Some Properties of the E Matrix in Two-View Motion Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A theory of self-calibration of a moving camera
International Journal of Computer Vision
Homotopies exploiting Newton polytopes for solving sparse polynomial systems
SIAM Journal on Numerical Analysis
Kruppa's Equations Derived from the Fundamental Matrix
IEEE Transactions on Pattern Analysis and Machine Intelligence
Self-Calibration of a Moving Camera from PointCorrespondences and Fundamental Matrices
International Journal of Computer Vision
Stratified Self-Calibration with the Modulus Constraint
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Case Against Kruppa's Equations for Camera Self-Calibration
IEEE Transactions on Pattern Analysis and Machine Intelligence
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Autocalibration and the absolute quadric
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Critical Motion Sequences for Monocular Self-Calibration and Uncalibrated Euclidean Reconstruction
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
The Modulus Constraint: A New Constraint for Self-Calibration
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
Euclidean Reconstruction from Constant Intrinsic Parameters
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
Three-Dimensional Projective Reconstruction from Three Views
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 1
Camera Autocalibration and Horopter Curves
International Journal of Computer Vision
Camera Self-Calibration: A New Approach for Solving the Modulus Constraint
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 4 - Volume 04
Globally Convergent Autocalibration Using Interval Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Euclidean path modeling for video surveillance
Image and Vision Computing
An automatic camera calibration method using GPS-enabled mobile device
ICACT'09 Proceedings of the 11th international conference on Advanced Communication Technology - Volume 1
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This paper presents a new approach for self-calibrating a moving camera with constant intrinsic parameters. Unlike existing methods, the proposed method turns the self-calibration problem into one of solving bivariate polynomial equations. In particular, we show that each pair of images partially identifies a pair of 3D points that lie on the plane at infinity. These points are parameterized in terms of the real eigenvalue of the homography of the plane at infinity. A triplet of images identifies six such points on which the coplanarity constraint is enforced leading to a set of quintic and sextic polynomial equations. These equations are solved using a homotopy continuation method. More images allow to isolate the real eigenvalue associated with each motion and thus, to fully identify the points at infinity. The method also presents inequality conditions that allow to eliminate spurious solutions. Degenerate motions, not allowing the calculation of the eigenvalues, are also presented here. Once the 3D points at infinity are localized, both the plane at infinity and the Kruppa's coefficients can be linearly estimated.