Following the "2nd generation image coding" dream improving current image transform codes will require to represent images with features that are meaningful for the scene analysis. Such an approach would allow us to build compact representations that can also be used for search in large data-bases of images. To achieve this goal, the first issue is to extract and efficiently represent the image geometry. An approach is presented with foveal wavelets and bandelets, with compression examples. The optimization of compression gives a well-defined mathematical and algorithmic framework to optimize what would be called "edge detection" in computer vision.