Optimal imaging geometry for vision-based tracking systems

Abstract

When vision sensors are used to track an object in an outdoor realistic navigational environment, they are subjected to unexpected movements or vibrations of the mounting platform. In this dissertation, the performance of monocular and stereo vision systems in terms of range and heading angle errors is studied. The noise introduced by the navigational environment is modeled in two ways: camera noise approach; sensor movement errors regarded as the noise source, and image noise approach; image coordinate errors regarded as the noise source. The parameter space of the vision system is divided into a controllable subspace and an uncontrollable subspace. In the monocular case, the controllable subspace consists of the relative height between the vision sensor and a tracked point, and the depression angle of the vision sensor. In the stereo case, the controllable subspace consists of the baseline or distance between the two vision sensors. The uncontrollable subspace consists of the object coordinates and rotation angle errors or image coordinates errors of the vision sensors. A consistent detectable region is obtained such that the tracked point is always seen by the sensor. Based on this region, a reliable region consisting of no singularity point is defined so that the range error does not become infinity. The optimal parameters of the controllable subspace with respect to the uncontrollable subspace are found by employing the mini-max and minimum mean-squared error estimators. The mini-max estimator is used to obtain the worst case performance while the minimum mean-squared to obtain the average performance. These estimators are implemented by using the Complex algorithm of numerical nonlinear optimization, and the Romberg and Gaussian algorithms of numerical integration. A comparison between the monocular and stereo vision systems is then made by using their optimal parameter values. From the results obtained, it is shown that how an optimal imaging geometry of vision-based tracking systems is designed for outdoor or noisy navigational environments.