Realistic stereo error models and finite optimal stereo baselines

Stereo reconstruction is an important research and application area, both for general 3D reconstruction and for operations like robotic navigation and remote sensing. This paper addresses the determination of parameters for a stereo system to optimize/minimize 3D reconstruction errors. Previous work on error analysis in stereo reconstruction optimized error in disparity space which led to the erroneous conclusion that, ignoring matching errors, errors decrease when the baseline goes to infinity. In this paper, we derive the first formal error model based on the more realistic “point-of-closest-approach” ray model used in modern stereo systems. We then show this results in finite optimal baseline that minimizes reconstruction errors in all three world directions. We also show why previous oversimplified error analysis results in infinite baselines. We derive the mathematical relationship between the error variances and the stereo system parameters. In our analysis, we consider the situations where errors exist in only one camera as well as errors in both cameras. We have derived the results for both parallel and verged systems, though only the simpler models are presented algebraically herein. The paper includes simulations to highlight the results and validate the approximations in the error propagation. The results should allow stereo system designers, or those using motion-stereo, to improve their system.