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