Characterizing the uncertainty of the fundamental matrix
Computer Vision and Image Understanding
Determining the Epipolar Geometry and its Uncertainty: A Review
International Journal of Computer Vision
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
The Geometry of Multiple Images: The Laws That Govern The Formation of Images of A Scene and Some of Their Applications
Epipolar Geometry in Stereo, Motion, and Object Recognition: A Unified Approach
Epipolar Geometry in Stereo, Motion, and Object Recognition: A Unified Approach
Concerning Bayesian Motion Segmentation, Model, Averaging, Matching and the Trifocal Tensor
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
Maximum Likelihood Robust Regression by Mixture Models
Journal of Mathematical Imaging and Vision
Real-time visuomotor update of an active binocular head
Autonomous Robots
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In this paper, we are going to answer the following question: assuming that we have estimates for the epipolar geometry and its uncertainty between two views, how probable is it that a new, independent point pair will satisfy the true epipolar geometry and be, in this sense, a feasible candidate correspondence pair? If we knew the true fundamental matrix, the answer would be trivial but in reality we do not know it because of estimation errors. So, as an independent point in the first view is given, we will show we may compute the point-probability-density function, termed as the epipolar pdf, for the epipolar line points in the second view that describes the current level of knowledge of the epipolar geometry between the views. This point-point-probability-density relation is a probabilistic form of the epipolar constraint that also approaches the true point-line relation as the number of training correspondences tends to infinity. In this paper, we will also show that the eigenvectors of the epipolar line covariance matrix have certain interpretations on the image plane, of which one is the previously observed, narrowest point of the epipolar envelope. The results of this paper are important since the uncertainty of the epipolar constraint can be now taken into account in a sound way in applications.