The Visual Computer

, Volume 30, Issue 12, pp 1347–1358 | Cite as

Constrained quadratic errors-in-variables fitting

  • Levente Hunyadi
  • István Vajk
Original Article


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.


Parameter estimation Direct methods Fitting with constraints Eigenvalue problem 



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 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Automation and Applied InformaticsBudapest University of Technology and EconomicsBudapestHungary
  2. 2.Department of Automation and Applied Informatics, MTA-BME Control Research GroupBudapest University of Technology and EconomicsBudapestHungary

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