Standard fractal image compression, proposed by Jacquin, is based on IFS (Iterated Function Systems) defined in R². This modelization implies restrictions in the set of images being able to be compressed. These images have to be self similar in R². We propose a new model, the projected IFS, to approximate and code grey level images. This model has the ability to define affine IFS in a high dimension space, and to project it through control points, resulting in a non strictly self similar object in R². We proposed a method for approximating curves with such a model. In this paper, we extend the model capabilities to surfaces and images. This includes the combination of projected IFS in a quadtree structure and a complete coding scheme. First results show that our method gives better results than standard fractal image compression. Furthermore, in the very low bitrate context, the distortion/rate performances are equivalent to those obtained with EZW algorithm.