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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.

M. Pilu, R. B. Fisher and A. Fitzgibbon, "Direct Least Square Fitting of Ellipses," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 21, no. , pp. 476-480, 1999.
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