I'm not quite sure what you mean by not flattening the image. Obviously it ends up flat.
But anyway, what I wanted to comment on was fractal resampling algorithms. Notice that the example picture is a woodland scene, exactly where this approach is strongest. It's not good for general purpose use, though, since it works by inventing artificial detail, which looks obviously poor if the image in question is a sign with lettering, or details of a human face.