0.72 & 0.47 & 0.52 & 0.46 & 1.59 & 1.35 \\
3 & 1.19 & 1.03 & 0.64 & 0.51 & 2.36 & 1.91 \\
4 & 1.21 & 1.01 & 1.31 & 1.10 & 3.17 & 2.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RMSE of check lines of conventional registration and LVR (pixel). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{} & \multicolumn{2}{c}{**Simulated Image**} & \multicolumn{2}{c}{**ISPRS Test Project Image**} & \multicolumn{2}{c}{**Real Image**} \\ \cline{2-7}  & **Conventional Registration** & **LVR** & **Conventional Registration** & **LVR** & **Conventional Registration** & **LVR** \\ \hline
1 & 1.16 & 1.02 & 0.17 & 0.08 & 0.92 & 0.49 \\
2 & 0.72 & 0.47 & 0.52 & 0.46 & 1.59 & 1.35 \\
3 & 1.19 & 1.03 & 0.64 & 0.51 & 2.36 & 1.91 \\
4 & 1.21 & 1.01 & 1.31 & 1.10 & 3.17 & 2.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RMSE of check lines of conventional registration and LVR (pixel). There are some limitations in the proposed algorithm, though the imaging rays in the image coordinate framework and their corresponding linear control features in LiDAR data coordinate framework can be effectively achieved by line vectors.