Optimal design and placement of omni-cameras in binocular vision systems for accurate 3-D data measurement

A new problem of automatically designing an optimal stereo vision system using two omni-directional catadioptric cameras to yield the highest 3-D data accuracy is studied. Factors of the system configuration considered in the design include camera pose, field of vision, and mirror shape. To find the optimal vision system configuration, an analytic formula is derived to model the 3-D measurement error, which takes into consideration the variations of pixel-quantization precisions and angular resolutions in images by conducting error propagation analysis in the data computation process. The formula is then used in an optimization framework to find the optimal system configurations for different shapes of system setup environments. For regular cases with rectangular cuboid-shaped 3-D measurement and camera placement areas, two fast algorithms are proposed to solve the problem, one being bisection-based and relatively slower for deriving the optimal solution, and the other faster using analytic formulas for deriving a suboptimal solution that is proved to be close to the optimal one in precision. Experimental results of simulations and real application cases show the feasibility of the proposed method.