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<p><b>Abstract</b>—This work presents a new efficient method for fitting ellipses to scattered data. Previous algorithms either fitted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4<it>ac</it>−<it>b</it><super>2</super> = 1, the new method incorporates the ellipticity constraint into the normalization factor. The proposed method combines several advantages: It is ellipse-specific, so that even bad data will always return an ellipse. It can be solved naturally by a generalized eigensystem. It is extremely robust, efficient, and easy to implement.</p>
Algebraic models, ellipse fitting, least squares fitting, constrained minimization, generalized eigenvalue problem.
Andrew Fitzgibbon, Maurizio Pilu, Robert B. Fisher, "Direct Least Square Fitting of Ellipses", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 21, no. , pp. 476-480, May 1999, doi:10.1109/34.765658
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