Direct least squares fitting of ellipses

This paper 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 4ac-b²=1 the new method incorporates the ellipticity constraint into the normalization factor. The new method combines several advantages: 1) it is ellipse-specific so that even bad data will always return an ellipse; 2) it can be solved naturally by a generalized eigensystem, and 3) it is extremely robust, efficient and easy to implement. We compare the proposed method to other approaches and show its robustness on several examples in which other nonellipse-specific approaches would fail or require computationally expensive iterative refinements