"RIV/68407700:21230/07:03135486!RIV08-MSM-21230___" . "Two Minimal Problems for Cameras with Radial Distortion"@cs . . "RIV/68407700:21230/07:03135486" . . . "Rio de Janeiro" . "Epipolar geometry and relative camera pose computation for uncalibrated cameras with radial distortion has recently been formulated as a minimal problem and successfully solved in floating point arithmetics. The singularity of the fundamental matrix has been used to reduce the minimal number of points to eight. It was assumed that the cameras were not calibrated but had same distortions. In this paper we formulate two new minimal problems for estimating epipolar geometry of cameras with radial distortion. First we present a minimal algorithm for partially calibrated cameras with same radial distortion. Using the trace constraint which holds for the epipolar geometry of calibrated cameras to reduce the number of necessary points from eight to six. We demonstrate that the problem is solvable in exact rational arithmetics. Secondly, we present a minimal algorithm for uncalibrated cameras with different radial distortions. We show that the problem can be solved using nine points in two vie" . . "Two Minimal Problems for Cameras with Radial Distortion" . "Ne\u010D\u00EDslov\u00E1no" . "Proceedings of Omnivis 2007: Workshop on Omnidirectional Vision and Camera Networks and Non-classical Cameras" . "Two Minimal Problems for Cameras with Radial Distortion"@cs . "Madison" . "Gr\u00F6bner basis; minimal problems; radial distortion"@en . . "978-1-4244-1630-1" . . "Pajdla, Tom\u00E1\u0161" . . "Z(MSM6840770038)" . "2007-10-20+02:00"^^ . . "Epipolar geometry and relative camera pose computation for uncalibrated cameras with radial distortion has recently been formulated as a minimal problem and successfully solved in floating point arithmetics. The singularity of the fundamental matrix has been used to reduce the minimal number of points to eight. It was assumed that the cameras were not calibrated but had same distortions. In this paper we formulate two new minimal problems for estimating epipolar geometry of cameras with radial distortion. First we present a minimal algorithm for partially calibrated cameras with same radial distortion. Using the trace constraint which holds for the epipolar geometry of calibrated cameras to reduce the number of necessary points from eight to six. We demonstrate that the problem is solvable in exact rational arithmetics. Secondly, we present a minimal algorithm for uncalibrated cameras with different radial distortions. We show that the problem can be solved using nine points in two vie"@cs . "[27D40823F613]" . . "21230" . "456116" . . "Two Minimal Problems for Cameras with Radial Distortion" . . "Epipolar geometry and relative camera pose computation for uncalibrated cameras with radial distortion has recently been formulated as a minimal problem and successfully solved in floating point arithmetics. The singularity of the fundamental matrix has been used to reduce the minimal number of points to eight. It was assumed that the cameras were not calibrated but had same distortions. In this paper we formulate two new minimal problems for estimating epipolar geometry of cameras with radial distortion. First we present a minimal algorithm for partially calibrated cameras with same radial distortion. Using the trace constraint which holds for the epipolar geometry of calibrated cameras to reduce the number of necessary points from eight to six. We demonstrate that the problem is solvable in exact rational arithmetics. Secondly, we present a minimal algorithm for uncalibrated cameras with different radial distortions. We show that the problem can be solved using nine points in two vie"@en . . "Omnipress" . "2"^^ . . "2"^^ . "Two Minimal Problems for Cameras with Radial Distortion"@en . . "K\u00FAkelov\u00E1, Zuzana" . . "8"^^ . . . "Two Minimal Problems for Cameras with Radial Distortion"@en .