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A recently developed method of image smoothing and segmentation makes use of a "pyramid" of images at successively lower resolutions. It establishes links between pixels at successive levels of the pyramid; the subtrees of the pyramid defined by these links yield a segmentation of the image into regions over which the smoothing takes place. This paper investigates several variations on the basic linking process with regard to such factors as initialization, criteria for linking, and iteration scheme used. It also studies generalizations in which the links are weighted rather than forced, and in which interactions among the pixels at a given level are also allowed. Finally, it extends the approach to links based on more than one feature of a pixel, e.g., on color components or local property values.