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Constrained quadratic errors-in-variables fitting

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Abstract

We propose an estimation method to fit conics and quadrics to data in the context of errors-in-variables where the fit is subject to constraints. The proposed algorithm is based on algebraic distance minimization and consists of solving a few generalized eigenvalue (or singular value) problems and is not iterative. Nonetheless, the algorithm produces accurate estimates, close to those obtained with maximum likelihood, while the constraints are also guaranteed to be satisfied. Important special cases, fitting ellipses, hyperbolas, parabolas, and ellipsoids to noisy data are discussed.

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Notes

  1. The only exceptions are long thin and short fat ellipsoids, in which case the proposed method might (but not necessarily will) require iterations for the bisection search on the value of k in (13), in the same way as in [15].

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Acknowledgements

We are grateful to the anonymous reviewers for their helpful comments. This work was supported by the fund of the Hungarian Academy of Sciences for control research, and partially by the European Union and the European Social Fund through project FuturICT.hu organized by VIKING Zrt. Balatonfüred (grant no. TÁMOP-4.2.2.C-11/1/KONV-2012-0013), and by the Hungarian Government via the National Development Agency financed by the Research and Technology Innovation Fund (grant no. KMR-12-1-2012-0441).

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Authors and Affiliations

  1. Department of Automation and Applied Informatics, Budapest University of Technology and Economics, Magyar tudósok krt. 2. (building Q), 1117, Budapest, Hungary

    Levente Hunyadi

  2. Department of Automation and Applied Informatics, MTA-BME Control Research Group, Budapest University of Technology and Economics, Magyar tudósok krt. 2. (building Q), 1117, Budapest, Hungary

    István Vajk

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  1. Levente Hunyadi
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  2. István Vajk
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Correspondence to Levente Hunyadi.

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Hunyadi, L., Vajk, I. Constrained quadratic errors-in-variables fitting. Vis Comput 30, 1347–1358 (2014). https://doi.org/10.1007/s00371-013-0885-2

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