Object and Texture recognition requireextracting stable, discriminative information out of noisy, high-dimensional signals.
Our perception of image and audio patterns is invariant under several transformations, such as illumination changes, translations or frequency transpositions, as well as small geometrical perturbations. Similarly, textures are examples of stationary, non-gaussian, intermittent processes which can be recognized from few realizations.
Scattering operators construct a non-linear signal representation by cascading wavelet modulus decompositions, shown to be stable to geometric deformations, and capturing key geometrical properties and high-order moments with low-variance estimators. Thanks to these properties, the resulting representation is very efficient on several recognition and reconstruction tasks.
Moreover, scattering moments provide an alternative theory of multifractal analysis, where intermittency and self-similarity can be consistently estimated from few realizations.
Although stability to geometric perturbations is necessary, it is not sufficient for the most challenging object recognition tasks, which require learning the invariance from data. We shall discuss how scattering operators can be generalized to this scenario, highlighting the close links between structured dictionary learning approaches and deep neural networks.
Finally, we will discuss how to generalize convolutional scattering networks to general datasets lacking the standard translational structure with spectral networks.