An approach for the segmentation of still and video synthetic aperture radar (SAR) images is described. A priori knowledge about the objects present in the image, e.g., target, shadow and background terrain, is introduced via Bayes' rule. Posterior probabilities obtained in this way are then anisotropically smoothed, and the image segmentation is obtained via MAP classifications of the smoothed data. When segmenting sequences of images, the smoothed posterior probabilities of past frames are used to learn the prior distributions in the succeeding frame. We show with examples from public data sets that this method provides an efficient and fast technique for addressing the segmentation of SAR data.