Preprint No. A-98-06

Christine H. Müller

On the use of high breakdown point estimators in the image analysis

Abstract: For eliminating noise from an image, Meer et al. (1990, 1991) have proposed to use high breakdown point estimators and in particular to use the least median of squares (LMS) estimator for linear regression. But, the highest breakdown points are attained by other estimators as the Cauchy estimator and some least trimmed squares (LTS) estimators. Therefore, in this paper the behavior of the Cauchy estimator and the LTS estimator in image analysis is studied and compared with that of the LMS estimator and the least squares (LS) estimator. For that, test images with 0\%, 14\%, 30\%, 44\% and 49\% noise are used. It turns out that the LTS estimator can eliminate a high amount of noise and preserves discontinuities while the Cauchy estimator behaves similar to the nonrobust LS estimator.

Keywords: breakdown point, least median of squares estimator, least trimmed squares estimator, Cauchy estimator, noisy images

Mathematics Subject Classification (MSC91): 62F35 Robustness and adaptive procedures , 62J05 Linear regression

Language: ENG


Contact: Müller, Christine H., Georg-August-University of Göttingen, Institute of Mathematical Stochastics, Lotzestr. 13, D-37083 Göttingen,Germany (

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