Issue No. 08 - Aug. (2013 vol. 35)
Joan Bruna , Courant Inst., New York Univ., New York, NY, USA
S. Mallat , Ecole Normale Super., Paris, France
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.
Scattering, Convolution, Fourier transforms, Wavelet coefficients, Computer architecture
J. Bruna and S. Mallat, "Invariant Scattering Convolution Networks," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 35, no. 8, pp. 1872-1886, 2013.