Measurement error models
Numerical recipes in C: the art of scientific computing
Numerical recipes in C: the art of scientific computing
Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter
Image and Vision Computing - Special issue: 5th Alvey vision meeting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ellipse detection and matching with uncertainty
Image and Vision Computing - Special issue: BMVC 1991
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
A note on the least squares fitting of ellipses
Pattern Recognition Letters
Artificial Intelligence - Special volume on computer vision
A buyer's guide to conic fitting
BMVC '95 Proceedings of the 6th British conference on Machine vision (Vol. 2)
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
Robust Parameter Estimation in Computer Vision
SIAM Review
Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint
International Journal of Computer Vision - Special issue on a special section on visual surveillance
Rationalising the Renormalisation Method of Kanatani
Journal of Mathematical Imaging and Vision
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
Nonparametric Segmentation of Curves into Various Representations
IEEE Transactions on Pattern Analysis and Machine Intelligence
What can be seen in three dimensions with an uncalibrated stereo rig
ECCV '92 Proceedings of the Second European Conference on Computer Vision
The Role of Total Least Squares in Motion Analysis
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
Motion analysis with a camera with unknown, and possibly varying intrinsic parameters
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Reduction of Bias in Maximum Likelihood Ellipse Fitting
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
Estimation with Bilinear Constraints in Computer Vision
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Pattern Recognition Letters
General Trajectory Triangulation
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
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
A General Framework for Trajectory Triangulation
Journal of Mathematical Imaging and Vision
FNS, CFNS and HEIV: A Unifying Approach
Journal of Mathematical Imaging and Vision
Stabilizing the Focal Length Computation for 3-D Reconstruction from Two Uncalibrated Views
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 Consistency of the Normalized Eight-Point Algorithm
Journal of Mathematical Imaging and Vision
Epipolar geometry estimation based on evolutionary agents
Pattern Recognition
Performance evaluation of iterative geometric fitting algorithms
Computational Statistics & Data Analysis
Journal of Mathematical Imaging and Vision
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
Multiple ellipses detection in noisy environments: A hierarchical approach
Pattern Recognition
Camera motion estimation by tracking contour deformation: Precision analysis
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
SIAM Journal on Matrix Analysis and Applications
Hyper least squares fitting of circles and ellipses
Computational Statistics & Data Analysis
Optimal two-view planar scene triangulation
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part II
Wide-baseline correspondence from locally affine invariant contour matching
ICIAR'11 Proceedings of the 8th international conference on Image analysis and recognition - Volume Part I
Hypersurface fitting via jacobian nonlinear PCA on riemannian space
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
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
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
Guaranteed ellipse fitting with the sampson distance
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
Robust hypersurface fitting based on random sampling approximations
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - 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
Geometric property based ellipse detection method
Journal of Visual Communication and Image Representation
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We consider the problem of estimating parameters of a model described by an equation of special form. Specific models arise in the analysis of a wide class of computer vision problems, including conic fitting and estimation of the fundamental matrix. We assume that noisy data are accompanied by (known) covariance matrices characterizing the uncertainty of the measurements. A cost function is first obtained by considering a maximum-likelihood formulation and applying certain necessary approximations that render the problem tractable. A novel, Newton-like iterative scheme is then generated for determining a minimizer of the cost function. Unlike alternative approaches such as Sampson's method or the renormalization technique, the new scheme has as its theoretical limit the minimizer of the cost function. Furthermore, the scheme is simply expressed, efficient, and unsurpassed as a general technique in our testing. An important feature of the method is that it can serve as a basis for conducting theoretical comparison of various estimation approaches.