Ellipse fitting by accumulating five-point fits
Pattern Recognition Letters
Direct Least Square Fitting of Ellipses
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient algorithms for mining outliers from large data sets
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
Orthogonal Distance Fitting of Implicit Curves and Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Algorithms for Mining Distance-Based Outliers in Large Datasets
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
Journal of Computational and Applied Mathematics
Outlier Detection Using k-Nearest Neighbour Graph
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
A Survey of Outlier Detection Methodologies
Artificial Intelligence Review
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Workshops - Volume 03
Spatial Outlier Detection: A Graph-Based Approach
ICTAI '07 Proceedings of the 19th IEEE International Conference on Tools with Artificial Intelligence - Volume 01
Robust Scale Estimation from Ensemble Inlier Sets for Random Sample Consensus Methods
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
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An outlier elimination algorithm for curve/surface fitting is proposed. This two-stage hybrid algorithm employs a proximity-based outlier detection algorithm, followed by a model-based one. First, a proximity graph is generated. Depending on the use of a hard/soft threshold of the connectivity of observations, two algorithms are developed, one graph-component-based and the other eigenspace-based. Second, a model-based algorithm, taking the classification of inliers/outliers of the first stage as its initial state, iteratively refits and retests the observations with respect to the curve/surface model until convergence. These two stages compensate for each other so that outliers of various types can be eliminated with a reasonable amount of computation. Compared to other algorithms, this hybrid algorithm considerably improves the robustness of ellipse/ellipsoid fitting for scenarios with large portions of outliers and high levels of inlier noise, as demonstrated by extensive simulations.