On robust corner-preserving smoothing in image processing

This Ph.D. thesis treats consistency, robustness and dicontinuity-preserving issues of M-kernel estimators in one- and two-dimensional regression. The M-kernel smoother was first introduced by Härdle and Gasser (1984) who provide a restricted valid proof of consistency for a monotone score function and show the minimax property. Chu et al. (1998) take a density as (redescending) score function. They observe a good jump-preserving property. However, as shown in this thesis, consistency cannot be achieved under the assumptions given in their paper. In this thesis, complete proofs for robustness and consistency of both monotone and redescending M-kernel smoothers are provided. Further, consistency close to a discontinuity (called 'jump-preserving' property) is shown for the redescending M-kernel smoother. In a further step the redescending M-kernel smoother is applied to images which can be regarded as two-dimensional regression functions. It is shown that the redescending M-kernel smoother even preserves sharp corners which is, in combination with qualitative asymptotic robustness, a unique property among nonparametric smoothers. To achieve a quantitative nonasymptotic robustness property, the Trimmed M-Kernel Estimator is introduced combining the corner-preserving property of the redescending M-kernel smoother and the robustness against outliers of the LTS estimator.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Oldenburg

Year

2003

Author dc:creator

• Hillebrand, Martin

• [Keine Schlagwörter von Autor/in vergeben.]

Repository record source_url

http://oops.uni-oldenburg.de/223

OAI identifier oai:identifier

oai:oops.uni-oldenburg.de:223