Two-point calibration method for a zoom camera with an approximate focal-invariant radial distortion model

A zoom camera can change its focal length and track moving objects with an adjustable resolution. To extract precise geometric information for the tracked objects, a zoom camera requires an accurate calibration method. High-precision camera calibration methods, however, usually require a number of control points that are not guaranteed in some practical situations. Most zoom cameras suffer radial distortion. Athough a traditional method can recover an undistorted image with known intrinsic parameters, it fails to work for a zoom camera with an unknown focal length. Motivated by these problems, we propose a two-point calibration method (TPCM). In this scheme, we first propose an approximate focal-invariant radial distortion (AFRD) model. With the AFRD model, an RGB image can be undistorted with an unknown focal length. After that, the TPCM method is presented to estimate the focal length and rotation matrix with only two control points for one image. Synthetic experiments demonstrate that the AFRD model is efficient. In the real data experiment, the mean reprojection error of the TPCM method is less than one pixel, which is smaller than current state-of-the-art methods, and we believe meets the demand for high-precision calibration.