# Generalized Rectifier Wavelet Covariance Models For Texture Synthesis

arXiv: https://arxiv.org/abs/2203.07902 · HTML: https://mlsanity.com/paper/2203.07902/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 14 Mar 2022.

## Builds on (most cited first, 15 of 15)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [A Theory of Generative ConvNet](https://mlsanity.com/paper/1602.03264/) (2016)
- [Combining Markov Random Fields and Convolutional Neural Networks for Image Synthesis](https://mlsanity.com/paper/1601.04589/) (2016)
- [Non-Stationary Texture Synthesis by Adversarial Expansion](https://mlsanity.com/paper/1805.04487/) (2018)
- [Cooperative Training of Descriptor and Generator Networks](https://mlsanity.com/paper/1609.09408/) (2016)
- [Texture Interpolation for Probing Visual Perception](https://mlsanity.com/paper/2006.03698/) (2020)
- [Texture Mixer: A Network for Controllable Synthesis and Interpolation of Texture](https://mlsanity.com/paper/1901.03447/) (2019)
- [Multiscale Sparse Microcanonical Models](https://mlsanity.com/paper/1801.02013/) (2018)
- [A survey of exemplar-based texture synthesis](https://mlsanity.com/paper/1707.07184/) (2017)
- [Maximum Entropy Models from Phase Harmonic Covariances](https://mlsanity.com/paper/1911.10017/) (2019)
- [Towards Metamerism via Foveated Style Transfer](https://mlsanity.com/paper/1705.10041/) (2017)
- [Texture Synthesis Through Convolutional Neural Networks and Spectrum Constraints](https://mlsanity.com/paper/1605.01141/) (2016)
- [Incorporating long-range consistency in CNN-based texture generation](https://mlsanity.com/paper/1606.01286/) (2016)
- [Image Inpainting for High-Resolution Textures using CNN Texture Synthesis](https://mlsanity.com/paper/1712.03111/) (2017)
- [Texture synthesis via projection onto multiscale, multilayer statistics](https://mlsanity.com/paper/2105.10825/) (2021)

## Built on by (most cited first, 5 of 5)

- [MGD: Moment Guided Diffusion for Maximum Entropy Generation](https://mlsanity.com/paper/2602.17211/) (2026)
- [Long Range Constraints for Neural Texture Synthesis Using Sliced Wasserstein Loss](https://mlsanity.com/paper/2211.11137/) (2022)
- [Mean-Field Microcanonical Gradient Descent](https://mlsanity.com/paper/2403.08362/) (2024)
- [GIST: Towards Photorealistic Style Transfer via Multiscale Geometric Representations](https://mlsanity.com/paper/2412.02214/) (2024)
- [Specific Algorithmic Interpretability of Neural Networks: A Case Study on Textures](https://mlsanity.com/paper/2610.04413/) (2026)

## Abstract (arXiv)

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. edges) in images. 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.