Résumé (EN)

This paper models a texture as a 2D mapping onto a nonlinear manifold representing the local structures of the image. This manifold is learned from the set of local patches from an exemplar texture. A multiscale decomposition of this manifold valued representation is computed that mimics the orthogonal wavelet transform. The key ingredient of this decomposition is a geometric association field that drives the computations along the manifold. Iterated predictions leads to the computation of details coefficients over the features manifold. The resulting transform is invertible, non-linear and represents efficiently the local geometric structures of the exemplar. The multiscale coefficients of this transform are used to perform analysis and synthesis of textures.