Direct least-squares fitting of ellipses

  • Andrew Fitzgibbon ,
  • M. Pilu ,
  • R. B. Fisher

IEEE Transactions on Pattern Analysis and Machine Intelligence, Proceedings of the International Conference on Pattern Recognition |

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 ac – b 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.