Generalized Rectifier Wavelet Covariance Models For Texture Synthesis

State-of-the-art maximum entropy models for texture synthesis are built from statistics relying on image representations defined by convolutional neural networks (CNN). Such representations capture rich structures in texture images, outperforming wavelet-based representations in this regard. However, conversely to neural networks, wavelets offer meaningful representations, as they are known to detect structures at multiple scales (e.g. In this work, we propose a family of statistics built upon non-linear wavelet based representations, that can be viewed as a particular instance of a one-layer CNN, using a generalized rectifier non-linearity. These statistics significantly improve the visual quality of previous classical wavelet-based models, and allow one to produce syntheses of similar quality to state-of-the-art models, on both gray-scale and color textures. We further provide insights on memorization effects in these models. In texture modeling, one of the standard approaches to synthesize textures relies on defining a maximum entropy model (Jaynes, 1957) using a single observed image (Raad et al., 2018). It consists of computing a set of prescribed statistics from the observed texture image, and then generating synthetic textures producing the same statistics as the observation. If the statistics correctly describe the structures present in the observation, then any new image with the same statistics should appear similar to the observation.