. "Epipolar geometry and relative camera pose computation are examples of tasks which can be formulated as minimal problems and solved from a minimal number of image points. Finding the solution leads to solving systems of algebraic equations. Often, these systems are not trivial and therefore special algorithms have to be designed to achieve numerical robustness and computational efficiency. In this paper we provide a solution to the problem of estimating radial distortion and epipolar geometry from eight correspondences in two images. Unlike previous algorithms, which were able to solve the problem from nine correspondences only, we enforce the determinant of the fundamental matrix be zero. This leads to a system of eight quadratic and one cubic equation in nine variables. We simplify this system by eliminating six of these variables. Then, we solve the system by finding eigenvectors of an action matrix of a suitably chosen polynomial. We show how to construct the action matrix without"@en . "Gr\u00F6bner basis; minimal problems; radial distortion"@en . . . "407948" . . . "1053-587X" . "RIV/68407700:21230/07:03135485" . . "Epipolar geometry and relative camera pose computation are examples of tasks which can be formulated as minimal problems and solved from a minimal number of image points. Finding the solution leads to solving systems of algebraic equations. Often, these systems are not trivial and therefore special algorithms have to be designed to achieve numerical robustness and computational efficiency. In this paper we provide a solution to the problem of estimating radial distortion and epipolar geometry from eight correspondences in two images. Unlike previous algorithms, which were able to solve the problem from nine correspondences only, we enforce the determinant of the fundamental matrix be zero. This leads to a system of eight quadratic and one cubic equation in nine variables. We simplify this system by eliminating six of these variables. Then, we solve the system by finding eigenvectors of an action matrix of a suitably chosen polynomial. We show how to construct the action matrix without" . "A minimal solution to the autocalibration of radial distortion"@cs . "CVPR 2007: Proceedings of the Computer Vision and Pattern Recognition conference" . . . . "Pajdla, Tom\u00E1\u0161" . "A minimal solution to the autocalibration of radial distortion"@en . "Los Alamitos" . . . "Minneapolis" . "Z(MSM6840770038)" . "Epipolar geometry and relative camera pose computation are examples of tasks which can be formulated as minimal problems and solved from a minimal number of image points. Finding the solution leads to solving systems of algebraic equations. Often, these systems are not trivial and therefore special algorithms have to be designed to achieve numerical robustness and computational efficiency. In this paper we provide a solution to the problem of estimating radial distortion and epipolar geometry from eight correspondences in two images. Unlike previous algorithms, which were able to solve the problem from nine correspondences only, we enforce the determinant of the fundamental matrix be zero. This leads to a system of eight quadratic and one cubic equation in nine variables. We simplify this system by eliminating six of these variables. Then, we solve the system by finding eigenvectors of an action matrix of a suitably chosen polynomial. We show how to construct the action matrix without"@cs . "A minimal solution to the autocalibration of radial distortion"@cs . "2007-06-18+02:00"^^ . "[59085CC1B0ED]" . "7"^^ . "1-4244-1180-7" . "2"^^ . "21230" . . "A minimal solution to the autocalibration of radial distortion"@en . . "A minimal solution to the autocalibration of radial distortion" . "2"^^ . . . "RIV/68407700:21230/07:03135485!RIV09-MSM-21230___" . "K\u00FAkelov\u00E1, Zuzana" . . "A minimal solution to the autocalibration of radial distortion" . . "IEEE Computer Society" .