The image segmentation problem may be considered as the search for a way to subdivide an image domain into regions which represent the projection of visible parts of objects in a real scene. The authors analyze the problem of image segmentation in the framework of the approximation theory as defined by D. Mumford and J. Shah (1988). They show that for real images the problem of the choice of the energy functional is dictated by the model of the world, and they propose a method to optimize it based on a deterministic algorithm processed at multiple levels of resolution. Problems encountered in dealing with real scenes lead to several modifications of the algorithm and the energy functional. Images are shown on which the algorithm was tested.>