"Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion"@en . . "A number of minimal problems of structure from motion for cameras with radial distortion have recently been studied and solved in some cases. These problems are known to be numerically very challenging and in several cases there exist no known practical algorithm yielding solutions in floating point arithmetic. We make some crucial observations concerning the floating point implementation of Gr\u00F6bner basis computations and use these new insights to formulate fast and stable algorithms for two minimal problems with radial distortion previously solved in exact rational arithmetic only: (i) simultaneous estimation of essential matrix and a common radial distortion parameter for two partially calibrated views and six image point correspondences and (ii) estimation of fundamental matrix and two different radial distortion parameters for two uncalibrated views and nine image point correspondences. We demonstrate on simulated and real experiments that these two problems can be efficiently solv" . "Gr\u00F6bner basis; minimal problems; radial distortion"@en . "Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion"@en . . "Medison" . . "A number of minimal problems of structure from motion for cameras with radial distortion have recently been studied and solved in some cases. These problems are known to be numerically very challenging and in several cases there exist no known practical algorithm yielding solutions in floating point arithmetic. We make some crucial observations concerning the floating point implementation of Gr\u00F6bner basis computations and use these new insights to formulate fast and stable algorithms for two minimal problems with radial distortion previously solved in exact rational arithmetic only: (i) simultaneous estimation of essential matrix and a common radial distortion parameter for two partially calibrated views and six image point correspondences and (ii) estimation of fundamental matrix and two different radial distortion parameters for two uncalibrated views and nine image point correspondences. We demonstrate on simulated and real experiments that these two problems can be efficiently solv"@cs . "A number of minimal problems of structure from motion for cameras with radial distortion have recently been studied and solved in some cases. These problems are known to be numerically very challenging and in several cases there exist no known practical algorithm yielding solutions in floating point arithmetic. We make some crucial observations concerning the floating point implementation of Gr\u00F6bner basis computations and use these new insights to formulate fast and stable algorithms for two minimal problems with radial distortion previously solved in exact rational arithmetic only: (i) simultaneous estimation of essential matrix and a common radial distortion parameter for two partially calibrated views and six image point correspondences and (ii) estimation of fundamental matrix and two different radial distortion parameters for two uncalibrated views and nine image point correspondences. We demonstrate on simulated and real experiments that these two problems can be efficiently solv"@en . "21230" . "Omnipress" . . . . "1063-6919" . "000259736802039" . "Z(MSM6840770038)" . "Pajdla, Tom\u00E1\u0161" . "8"^^ . "RIV/68407700:21230/08:03149972!RIV09-MSM-21230___" . . "K\u00FAkelov\u00E1, Zuzana" . . "Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion"@cs . "[149CFFEAD171]" . "\u00C4str\u00F6m, K." . "Josephson, K." . "RIV/68407700:21230/08:03149972" . "Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion" . "5"^^ . "Anchorage, Alaska" . "Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion" . . . . . . . . "Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion"@cs . "978-1-4244-2242-5" . . "2"^^ . "CVPR 2008: Proceedings of the 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition" . "367686" . "Byr\u00F6d, M." . "2008-06-24+02:00"^^ . .