Adaptive order statistic filters for noise smoothing in digital images are presented. Two classes of adaptive filters are studied, namely, the least mean squares (LMS)-based adaptive order statistic filters and the signal-adaptive filters. The filter structures in the first class require a noise-free image to be used as a reference image, whereas those in the second class do not require a reference image. Two filter structures from the former class are examined: the adaptive locationinvariant L-filter and the adaptive Ll -filter. A novel signal-adaptive filter, namely, the morphological signal-adaptive median (MSAM) filter is proposed in the second class. It employs an anisotropic window adaptation procedure based on mathematical morphology operations. The noisesmoothing capabilities and the computational complexity of the LMSbased adaptive order statistic filters studied serves as a baseline in the assessment of the properties of the proposed MSAM filter. Quantitative criteria (e.g., the SNR, the peak SNR, the mean absolute error, and the mean squared error) as well as qualitative criteria (e.g., the perceived visual quality of the processed images) are employed to assess the performance of the filters in various corruption cases by different noise models.