# Study of the Error Caused by Camera Movement for the Stereo-Vision System
## 5 Conclusions  
Under harsh working conditions, the perfect stability of the two cameras in a stereo-vision system cannot be realized, especially in an outdoor environment. Any slight movements of the cameras can significantly influence the 3D measurement accuracy. In this paper, we have investigated the impact of the camera movement on 3D measurements in detail. The camera movements are divided into four categories, viz., identical translation  
Figure 12: The 3D coordinates and distance measurement errors introduced by the relative rotation: (**a,b**) Impact of the relative rotation on the 3D coordinate measurement errors when the right camera is rotated around the \(X\)-axis and \(Y\)-axis, respectively; (**c,d**): Impact of the relative rotation on the distance measurement.  
and rotation, and relative translation and rotation. For each case, the calculation model of the 3D coordinate and distance measurement error was derived. Experimental verification was performed with high-precision translation and rotation stages. The theoretical analysis and experiments have brought some valuable conclusions as follows.  
For identical translations, the 3D coordinate measurement error increases linearly with the increasing change in both cameras' positions while the measurement of the distance between two points remains unaffected.  
For identical rotations, the 3D coordinate error is introduced only in the rotating plane, and it is proportional to the rotation angle within 10\({}^{\circ}\). The identical rotation angle of both cameras has no impact on the distance measurement.  
For the relative translation, the coordinate error of any measured point in three directions keeps linearly increasing with the increasing translation. Particularly, the coordinate error varies among different points on the object. The distance measurement error is proportional to the change in positions between the two cameras. Furthermore, the errors of the 3D coordinate and distance, caused by the right camera translation along its own optical axis, are less than for those along other directions.  
For the relative rotation, the relationship between the 3D coordinate error of a point and the rotation angle can be described as the nonlinear trend of a sine-cosine curve. The distance measurement error does not increase monotonically with the relative rotation angle. Furthermore, the errors of the 3D coordinate and distance measurement, caused by the relative rotation, are significantly larger than those caused by other cases of the camera movement. Even for the occurrence of a rotation angle of 10\({}^{\circ}\) during images acquisition, the resultant maximum coordinate error is up to 2000 mm, and the distance error reaches 220%. The stereo-vision system is highly sensitive to the relative rotation between the two cameras.  
In brief, we have meticulously analyzed the effect of the unavoidable slight movements of the two cameras on the 3D measurement of an object. The ensuing results are recommended as a guideline to correct the effect of the camera movement, while using a stereo-vision system in a noisy or outdoor environment.  
Methodology, Y.L.; validation, Y.L., Z.G., X.S. and Y.Y.; investigation, Y.L.; writing--original draft preparation, Y.L.; writing--review and editing, Y.L., Z.G. and X.G.; visualization, Y.L.; supervision, X.G. and T.S.; funding acquisition, X.G., T.S. and Q.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Nos. 11772268, 11602202, 12072279, 12002215); National Key Research and Development Program of China (No. 2019 YFC1511102); Natural Science Basic Research Plan in Shaanxi province of China (No. 2018 JQ1060).  
Not applicable.  
Data sharing is not applicable to this article.  
The authors declare no conflict of interest.