Journal article
Outlier robust corner-preserving methods for reconstructing noisy images
Publication Details
Authors: | Hillebrand, M.; Müller, C. |
Publication year: | 2007 |
Journal: | The Annals of Statistics |
Pages range : | 132-165 |
Volume number: | 35 |
ISSN: | 0090-5364 |
eISSN: | 2168-8966 |
DOI-Link der Erstveröffentlichung: |
Abstract
The ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother. Unfortunately, they usually seem to be at odds with each other; one can only improve one property at the cost of the other. By combining M-smoothing and least-squares-trimming, the TM-smoother is introduced as a means to unify corner-preserving properties and outlier robustness. To identify edge- and corner-preserving properties, a new theory based on differential geometry is developed. Further, robustness concepts are transferred to image processing. In two examples, the TM-smoother outperforms other comer-preserving smoothers. A software package containing both the TM- and the M-smoother can be downloaded from the Internet.
The ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother. Unfortunately, they usually seem to be at odds with each other; one can only improve one property at the cost of the other. By combining M-smoothing and least-squares-trimming, the TM-smoother is introduced as a means to unify corner-preserving properties and outlier robustness. To identify edge- and corner-preserving properties, a new theory based on differential geometry is developed. Further, robustness concepts are transferred to image processing. In two examples, the TM-smoother outperforms other comer-preserving smoothers. A software package containing both the TM- and the M-smoother can be downloaded from the Internet.
