Automatically obtaining the correspondences of four coplanar points for an uncalibrated camera

For an uncalibrated camera, the problem of automatically determining the correspondences of four given coplanar points has not yet been solved. Previous algorithms [mostly related to two-dimensional (2D) homography] avoided this correspondence problem and required people to manually choose the correct image point one by one. In this paper, we propose a novel three-step method to automatically identify the correct correspondence. First, prejudge the possibilities of correspondences (PoC) based on the analysis of why ambiguous correspondences occur. Second, set a cuboid bound for the optical center to verify if the center circle computed from the homography intersects it. Third, utilize the reasonability and stability of the intrinsic parameters to remove the still-wrong PoC. Besides applications in recovering 2D Euclidean structure and camera calibration, we can also extend the proposed method to detect multiple quadrangle objects, no matter if they are coplanar or not. Many experiments with simulated and real data show that our method has good performance and important applied value.