3D motion recovery via affine epipolar geometry
International Journal of Computer Vision
Artificial Intelligence - Special volume on computer vision
In Defense of the Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Epipolar Geometry in Stereo, Motion, and Object Recognition: A Unified Approach
Epipolar Geometry in Stereo, Motion, and Object Recognition: A Unified Approach
Optimal Motion and Structure Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A general expression of the fundamental matrix for both perspective and affine cameras
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
A Multi-Frame Structure-from-Motion Algorithm under Perspective Projection
International Journal of Computer Vision - Special issue on computer vision research at NEC Research Institute
Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint
International Journal of Computer Vision - Special issue on a special section on visual surveillance
On the Fitting of Surfaces to Data with Covariances
IEEE Transactions on Pattern Analysis and Machine Intelligence
Rationalising the Renormalisation Method of Kanatani
Journal of Mathematical Imaging and Vision
A New Structure-from-Motion Ambiguity
IEEE Transactions on Pattern Analysis and Machine Intelligence
Exact Two-Image Structure from Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Bootstrapping Errors-in-Variables Models
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Revisiting Hartley's Normalized Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust and Rapid Generation of Animated Faces from Video Images: A Model-Based Modeling Approach
International Journal of Computer Vision - Special Issue on Research at Microsoft Corporation
Globally Optimal Estimates for Geometric Reconstruction Problems
International Journal of Computer Vision
Error Analysis in Homography Estimation by First Order Approximation Tools: A General Technique
Journal of Mathematical Imaging and Vision
Efficient tracking and ego-motion recovery using gait analysis
Signal Processing
Estimating the fundamental matrix using second-order cone programming
AICI'11 Proceedings of the Third international conference on Artificial intelligence and computational intelligence - Volume Part III
Hessian Matrix vs. Gauss-Newton Hessian Matrix
SIAM Journal on Numerical Analysis
Computer Vision and Image Understanding
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The three best-known criteria in two-view motion analysis are based, respectively, on the distances between points and their corresponding epipolar lines, on the gradient-weighted epipolar errors, and on the distances between points and the reprojections of their reconstructed points. The last one has a better statistical interpretation, but is, however, significantly slower than the first two. In this paper, I show that, given a reasonable initial guess of the epipolar geometry, the last two criteria are equivalent when the epipoles are at infinity, and differ from each other only a little even when the epipoles are in the image, as shown experimentally. The first two criteria are equivalent only when the epipoles are at infinity and when the observed object/scene has the same scale in the two images. This suggests that the second criterion is sufficient in practice because of its computational efficiency. Experiments with several thousand computer simulations and four sets of real data confirm the analysis. The result is valid for both calibrated and uncalibrated images.