On the conic section fitting problem

Authors:
Sergiy Shklyar;Alexander Kukush;Ivan Markovsky;Sabine Van Huffel
Affiliations:
Kiew National Taras Shevchenko University, Vladimirskaya st. 64, 01033, Kiev, Ukraine;Kiew National Taras Shevchenko University, Vladimirskaya st. 64, 01033, Kiev, Ukraine;K.U.Leuven, ESAT-SCD, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium;K.U.Leuven, ESAT-SCD, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium
Venue:
Journal of Multivariate Analysis
Year:
2007

Citing 2
Cited 0

Statistical Bias of Conic Fitting and Renormalization

IEEE Transactions on Pattern Analysis and Machine Intelligence
Consistent least squares fitting of ellipsoids

Numerische Mathematik

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Abstract

Adjusted least squares (ALS) estimators for the conic section problem are considered. Consistency of the translation invariant version of ALS estimator is proved. The similarity invariance of the ALS estimator with estimated noise variance is shown. The conditions for consistency of the ALS estimator are relaxed compared with the ones of the paper Kukush et al. [Consistent estimation in an implicit quadratic measurement error model, Comput. Statist. Data Anal. 47(1) (2004) 123-147].