Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
In Defense of the Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Vision and Image Understanding
Determining the Epipolar Geometry and its Uncertainty: A Review
International Journal of Computer Vision
Multiple view geometry in computer vision
Multiple view geometry in computer vision
Bayesian Model Estimation and Selection for Epipolar Geometry and Generic Manifold Fitting
International Journal of Computer Vision
Motion Parameter Estimation from Global Flow Field Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Moving Object Recognition Method by Optical Flow Analysis
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
Motion Estimation Using the Differential Epipolar Equation
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
Recovery of Epipolar Geometry as a Manifold Fitting Problem
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Uncalibrated Two-View Metrology
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 1 - Volume 01
Mobile robot visual navigation using multiple features
EURASIP Journal on Applied Signal Processing
Direct Computation of the Focus of Expansion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Focus of expansion localization through inverse C-velocity
ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing: Part I
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For the FOE estimation, there are basically three kinds of estimation methods in the literature: algebraic, geometric, and the maximum likelihood-based ones. In this paper, our attention is focused on the geometric method. The computational complexity of the classical geometric method is usually very high because it needs to solve a non-linear minimum problem with many variables. In this work, such a minimum problem is converted into an equivalent one with only two variables and accordingly a simplified geometric method is proposed. Based on the equivalence of the classical geometric method and the proposed simplified geometric method, we show that the measurement errors can at most be ''corrected'' only in one of the two images by geometric methods. In other words, it is impossible to correct the measurement errors in both of the two images. In addition, we show that the ''corrected'' corresponding pairs by geometric methods cannot in general meet some of the inherent constraints of corresponding pairs under pure camera translations. Hence, it is not proper to consider the ''corrected'' corresponding pairs as ''faithful'' corresponding pairs in geometric methods, and the estimated FOE from such pairs is not necessarily trustworthier. Finally, a new geometric algorithm, which automatically enforces the inherent constraints, is proposed in this work, and better FOE estimation and more faithful corresponding pairs are obtained.