Robust Fitting of Parametric Curves

We consider the problem of fitting a parametric curve to a given point cloud (e.g., measurement data). Least-squares approximation, i.e., minimization of the l2 norm of residuals (the Euclidean distances to the data points), is the most common approach. This is due to its computational simplicity [1]. However, in the case of data that is affected by noise or contains outliers, this is not always the best choice, and other error functions, such as general lp norms have been considered [2]. We describe an extension of the least-squares approach which leads to Gauss-Newton-type methods for minimizing other, more general functions of the residuals, without increasing the computational costs significantly.