Invariant Scattering Convolution Networks

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.

Rotation, Scaling and Deformation Invariant Scattering for Texture Discrimination

“…Wavelets are designed so that W 1 is contractive and potentially unitary [1,9]. We use complex wavelets whose real and imaginary parts have a quadrature phase.…”

“…These invariants can be adapted to each signal class by optimizing a linear kernel at the supervised classification stage. This may be done by an SVM but we shall rather use a generative PCA classifier as in [1]. Such classifiers can indeed perform better when the training set is small.…”

“…As in [1], we use a simple quadratic classifier which associates to each signal x the class indexĉ which minimizes Figure 6: Each row shows images from the same texture class in the UIUC database [10], with important rotation, scaling and deformation variability.…”

“…The space V c is thus generated by the D scattering vectors of the training set. For larger training databases, it must be adjusted with a cross validation as in [1].…”

“…The rows "trans. scatt" correspond to a translation invariant scattering as in [1]. It is computed on image patches of size 2 J , with a final spatial averaging of all the patch scattering vector.…”