Camera calibration based on 3D/2D correspondences is of high significance in various applications.Herein,considering 3D/2D correspondences,the perspective-n-points-focal-radial(Pn Pfr)method aims to estimate the camera pose,focal length,and radial distortion.Therefore,this study proposed a novel solution to its minimal problem,such as the P4Pfr problem.First,four pseudo-depth factors are defined based on the pinhole and radial distortion models.Then,the translation vector is eliminated by decentralizing the 3D points,yielding a robust P4Pfr model.Finally,the rotation matrix is parameterized with respect to this model and solved by rotation constraints.Within this framework,ordinary and planar configurations are handled separately,with the former solved by Gröebner basis and the latter simplified to a six-degree univariate equation.The accuracy,robustness,and efficiency of the proposed algorithm are evaluated using a numerical simulation and dataset.The results reveal that the ordinary solver provides the highest robustness.Moreover,the robustness of the planar solver is comparable to that of the state-of-the-arts applications.Both the two solvers achieve the fastest solving speed to date.
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