**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
**Available:** Pr-A-98-06.ps

**Contact**: Müller, Christine H., Georg-August-University of Göttingen, Institute of Mathematical Stochastics, Lotzestr. 13, D-37083 Göttingen,Germany
(chmuelle@math.uni-goettingen.de)

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