# Study of the Error Caused by Camera Movement for the Stereo-Vision System
## 1 Introduction
[31] developed a semi-physical simulation system to investigate the effect of camera parameter error on 3D reconstruction accuracy in a stereo-vision system. They pointed out that extrinsic parameter error has a relatively large impact on system reconstruction accuracy by affecting baseline distance and the angle between cameras. In their works, only the relative movement between the cameras was studied without considering the movement of the two cameras together (identical movement). [PERSON] et al. [32] analyzed the impact of system structure parameters and camera calibration parameters on location accuracy in binocular stereo vision system. However, it also did not include the error caused by identical movement. [PERSON] and [PERSON] [19] performed bridge deflection measurement outside using digital image correlation with a single camera where the effect of camera movement is corrected by perspective transformation. However, the 2D DIC setup requires a perpendicular alignment of the camera towards the planar specimen, which limits the applicability. [PERSON] et al. [33] developed marker-based displacement measurement models for correcting the systematic errors caused by camera movements. However, an assumption made is that the structural displacement occurs on a two-dimensional plane. [PERSON] and [PERSON] [34] investigated the influence of input data errors on the quality of reconstructed 3D points in the stereo-vision process while they only considered those particular camera calibration and 3D reconstruction algorithms which employ singular value decomposition (SVD) methods. [PERSON] [35] presented a study of the influence of calibration errors on the uncertainty in 3D position and object motion for the stereo-DIC system using the Monte Carlo approach. However, this \"black-box\" method lacks the support of an analytically derived model. [PERSON] et al. [36] analyzed the depth measurement error of binocular stereo vision and proposed some strategies to reduce the errors. They had not given the error models of 3D coordinates and distance. [PERSON] et al. [37] proposed a new method to calibrate the stereo-DIC system automatically with feature correspondences in an unconstrained scene, but the performance with respect to the feature matching errors rather than the camera movement error was evaluated. The aforementioned studies primarily focus on analyzing the errors of the camera movements in the monocular vision system, or investigating the camera movement errors using either simulated or numerically altered images. The works attempting to quantify the effect of both identical and relative camera movement in a stereo-vision system on 3D measurement by both analytical and experimental approaches are insufficient. The contributions are that the calculation models of 3D coordinates and distance measurement error are derived by considering the identical and relative movement. The effect characteristic of each case was verified and analyzed, and the main factor was determined as relative rotation. Some strategies are proposed to reduce the measurement errors caused by camera movement. The rest of this paper is organized as follows. In Section 2, the principle of stereo-vision 3D measurement is introduced. In Section 3, the measurement error models for different types of camera movements are established. In Section 4, four groups of experiments are performed to validate our analysis. Finally, the conclusions of this study are given in Section 5.