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 ℓ 2 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 ℓ p 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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)