SIAM Journal on Matrix Analysis and Applications
Robust regression methods for computer vision: a review
International Journal of Computer Vision
In Defense of the Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Solutions to Least-Squares Problems with Uncertain Data
SIAM Journal on Matrix Analysis and Applications
Parameter Estimation in the Presence of Bounded Data Uncertainties
SIAM Journal on Matrix Analysis and Applications
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
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
The Role of Total Least Squares in Motion Analysis
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
In defence of the 8-point algorithm
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
From FNS to HEIV: A Link between Two Vision Parameter Estimation Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Further Improving Geometric Fitting
3DIM '05 Proceedings of the Fifth International Conference on 3-D Digital Imaging and Modeling
Computational Statistics & Data Analysis
Error Analysis in Homography Estimation by First Order Approximation Tools: A General Technique
Journal of Mathematical Imaging and Vision
Identification of neurofuzzy models using GTLS parameter estimation
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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A variety of least-squares estimators of significantly different complexity and generality are available to solve over-constrained linear systems. The most theoretically general may not necessarily be the best choice in practice; problem conditions may be such that simpler and faster algorithms, if theoretically inferior, would yield acceptable errors. We investigate when this may happen using homography estimation as the reference problem. We study the errors of LS, TLS, equilibrated TLS and GTLS algorithms with different noise types and varying intensity and correlation levels. To allow direct comparisons with algorithms from the applied mathematics and computer vision communities, we consider both inhomogeneous and homogeneous systems. We add noise to image co-ordinates and system matrix entries in separate experiments, to take into account the effect on noise properties (heteroscedasticity) of pre-processing data transformations. We find that the theoretically most general algorithms may not always be worth their higher complexity; comparable results are obtained with moderate levels of noise intensity and correlation. We identify such levels quantitatively for the reference problem, thus suggesting when simpler algorithms can be applied with limited errors in spite of their restrictive assumptions.