Direct Least Square Fitting of Ellipses

This work presents a new e cient method for tting ellipses to scattered data. Previous algorithms either tted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4ac b = 1 the new method incorporates the ellipticity constraint into the normalization factor. The proposed method combines several advantages: (i) It is ellipse-speci c so that even bad data will always return an ellipse; (ii) It can be solved naturally by a generalized eigensystem and (iii) it is extremely robust, e cient and easy to implement.