Camera calibration with one-dimensional objects

Camera calibration has been studied extensively in computer vision and photogrammetry and the proposed techniques in the literature include those using 3D apparatus (two or three planes orthogonal to each other or a plane undergoing a pure translation, etc.), 2D objects (planar patterns undergoing unknown motions), and 0D features (self-calibration using unknown scene points). Yet, this paper proposes a new calibration technique using 1D objects (points aligned on a line), thus filling the missing dimension in calibration. In particular, we show that camera calibration is not possible with free-moving 1D objects, but can be solved if one point is fixed. A closed-form solution is developed if six or more observations of such a 1D object are made. For higher accuracy, a nonlinear technique based on the maximum likelihood criterion is then used to refine the estimate. Singularities have also been studied. Besides the theoretical aspect, the proposed technique is also important in practice especially when calibrating multiple cameras mounted apart from each other, where the calibration objects are required to be visible simultaneously.