Optimal ellipse fitting method based on least-square principle

The fragmental ellipse fitting algorithm based on least square was studied. The ellipse-constraint algebraic fitting always provides an elliptical solution, but the bias is inevitably added to result because the algorithm involves all the sample data including some much biased data. Based on this situation, the random theory was introduced. First, an ellipse was fitted by six points which were selected randomly. Then the number of points which match the ellipse was calculated. Repeating the process some times, according to the voting mechanism, the best ellipse is the ellipse whose matching point number is largest. A rapid algorithm with the ability to abandon the biased sample data was presented. The application of algorithm in a real-time image processing system demonstrates that this algorithm can efficiently fit an ellipse to experimental data including a significant percentage of gross errors and the rapidity of the algorithm can meet the requirement of real-time system.