Premium
Robust fitting of parametric curves
Author(s) -
Aigner Martin,
Jüttler Bert
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700009
Subject(s) - outlier , parametric statistics , curve fitting , data point , least squares function approximation , parametric equation , mathematics , extension (predicate logic) , gauss , minification , non linear least squares , euclidean geometry , algorithm , mathematical optimization , norm (philosophy) , computer science , statistics , estimation theory , geometry , physics , quantum mechanics , estimator , political science , law , programming language
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)