Direct Least Square Fitting of Ellipses

  • Authors:
  • Andrew Fitzgibbon;Maurizio Pilu;Robert B. Fisher

  • Affiliations:
  • Univ. of Oxford, Oxford, England;Hewlett-Packard Research Labs, Bristol, England;Univ. of Edinburgh, Edinburgh, United Kingdom

  • Venue:
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
  • Year:
  • 1999

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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驴b2 = 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.