Open Access

Two-Stage Outlier Elimination for Robust Curve and Surface Fitting

  • Jieqi Yu1Email author,
  • Haipeng Zheng1,
  • Sanjeev R. Kulkarni1 and
  • HVincent Poor1
EURASIP Journal on Advances in Signal Processing20102010:154891

Received: 1 January 2010

Accepted: 7 June 2010

Published: 29 June 2010


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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Authors’ Affiliations

Department of Electrical Engineering, Princeton University, Princeton, USA


© Jieqi Yu et al. 2010

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.