Constraints on general motions for camera calibration with one-dimensional objects

This paper focuses on two problems in camera calibration with one-dimensional (1D) objects: (a) to find out the general motion patterns well suited for solving the calibration problem, and (b) to improve the robustness and accuracy of the method. Firstly, a sufficient and necessary condition for the solvability of 1D calibration with general motions is proved. Then the special motion of tossing a 1D object is provided as an example to illustrate the correctness and feasibility of this condition. After that some practical issues on obtaining the solution are inspected. By avoiding singularities, the precision and robustness of the method are improved: the relative mean errors are reduced to less than 5% at the noise level of one pixel which surpasses the state-of-the-art methods of the same category.