Research On Camera Calibration With One-dimensional Objects

Camera calibration is a process of determining the imaging parameters of one or more cameras, which is generally a necessary step to extract three-dimensional information from two-dimensional images in many computer vision applications. The new one-dimensional calibration method is very suitable for multi-camera systems since the 1D object is without self-occlusion and easy to construct and carry, so the one-dimensional calibration has received many attentions. However existing one-dimensional calibration methods suffer from poor accuracy because image noises inevitably occur in practice, the measurement matrix with such a large condition number due to image noises results in poor estimation accuracy of relative depths, and all constraints currently are equally treated without considering their specifics. The another problem is that most existing algorithms are local optimization algorithm, which can only obtain the local optimal solution rather than the global optimal solution and in some cases even result in calibration failure. To due with these problems, some improvements on 1D calibration accuracy are made in this paper, main contents of which are as follows:Firstly, the basic principle of camera calibration is introduced, then several typical 1D camera calibration methods, for example Zhang’s linear algorithm, Franca et al.’s normalized linear algorithm and weighted algorithm are analyzed. Through the analysis of these calibration methods and the experimental validation of their algorithms, their algorithm programming models are established.Secondly, using theoretical analysis, it is find that one reason for poor accuracy of one-dimensional calibration accuracy is that all constraints currently are equally treated. So an adaptively weighted one-dimensional calibration algorithm with high accuracy is presented. The innovations and contributions of such an algorithm are two-fold: One is that data normalization is used to improve estimation accuracy of the relative depths of marker points on the one-dimensional calibration object; The other is that a weighted coefficient is adaptively assigned to each constraint on camera parameters by analyzing the data error involved in the constraint. Experiments with synthetic and real image data show that the accuracy of the proposed algorithm is much higher than that of classical one-dimensional calibration.Finally, an accurate global optimization algorithm for one-dimensional calibration based on the linear matrix inequality is proposed. It firstly constructs cost function of the absolute conic, according to the relative depth of makers and calibration characteristics. Then, the cost function is minimized by a convex relaxation based on the linear matrix inequality and the global optimal solution of camera intrinsic matrix are obtained. Compared with exiting algorithms, the proposed algorithm has advantages of high accuracy, weak insensitivity to initial conditions and fast global convergence. Experiments with both synthetic and real image data validate the proposed algorithm.