Image classification requires to reduce variability with invariant representations, which are stable to deformations and retain enough information for disrimination.Canonical invariants, Fourier or wavelet transforms do not satisfy these properties. Scattering operators iteratively apply wavelet transforms and modulus operators that remove the phase. They are proved to be invariant to translations and stable to deformations. They characterize the geometric distribution of image structures. Scattering operators also provide representations of stationary processes, including high order moments which discriminate different processes having same Fourier spectrum. Classification results are shown on data bases of structured image patterns and textures. Extension beyond the translation group, and group learning is discussed.