On Robust Corner-preserving Smoothingin Image Processing

Removing a high amount of noise and preserving most structureare desirable properties of an image smoother. Unfortunately, theyseem to be contradictory: usually one can only improve one propertyat the cost of the other one. This thesis shows how this can be resolved:for a deeper understanding of the problem, consistency, robustness anddiscontinuity-preserving issues of M-kernel estimators in one-and two-dimensional regression are treated in detail. To identify edge- andcorner-preserving properties, a new theory based on differential geometryis developed. Finally, by combining M-smoothing and leastsquares-trimming, the TM-smoother is introduced unifying cornerpreservingproperties and outlier robustness.