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We present a new approach to two-dimensional (2-D) robust spline image smoothing based on the M-estimator algorithm. Unlike in other M-estimator based image processing algorithms, the new algorithm takes into consideration the spatial relations between picture elements. The contribution of the sample to the model depends not only on the current residual of that sample, but also on the neighboring residuals. A smoothing parameter is estimated separately for each processing window and it adapts to the local structure of the image. The proposed algorithm is applied to image filtering. The resulting filter preserves details and suppresses additive Gaussian and impulsive noise efficiently