AID object is a segment with several known-distance markers, and calibration methods with ID objects are more flexible than those with 2D/3D objects. Under the pinhole camera model, it is proved that the calibration with free-moving ID objects is not possible. For a central catadioptric camera setup, can the camera be calibrated by a ID object under general motions? In this paper, we prove that a central catadioptric camera can indeed be calibrated, and propose a catadioptric camera calibration method using ID objects undertaking general motions. The proposed method consists of two steps. Firstly, the principal point is calculated with geometric invariants under catadioptric camera model; Secondly, we use images of ID object to calibrate the focal lengths, skew factor and mirror parameter. The method needs neither prior knowledge of catadioptric parameters nor conic fitting, and it is linear, which makes it easy to implement. Experiments demonstrate its usefulness and stability.