A Comparative Study Of Ellipses Fitting Methods

Ellipses Fitting is a classical problem in data processing. It has very importantapplications in digital image processing, machine vision and pattern recognition.However, it is difficult to find a fitting method which is robust, efficient and easy toimplement when both noise and outliers exist in real data. In this thesis we discusssome popular ellipse fitting techniques, such as least squares fitting, Hough transform,five points ellipse fitting and so on. We implement some of them and compare theirresults, then we raise two important problems in ellipse fitting: the interference fromoutliers; and the instability in the fitting of short curve sections with nosie.To resolve these two problems, we first detect the outliers in the initial fittingdeviations using the method of VfM(variance-from-median)and remove them by iterationto reduce the interference from outliers; then we use the extended Kalman filter to fulfillthe ellipse fitting with the processed data, and make a prediction with confidence regionsfor the fitting result. Experimental results show that this new method is really robust,efficient and easy to implement.