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The transmission of high resolution raster images over low-bandwidth communication lines requires a great amount of time. User interaction in such a transmission environment can be frustrating. The problem can be eased somewhat by transmitting a series of low resolution approximations which converge to the final image. Several methods of computing such a series of images are presented. Each is related to a particular type of pyramid data structure. They rely on the ability of the local display device to overpaint an existing image, and generally require some transmission and computation overhead. However, one of the methods requires no transmission overhead and only a small amount of local computation. A notation is introduced that permits concise descriptions of the image refinement processes.