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This paper shows how a simple label propagation technique, in conjunction with some novel ideas about how labels can be applied to an image to express semantic knowledge, lead to the simplification of a number of diverse and difficult image analysis tasks (e.g., sketch completion and shape abstraction). A single algorithm technique, based on skeleton and distance transform concepts, is applied to appropriately labeled images to obtain the desired results. A key point is that the initial semantic labeling is not required at every location in the image, but only at those few critical locations where significant changes or discontinuities occur.