The sequential sampling, transmission, and rendering of images has been studied in three related contexts: image transmission, vision, and graphics. The solutions developed in these contexts can be viewed as (different) specializations of a single adaptive sampling scheme. We present an analysis of this general scheme, and show how to specialize it. Our basic assumptions are that we can identify an original image (sometimes a model, sometimes the real world), a transmitter which can directly access the original, and a receiver interested in creating a reconstructed image. Different methods are motivated by different goals and constraints, especially the amount of knowledge that the transmitter is allowed to use (but not communicate). In the image synthesis problem, the process which evaluates the image function at a sample point can be viewed as the transmitter. The process which assembles an image from the individual point samples can be viewed as the receiver. In the progressive transmission problem, the transmitter selects or encodes values from a digital image. The receiver reconstructs increasingly accurate approximations of the image, as the samples arrive. These problems share three subproblems: selection of efficient sampling patterns, methods to adaptively control the sample rate, and filters for image reconstruction. In this paper, we explore several related methods of handling these problems, based on different constraints, and different weighting of the goals.