Robust regression and outlier detection
Robust regression and outlier detection
In Defense of the Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
The Role of Total Least Squares in Motion Analysis
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
Matching with PROSAC " Progressive Sample Consensus
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Two-View Geometry Estimation Unaffected by a Dominant Plane
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Guided-MLESAC: Faster Image Transform Estimation by Using Matching Priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Performance Evaluation of Local Descriptors
IEEE Transactions on Pattern Analysis and Machine Intelligence
Globally Optimal Estimates for Geometric Reconstruction Problems
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Dynamic Measurement Clustering to Aid Real Time Tracking
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
A Comparison of Affine Region Detectors
International Journal of Computer Vision
Balanced Exploration and Exploitation Model Search for Efficient Epipolar Geometry Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple-View Geometry Under the {$L_\infty$}-Norm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Model Fitting with Sufficient Random Sample Coverage
International Journal of Computer Vision
Accelerated hypothesis generation for multi-structure robust fitting
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Planar affine rectification from change of scale
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part IV
Direct estimation of homogeneous vectors: an ill-solved problem in computer vision
ICVGIP'06 Proceedings of the 5th Indian conference on Computer Vision, Graphics and Image Processing
Accelerated Hypothesis Generation for Multistructure Data via Preference Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computational Statistics & Data Analysis
The Random Cluster Model for robust geometric fitting
CVPR '12 Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
Dynamic and hierarchical multi-structure geometric model fitting
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
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When sampling minimal subsets for robust parameter estimation, it is commonly known that obtaining an all-inlier minimal subset is not sufficient; the points therein should also have a large spatial extent. This paper investigates a theoretical basis behind this principle, based on a little known result which expresses the least squares regression as a weighted linear combination of all possible minimal subset estimates. It turns out that the weight of a minimal subset estimate is directly related to the span of the associated points. We then derive an analogous result for total least squares which, unlike ordinary least squares, corrects for errors in both dependent and independent variables. We establish the relevance of our result to computer vision by relating total least squares to geometric estimation techniques. As practical contributions, we elaborate why naive distance-based sampling fails as a strategy to maximise the span of all-inlier minimal subsets produced. In addition we propose a novel method which, unlike previous methods, can consciously target all-inlier minimal subsets with large spans.