IEEE Transactions on Pattern Analysis and Machine Intelligence
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Cramer-Rao lower bounds for curve fitting
Graphical Models and Image Processing
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
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Bundle Adjustment - A Modern Synthesis
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
Nonlinear Estimation of the Fundamental Matrix with Minimal Parameters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of Nonlinear Errors-in-Variables Models for Computer Vision Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ellipse Fitting with Hyperaccuracy
IEICE - Transactions on Information and Systems
Performance evaluation of iterative geometric fitting algorithms
Computational Statistics & Data Analysis
Practical Global Optimization for Multiview Geometry
International Journal of Computer Vision
International Journal of Computer Vision
SBA: A software package for generic sparse bundle adjustment
ACM Transactions on Mathematical Software (TOMS)
Optimal algorithms in multiview geometry
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part I
Conic fitting using the geometric distance
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
Hyper least squares fitting of circles and ellipses
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
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We overview techniques for optimal geometric estimation from noisy observations for computer vision applications. We first describe estimation techniques based on minimization of given cost functions: least squares (LS), maximum likelihood (ML), which includes reprojection error minimization (Gold Standard) as a special case, and Sampson error minimization. We then formulate estimation techniques not based on minimization of any cost function: iterative reweight, renormalization, and hyper-renormalization. Showing numerical examples, we conclude that hyper-renormalization is robust to noise and currently is the best method.