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Two-Stage Outlier Elimination for Robust Curve and Surface Fitting


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.

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Correspondence to Jieqi Yu.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Yu, J., Zheng, H., Kulkarni, S.R. et al. Two-Stage Outlier Elimination for Robust Curve and Surface Fitting. EURASIP J. Adv. Signal Process. 2010, 154891 (2010).

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