# Study of the Error Caused by Camera Movement for the Stereo-Vision System
## 1 Introduction  
In recent years, the stereo-vision system has been used widely in many fields, e.g., industrial manufacturing and inspection [1; 2; 3; 4], experimental mechanics [5; 6; 7; 8], structural health monitoring [9; 10; 11], medical diagnosis [12] and aerospace engineering [13; 14; 15]. To obtain accurate 3D information, the two cameras in the stereo-vision system should remain stationary during the whole test period. This is because most stereo-vision systems calibrate the camera parameters at the beginning of the measurement [16; 17; 18]. Any slight camera movements during the tests can cause the extrinsic parameters (positions and orientations of the cameras) to vary and then decrease measurement accuracy. However, it is often impractical for the two cameras in a stereoscopic system to stay stationary in harsh working conditions, particularly in an outdoor environment. For example, when performing deflection measurement by digital image correlation in the outdoors for the inspection of bridge structures [19], the changes in the position and orientation of the stereo cameras often occur owing to various factors like wind, oscillations, and the lackof stability of the ground. When the stereo-vision systems are employed in autonomous land navigation [20], the road roughness can cause unpredictable camera movements. A strong vibration induced by a heavy steam hammer at high-speed is an unavoidable factor to compromise the measurement accuracy while using the stereo vision to measure the ram speed in forming workpieces [21]. Furthermore, a stereoscopic camera system has already been demonstrated for wing deformation measurements. Nevertheless, they have to cope with the problems of camera movements induced by the high aerodynamic loads and mechanical vibration during a measurement. Particularly, it is difficult to avoid these movements for in-flight applications [22], since the high vibration level occurs during the dynamic flight maneuvers. In all of the above cases, one common issue is camera movement, which adversely affects the applicability and versatility of the vision method. [PERSON] and [PERSON] [20] used mini-max and minimum-mean-square estimators to analyze the error caused by camera movements in a monocular vision-based tracking system while the effects of camera movement on 3D measurement of stereo-vision systems were not involved. Many researchers used monocular camera systems to measure the structural displacements that are parallel to the imaging plane in an outdoor environment [23; 24; 25; 26]. They found that it is difficult to keep the monitoring camera stationary during the entire process, which affected the accuracy of displacement measurements. Several compensation methods [26; 27] have been developed to compensate for the camera movements. For instance, to address this challenge of camera movement, [PERSON] et al. [28] calculated and removed the nonstationary motion of the camera by tracking the background feature points to obtain the accurate absolute displacement. However, the out-of-plane displacement of the structure is neglected. These methods consider structural displacements to be in-plane translations. [PERSON] et al. [29] presented a hybrid inertial vision-based system that can measure three-dimensional structural displacements by using a monocular camera. This system does not require the camera to remain stationary during the measurements, but the camera movements, i.e., rotations and translations during the measurement process are compensated by using a stationary calibration target in the field of view and an attached tilt sensor. [PERSON] [30] performed an in-flight wing deformation measurement on a Cobra VUT100 airplane using the stereo image pattern correlation technique. They found that relative camera movement led to a decalibration of the stereo system and then affected the precision of the measured 3D position significantly. [PERSON] et al.