# A Fast and Simple Method for Absolute Orientation Estimation Using a Single Vanishing Point
## 4 Discussion
### Difference and Advantage  
Similar to many existing methods, our proposed method uses some prior knowledge (i.e., roll angle in this paper) to simplify the problem when estimating the camera orientation. However, prior knowledge has errors and these errors might affect the accuracy of the estimation seriously. If this happens, the robustness of the estimation would decrease and the applicable range of the corresponding methods would also decrease, even though the problem might be simplified. Fortunately, our proposed method has good robustness to prior knowledge, even if it contains noise, as shown in Section 3.1.1. This result shows that our proposed method using known roll angle simplifies the problem of estimation and also does not decrease the accuracy (actually, the decrease exists, but it is very slight). In addition, the cost of obtaining prior knowledge might be high for many existing methods, or a mechanical structure with precision machining is needed, which also increases the cost greatly and might make the device heavy. However, the IMU used in this paper has some  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Proposed Method** & **P3P** & **RPnP** \\ \hline Position error/m & 0.049 & 0.129 & 0.114 \\ Reprojection error/pixel & 0.46 & 0.94 & 0.82 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The position error and reprojection error in the second case.  
advantages, i.e., a low cost, high accuracy, and small size. These advantages of the IMU also extend the range of applications for our proposed method.  
What is more, the level of simplification using prior knowledge is different, which means the benefit might be high or low for different methods. Our proposed method can simplify the problem of estimation extremely using the known roll angle. We estimate the orientation independently in order to decrease the coupling degree with a single vanishing point, and this is one reason why our proposed method has better numerical stability, as shown in Section 3.1.2. In addition, from Section 2.1, it can be seen that our proposed method does not solve the system of linear equations and non-linear equations, it just needs to solve the simple trigonometric equation. This is the main reason our proposed method has a better performance in terms of numerical stability, noise sensitivity, and computational speed, as shown in Sections 3.1.2-3.1.4 and 3.2. In Section 2.2, we add orientation refining and this is another reason our proposed method has a better performance for noise sensitivity.  
In addition, our proposed method uses only one vanishing point, but at least two are used for most of the existing methods, which means our proposed method needs fewer feature lines in the surroundings and has a higher adaptation.  
However, the main disadvantage of our proposed method is that there is a limitation regarding parallel lines for the vanishing point, as shown in Section 2.3. The direction vector of the parallel lines for the vanishing point in our proposed method cannot be \(\big{(}0\quad 0\quad 1\big{)}\) and the reason has been thoroughly analyzed. Hence, this case must be avoided when the proposed method is used.  
In brief, our proposed method has the following advantages: (1) the orientation of the camera pose can be estimated independently, (2) only one vanishing point is needed, (3) it has a higher numerical stability and accuracy, (4) it has a faster computational speed, and (5) it has good robustness to roll angle noise.