Introduction

Ellipse fitting is one of the classic problems of pattern recognition and has been subject to considerable attention in the past ten years for its many application. Several techniques for fitting ellipses are based on mapping sets of points to the parameter space (notably the Hough transform).

In this paper we are concerned with the more fundamental problem of least squares (LSQ) fitting of ellipses to scattered data. Previous methods achieved ellipse fitting by using generic conic fitters that perform poorly, often yielding hyperbolic fits with noisy data, or by employing iterative methods, which are computationally expensive.

In this paper we presents and demonstrate the first ellipse-specific direct least squares fitting method that has the following desirable features: i) always yields elliptical fits ii) has low-eccentricity bias, and iii) is robust to noise.