An empirical study on the effects of spatial discretization error in a stereo vision system

considered the case in which the images are in the same imaging plane and the optical axes of the two images are parallel. The triangulation error is inversely proportional to the product of baseline x focal length. At a given focal length, a wider baseline reduces triangulation error but increases both geometric and photometric distortions in images which in turn makes matching of these images more difficult. The region covered by the fields of view of both images is reduced as the baseline increases. Only the overlapped region will give 3D measurements. The separation between two views should be small in order to facilitate matching and to recover a larger proportion of the 3D scene. There is therefore a conflict in different requirements for setting up an ideal stereo imaging system. The spatial discretization error in an image causes triangulation error, camera calibration error in a stereo imaging system. Camera calibration error in turn causes difficulty in applying the epipolar line constraint for matching stereo images as well as causing triangulation error. We derive an empirical relationship between the uncertainty volume of triangulation at the vergence point of convergent stereo viewing and the average triangulation error in such a set-up. Given the stereo imaging parameters it is possible to estimate the average triangulation error in the stereo system. We have studied by simulation the effects of spatial discretization error on the camera calibration, triangulation accuracy and the calculation of epipolar line. We have also examined the effect of the spatial discretization error on triangulation, camera calibration and calculation of the epipolar lines at different viewing angles. The results obtained enable us to choose a compromise viewing angle such that the effects of spatial discretization error may be reduced in a near optimum way. The results also indicate how camera calibration accuracy may be improved.