Measurement error models
SIAM Journal on Matrix Analysis and Applications
Robust regression methods for computer vision: a review
International Journal of Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Artificial Intelligence - Special volume on computer vision
Unbiased Estimation of Ellipses by Bootstrapping
IEEE Transactions on Pattern Analysis and Machine Intelligence
Matrix computations (3rd ed.)
In Defense of the Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Development and Comparison of Robust Methodsfor Estimating the Fundamental Matrix
International Journal of Computer Vision
On the Optimization Criteria Used in Two-View Motion Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Determining the Epipolar Geometry and its Uncertainty: A Review
International Journal of Computer Vision
Direct Least Square Fitting of Ellipses
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Unbiased Estimation and Statistical Analysis of 3-D Rigid Motion from Two Views
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Bias of Conic Fitting and Renormalization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Epipolar Geometry and Linear Subspace Methods: A New Approach to Weak Calibration
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Epipole and fundamental matrix estimation using virtual parallax
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Statistical analysis of quadratic problems in computer vision
Statistical analysis of quadratic problems in computer vision
An Adaptive Contour Closure Algorithm and Its Experimental Evaluation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Implementing a Multi-Model Estimation Method
International Journal of Computer Vision
Factorization with Uncertainty
International Journal of Computer Vision
Pattern Recognition Letters
Another Way of Looking at Plane-Based Calibration: The Centre Circle Constraint
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part IV
Revisiting Hartley's Normalized Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
From FNS to HEIV: A Link between Two Vision Parameter Estimation Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the complexity of curve fitting algorithms
Journal of Complexity
An Information Fusion Framework for Robust Shape Tracking
IEEE Transactions on Pattern Analysis and Machine Intelligence
FNS, CFNS and HEIV: A Unifying Approach
Journal of Mathematical Imaging and Vision
Least Squares Fitting of Circles
Journal of Mathematical Imaging and Vision
Motion Recovery by Integrating over the Joint Image Manifold
International Journal of Computer Vision
Stabilizing the Focal Length Computation for 3-D Reconstruction from Two Uncalibrated Views
International Journal of Computer Vision
An Analysis of Linear Subspace Approaches for Computer Vision and Pattern Recognition
International Journal of Computer Vision
When are Simple LS Estimators Enough? An Empirical Study of LS, TLS, and GTLS
International Journal of Computer Vision
Estimation of Nonlinear Errors-in-Variables Models for Computer Vision Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Convergence of Fitting Algorithms in Computer Vision
Journal of Mathematical Imaging and Vision
Consistency of robust estimators in multi-structural visual data segmentation
Pattern Recognition
On the Consistency of the Normalized Eight-Point Algorithm
Journal of Mathematical Imaging and Vision
Performance evaluation of iterative geometric fitting algorithms
Computational Statistics & Data Analysis
Journal of Mathematical Imaging and Vision
International Journal of Computer Vision
Rank Constraints for Homographies over Two Views: Revisiting the Rank Four Constraint
International Journal of Computer Vision
Compact Fundamental Matrix Computation
PSIVT '09 Proceedings of the 3rd Pacific Rim Symposium on Advances in Image and Video Technology
Error Analysis in Homography Estimation by First Order Approximation Tools: A General Technique
Journal of Mathematical Imaging and Vision
Linear Quasi-Parallax SfM Using Laterally-Placed Eyes
International Journal of Computer Vision
A new approach to estimating fundamental matrix
Image and Vision Computing
Highest accuracy fundamental matrix computation
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
Unified Computation of Strict Maximum Likelihood for Geometric Fitting
Journal of Mathematical Imaging and Vision
Robust fitting of ellipses and spheroids
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Hyper least squares fitting of circles and ellipses
Computational Statistics & Data Analysis
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Ellipse fitting with hyperaccuracy
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Robust ellipse and spheroid fitting
Pattern Recognition Letters
Optimal estimation of homogeneous vectors
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
An extended system method for consistent fundamental matrix estimation
ICIC'05 Proceedings of the 2005 international conference on Advances in Intelligent Computing - Volume Part I
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
Renormalization returns: hyper-renormalization and its applications
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
Optimization techniques for geometric estimation: beyond minimization
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Generalized, basis-independent kinematic surface fitting
Computer-Aided Design
Geometric property based ellipse detection method
Journal of Visual Communication and Image Representation
Hi-index | 0.00 |
We present an algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise, i.e., each data point having a different covariance matrix. The algorithm is motivated by the recovery of bilinear forms, one of the fundamental problems in computer vision which appears whenever the epipolar constraint is imposed, or a conic is fit to noisy data points. We employ the errors-in-variables (EIV) model and show why already at moderate noise levels most available methods fail to provide a satisfactory solution. The improved behavior of the new algorithm is due to two factors: taking into account the heteroscedastic nature of the errors arising from the linearization of the bilinear form, and the use of generalized singular value decomposition (GSVD) in the computations. The performance of the algorithm is compared with several methods proposed in the literature for ellipse fitting and estimation of the fundamental matrix. It is shown that the algorithm achieves the accuracy of nonlinear optimization techniques at much less computational cost.