Direct least square fitting of ellipses

TLDR

Previous algorithms either fitted general conics or were computationally expensive. This work presents a new efficient method for fitting ellipses to scattered data. By minimizing the algebraic distance subject to the constraint 4ac−b²=1, the new method incorporates the ellipticity constraint into the normalization factor and can be solved naturally by a generalized eigensystem. The proposed method is ellipse‑specific, robust, efficient, and easy to implement, ensuring that even bad data always return an ellipse.

Abstract

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 4ac-b/sup 2/=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.