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In practice the relevant details of images exist only over a restricted range of scale. Hence it is important to study the dependence of image structure on the level of resolution. It seems clear enough that visual perception treats images on several levels of resolution simultaneously and that this fact must be important for the study of perception. However, no applicable mathematically formulated theory to deal with such problems appers to exist. In this paper it is shown that any image can be embedded in a one-parameter family of derived images (with resolution as the parameter) in essentially only one unique way if the constraint that no spurious detail should be generated when the resolution is diminished, is applied. The structure of this family is governed by the well known diffusion equation (a parabolic, linear, partial differential equation of the second order). As such the structure fits into existing theories …