E ects of Camera Alignment Errors on StereoscopicDepth

We present in this paper a new analysis of relative sensitivity/importance of camera calibra-tion/alignment parameters on the performance of stereoscopic depth reconstruction. For a given stereoscopic vision system, once stereo correspondence is successfully established, the accuracy of 3D measurements depends on the overall geometric structure of the model in relation to object distances. The geometric structure (and hence the error) depends on (1) xed design parameters such as interpixel distance, focal length and baseline; and (2) the accuracy with which these parameters are known, i.e., camera calibration and alignment. The errors due to the xed design parameters of the geometric structure have been investigated intensively by others. However, the role of calibration error and misalignment on the accuracy of the stereoscopically computed 3D information has not been studied. The alignment accuracy is perhaps more important than individual camera calibration since it is the relative alignment that aaects the epipolar constraints used during the correspondence process. Also, poor camera calibration/alignment may aaect the establishment of feature/region correspondence at the outset. Most research done in camera calibration has dealt with the question of how to calibrate a single camera or multiple cameras, and also on the derivation of error bounds of diierent calibration parameters. But in many situations, it may be very diicult to get perfect calibration. Further, even if the calibration is excellent, the camera setting may change during the use of the system. This raises two important questions: How do these cal-ibration/alignment errors aaect 3D estimates? Given the accuracy requirements that a practical, application-speciic stereoscopic vision system must satisfy, how much error can we endure for each parameter we calibrate? The quantitative analysis presented here provides formulae which relate diierent calibration or alignment parameter errors to the 3D reconstruction measurements. The results of this analysis provide speciications of acceptable tolerances in individual calibration parameters for given 3D measurement error tolerances. This information is useful in designing practical stereoscopic vision systems. Abstract: We present in this paper a new analysis of relative sensitivity/importance of camera calibration/alignment parameters on the performance of stereoscopic depth reconstruction. This quantitative analysis provides formulae which relate diierent parameter errors to the 3D reconstruction measurements. The results of this analysis provide speciications of acceptable tolerances in individual calibration parameters for given 3D measurement error tolerances. This information is useful in designing practical stereoscopic vision systems.