Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Active tracking of foveated feature clusters using affine structure
International Journal of Computer Vision
Matrix computations (3rd ed.)
Direct Least Square Fitting of Ellipses
IEEE Transactions on Pattern Analysis and Machine Intelligence
Affine Structure and Motion from Points, Lines and Conics
International Journal of Computer Vision
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
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Linear fitting with missing data for structure-from-motion
Computer Vision and Image Understanding
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Factorization with Uncertainty
International Journal of Computer Vision
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
Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling
IEEE Transactions on Pattern Analysis and Machine Intelligence
Structure and Motion from Points, Lines and Conics with Affine Cameras
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
A Unified Factorization Algorithm for Points, Line Segments and Planes with Uncertainty Models
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Rank 1 Weighted Factorization for 3D Structure Recovery: Algorithms and Performance Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Motion segmentation with missing data using power factorization and GPCA
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
The geometry of weighted low-rank approximations
IEEE Transactions on Signal Processing
Recovering the missing components in a large noisy low-rank matrix: application to SFM
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimization Algorithms on Subspaces: Revisiting Missing Data Problem in Low-Rank Matrix
International Journal of Computer Vision
Rank Constraints for Homographies over Two Views: Revisiting the Rank Four Constraint
International Journal of Computer Vision
Error Analysis in Homography Estimation by First Order Approximation Tools: A General Technique
Journal of Mathematical Imaging and Vision
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In this paper, we employ low-rank matrix approximation to solve a general parameter estimation problem: where a non-linear system is linearized by treating the carrier terms as separate variables, thereby introducing heteroscedastic noise. We extend the bilinear approach to handle cases with heteroscedastic noise, in the framework of low-rank approximation. The ellipse fitting problem is investigated as a specific example of the general theory. Despite the impression given in the literature, the ellipse fitting problem is still unsolved when the data comes from a small section of the ellipse. Although there are already some good approaches to the problem of ellipse fitting, such as FNS and HEIV, convergence in these iterative approaches is not ensured, as pointed out in the literature. Another limitation of these approaches is that they cannot model the correlations among different rows of the "general measurement matrix". Our method, of employing the bilinear approach to solve the general heteroscedastic parameter estimation problem, overcomes these limitations: it is convergent, at least to a local optimum, and can cope with a general heteroscedastic problem. Experiments show that the proposed bilinear approach performs better than other competing approaches: although it is still far short of a solution when the data comes from a very small arc of the ellipse.