Abstract

When faced with an ellipse fitting problem, practitioners fre- quently resort to algebraic ellipse fitting methods due to their simplicity and efficiency. Currently, practitioners must choose between algebraic methods that guarantee an ellipse fit but exhibit high bias, and geo- metric methods that are less biased but may no longer guarantee an ellipse solution. We address this limitation by proposing a method that strikes a balance between these two ob jectives. Specifically, we propose a fast stable algorithm for fitting a guaranteed ellipse to data using the Sampson distance as a data-parameter discrepancy measure. We vali- date the stability, accuracy, and efficiency of our method on both real and synthetic data. Experimental results show that our algorithm is a fast and accurate approximation of the computationally more expensive orthogonal-distance-based ellipse fitting method. In view of these quali- ties, our method may be of interest to practitioners who require accurate and guaranteed ellipse estimates.