Antoine Houdard

Jean Prost, Antoine Houdard, Andrés Almansa et al.

In this paper, we propose to regularize ill-posed inverse problems using a deep hierarchical variational autoencoder (HVAE) as an image prior. The proposed method synthesizes the advantages of i) denoiser-based Plug \& Play approaches and ii) generative model based approaches to inverse problems. First, we exploit VAE properties to design an efficient algorithm that benefits from convergence guarantees of Plug-and-Play (PnP) methods. Second, our approach is not restricted to specialized datasets and the proposed PnP-HVAE model is able to solve image restoration problems on natural images of any size. Our experiments show that the proposed PnP-HVAE method is competitive with both SOTA denoiser-based PnP approaches, and other SOTA restoration methods based on generative models.

Clément Weinreich, Louis de Oliveira, Antoine Houdard et al.

Neural materials typically consist of a collection of neural features along with a decoder network. The main challenge in integrating such models in real-time rendering pipelines lies in the large size required to store their features in GPU memory and the complexity of evaluating the network efficiently. We present a neural material model whose features and decoder are specifically designed to be used in real-time rendering pipelines. Our framework leverages hardware-based block compression (BC) texture formats to store the learned features and trains the model to output the material information continuously in space and scale. To achieve this, we organize the features in a block-based manner and emulate BC6 decompression during training, making it possible to export them as regular BC6 textures. This structure allows us to use high resolution features while maintaining a low memory footprint. Consequently, this enhances our model's overall capability, enabling the use of a lightweight and simple decoder architecture that can be evaluated directly in a shader. Furthermore, since the learned features can be decoded continuously, it allows for random uv sampling and smooth transition between scales without needing any subsequent filtering. As a result, our neural material has a small memory footprint, can be decoded extremely fast adding a minimal computational overhead to the rendering pipeline.

Jean Prost, Antoine Houdard, Andrés Almansa et al.

We investigate the problem of producing diverse solutions to an image super-resolution problem. From a probabilistic perspective, this can be done by sampling from the posterior distribution of an inverse problem, which requires the definition of a prior distribution on the high-resolution images. In this work, we propose to use a pretrained hierarchical variational autoencoder (HVAE) as a prior. We train a lightweight stochastic encoder to encode low-resolution images in the latent space of a pretrained HVAE. At inference, we combine the low-resolution encoder and the pretrained generative model to super-resolve an image. We demonstrate on the task of face super-resolution that our method provides an advantageous trade-off between the computational efficiency of conditional normalizing flows techniques and the sample quality of diffusion based methods.

Johannes Hertrich, Antoine Houdard, Claudia Redenbach

In this paper, we introduce a Wasserstein patch prior for superresolution of two- and three-dimensional images. Here, we assume that we have given (additionally to the low resolution observation) a reference image which has a similar patch distribution as the ground truth of the reconstruction. This assumption is e.g. fulfilled when working with texture images or material data. Then, the proposed regularizer penalizes the $W_2$-distance of the patch distribution of the reconstruction to the patch distribution of some reference image at different scales. We demonstrate the performance of the proposed regularizer by two- and three-dimensional numerical examples.

Jean Prost, Antoine Houdard, Andrés Almansa et al.

In this work, we propose a framework to learn a local regularization model for solving general image restoration problems. This regularizer is defined with a fully convolutional neural network that sees the image through a receptive field corresponding to small image patches. The regularizer is then learned as a critic between unpaired distributions of clean and degraded patches using a Wasserstein generative adversarial networks based energy. This yields a regularization function that can be incorporated in any image restoration problem. The efficiency of the framework is finally shown on denoising and deblurring applications.

Antoine Houdard, Arthur Leclaire, Nicolas Papadakis et al.

The use of optimal transport cost for learning generative models has become popular with Wasserstein Generative Adversarial Networks (WGAN). Training of WGAN relies on a theoretical background: the calculation of the gradient of the optimal transport cost with respect to the generative model parameters. We first demonstrate that such gradient may not be defined, which can result in numerical instabilities during gradient-based optimization. We address this issue by stating a valid differentiation theorem in the case of entropic regularized transport and specify conditions under which existence is ensured. By exploiting the discrete nature of empirical data, we formulate the gradient in a semi-discrete setting and propose an algorithm for the optimization of the generative model parameters. Finally, we illustrate numerically the advantage of the proposed framework.

Antoine Houdard, Arthur Leclaire, Nicolas Papadakis et al.

We propose GOTEX, a general framework for texture synthesis by optimization that constrains the statistical distribution of local features. While our model encompasses several existing texture models, we focus on the case where the comparison between feature distributions relies on optimal transport distances. We show that the semi-dual formulation of optimal transport allows to control the distribution of various possible features, even if these features live in a high-dimensional space. We then study the resulting minimax optimization problem, which corresponds to a Wasserstein generative model, for which the inner concave maximization problem can be solved with standard stochastic gradient methods. The alternate optimization algorithm is shown to be versatile in terms of applications, features and architecture; in particular it allows to produce high-quality synthesized textures with different sets of features. We analyze the results obtained by constraining the distribution of patches or the distribution of responses to a pre-learned VGG neural network. We show that the patch representation can retrieve the desired textural aspect in a more precise manner. We also provide a detailed comparison with state-of-the-art texture synthesis methods. The GOTEX model based on patch features is also adapted to texture inpainting and texture interpolation. Finally, we show how to use our framework to learn a feed-forward neural network that can synthesize on-the-fly new textures of arbitrary size in a very fast manner. Experimental results and comparisons with the mainstream methods from the literature illustrate the relevance of the generative models learned with GOTEX.