Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric computation for machine vision
Geometric computation for machine vision
Describing Complicated Objects by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical analysis of geometric computation
CVGIP: Image Understanding
Using Geometric Distance Fits for 3-D Object Modeling and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint
International Journal of Computer Vision - Special issue on a special section on visual surveillance
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
A Bayesian Method for Fitting Parametric and Nonparametric Models to Noisy Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Bayesian Model Estimation and Selection for Epipolar Geometry and Generic Manifold Fitting
International Journal of Computer Vision
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Bias of Conic Fitting and Renormalization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of Relative Camera Positions for Uncalibrated Cameras
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Camera Self-Calibration: Theory and Experiments
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
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
Matching constraints and the joint image
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Recovery of Epipolar Geometry as a Manifold Fitting Problem
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
All points considered: a maximum likelihood method for motion recovery
Proceedings of the 11th international conference on Theoretical foundations of computer vision
A Probabilistic Method for Point Matching in the Presence of Noise and Degeneracy
Journal of Mathematical Imaging and Vision
Robust Algebraic Segmentation of Mixed Rigid-Body and Planar Motions from Two Views
International Journal of Computer Vision
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Recovery of epipolar geometry is a fundamental problem in computer vision. The introduction of the "joint image manifold" (JIM) allows to treat the recovery of camera motion and epipolar geometry as the problem of fitting a manifold to the data measured in a stereo pair. The manifold has a singularity and boundary, therefore special care must be taken when fitting it.Four fitting methods are discussed--direct, algebraic, geometric, and the integrated maximum likelihood (IML) based method. The first three methods are the exact analogues of three common methods for recovering epipolar geometry. The more recently introduced IML method seeks the manifold which has the highest "support," in the sense that the largest measure of its points are close to the data. While computationally more intensive than the other methods, its results are better in some scenarios. Both simulations and experiments suggest that the advantages of IML manifold fitting carry over to the task of recovering epipolar geometry, especially when the extent of the data and/or the motion are small.