Geometric computation for machine vision
Geometric computation for machine vision
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Robust recovery of the epipolar geometry for an uncalibrated stereo rig
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
Performance characterization of fundamental matrix estimation under image degradation
Machine Vision and Applications - Special issue on performance evaluation
Self-Calibration of a Moving Camera from PointCorrespondences and Fundamental Matrices
International Journal of Computer Vision
The Development and Comparison of Robust Methodsfor Estimating the Fundamental Matrix
International Journal of Computer Vision
Determining the Epipolar Geometry and its Uncertainty: A Review
International Journal of Computer Vision
Robust detection of degenerate configurations while estimating the fundamental matrix
Computer Vision and Image Understanding
Estimation of Relative Camera Positions for Uncalibrated Cameras
ECCV '92 Proceedings of the Second European Conference on Computer Vision
What can be seen in three dimensions with an uncalibrated stereo rig
ECCV '92 Proceedings of the Second European Conference on Computer Vision
In defence of the 8-point algorithm
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
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In this paper we consider the problem of estimating the fundamental matrix from point correspondences. It is well known that the most accurate estimates of this matrix are obtained by criteria minimizing geometric errors when the data are affected by noise. It is also well known that these criteria amount to solving non-convex optimization problems and, hence, their solution is affected by the optimization starting point. Generally, the starting point is chosen as the fundamental matrix estimated by a linear criterion but this estimate can be very inaccurate and, therefore, inadequate to initialize methods with other error criteria. Here we present a method for obtaining a more accurate estimate of the fundamental matrix with respect to the linear criterion. It consists of the minimization of the algebraic error taking into account the rank 2 constraint of the matrix. Our aim is twofold. First, we show how this nonconvex optimization problem can be solved avoiding local minima using recently developed convexification techniques. Second, we show that the estimate of the fundamental matrix obtained using our method is more accurate than the one obtained from the linear criterion, where the rank constraint of the matrix is imposed after its computation by setting the smallest singular value to zero. This suggests that our estimate can be used to initialize non-linear criteria such as the distance to epipolar lines and the gradient criterion, in order to obtain a more accurate estimate of the fundamental matrix. As a measure of the accuracy, the obtained estimates of the epipolar geometry are compared in experiments with synthetic and real data.