In this paper we present a new efficient method for fitting ellipse to scattered data based on the Legendre moments. The least squares method is the most commonly used technique for fitting an ellipse. However, it has a low breakdown, which means that it performs poorly in the presence of outliers. Our new statistical approach is based on the expansion of the probability density function (p.d.f) in terms of Legendre polynomials which guarantees the extraction of an ellipse even for high rate of outliers and an important level of noise. Any constraint has been required in our approach; this leads to be applied for general conic fitting. A comparison is given between our approach and Direct Least Squares fitting of ellipses approach. Several tests demonstrate that it is preferment in terms of accuracy and robustness.

Ellipse fitting, Legendre moments, Probability density function, Maximum Entropy Principal, least squares