Invariant Scattering Convolution Networks

TLDR

Wavelet scattering networks produce translation‑invariant, deformation‑stable image representations that retain high‑frequency details for classification. The method cascades wavelet convolutions with modulus and averaging, building higher‑order scattering coefficients that capture texture statistics beyond the Fourier spectrum. The network’s first layer yields SIFT‑like descriptors, while deeper layers supply complementary invariants that enhance classification, achieving state‑of‑the‑art results on handwritten digits and texture discrimination using Gaussian‑kernel SVMs and generative PCA classifiers.

Abstract

A wavelet scattering network computes a translation invariant image representation which is stable to deformations and preserves high-frequency information for classification. It cascades wavelet transform convolutions with nonlinear modulus and averaging operators. The first network layer outputs SIFT-type descriptors, whereas the next layers provide complementary invariant information that improves classification. The mathematical analysis of wavelet scattering networks explains important properties of deep convolution networks for classification. A scattering representation of stationary processes incorporates higher order moments and can thus discriminate textures having the same Fourier power spectrum. State-of-the-art classification results are obtained for handwritten digits and texture discrimination, with a Gaussian kernel SVM and a generative PCA classifier.