"2"^^ . "Many vision tasks require efficient solvers of systems of polynomial equations. Epipolar geometry and relative camera pose computation are tasks which can be formulated as minimal problems which lead 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 work we suggest improvements of current techniques for solving systems of polynomial equations suitable for some vision problems. We introduce two tricks. The first trick helps to reduce the number of variables and degrees of the equations. The second trick can be used to replace computationally complex construction of Gr\u00F6bner basis by a simpler procedure. We demonstrate benefits of our technique by providing 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 probl"@cs . . "Pajdla, Tom\u00E1\u0161" . . "Solving polynomial equations for minimal problems in computer vision" . "CVWW 2007: Proceedings of the 12th Computer Vision Winter Workshop" . . "8"^^ . . "RIV/68407700:21230/07:03135394!RIV08-MSM-21230___" . "Z(MSM6840770038)" . . . "978-3-902465-60-3" . . "Solving polynomial equations for minimal problems in computer vision"@en . . . . . . . "Solving polynomial equations for minimal problems in computer vision" . "Solving polynomial equations for minimal problems in computer vision"@cs . "450986" . . "Gr\u00F6bner basis; minimal problems; radial distortion"@en . "21230" . "Solving polynomial equations for minimal problems in computer vision"@cs . "[4E31F2D11211]" . "2007-02-06+01:00"^^ . "Graz" . "12;19" . . "Many vision tasks require efficient solvers of systems of polynomial equations. Epipolar geometry and relative camera pose computation are tasks which can be formulated as minimal problems which lead 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 work we suggest improvements of current techniques for solving systems of polynomial equations suitable for some vision problems. We introduce two tricks. The first trick helps to reduce the number of variables and degrees of the equations. The second trick can be used to replace computationally complex construction of Gr\u00F6bner basis by a simpler procedure. We demonstrate benefits of our technique by providing 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 probl"@en . "Verlag der Technischen Universit\u00E4t Graz" . . "K\u00FAkelov\u00E1, Zuzana" . "Solving polynomial equations for minimal problems in computer vision"@en . "RIV/68407700:21230/07:03135394" . . "St. Lambrecht" . "Many vision tasks require efficient solvers of systems of polynomial equations. Epipolar geometry and relative camera pose computation are tasks which can be formulated as minimal problems which lead 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 work we suggest improvements of current techniques for solving systems of polynomial equations suitable for some vision problems. We introduce two tricks. The first trick helps to reduce the number of variables and degrees of the equations. The second trick can be used to replace computationally complex construction of Gr\u00F6bner basis by a simpler procedure. We demonstrate benefits of our technique by providing 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 probl" . "2"^^ .