Ellipse-specific direct least-square fitting

Ellipse fitting is one of the classic problems of pattern recognition and has been subject to considerable attention because of its many applications. This article presents the first direct method for specifically fitting ellipses in the least squares sense. Previous approaches used either generic conic fitting or relied on iterative methods to recover elliptic solutions. The proposed method is (i) ellipse-specific, (ii) directly solved by a generalised eigen-system, (iii) has a desirable low-eccentricity bias, and (iv) is robust to noise. We provide a theoretical demonstration, several examples and the Matlab coding of the algorithm