Nicolas Papadakis

Vincent Herfeld, Baudouin Denis de Senneville, Arthur Leclaire et al.

In this paper we analyze the Gradient-Step Denoiser and its usage in Plug-and-Play algorithms. The Plug-and-Play paradigm of optimization algorithms uses off the shelf denoisers to replace a proximity operator or a gradient descent operator of an image prior. Usually this image prior is implicit and cannot be expressed, but the Gradient-Step Denoiser is trained to be exactly the gradient descent operator or the proximity operator of an explicit functional while preserving state-of-the-art denoising capabilities.

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.

Rémi Giraud, Vinh-Thong Ta, Nicolas Papadakis

In this work, we propose a fast superpixel-based color transfer method (SCT) between two images. Superpixels enable to decrease the image dimension and to extract a reduced set of color candidates. We propose to use a fast approximate nearest neighbor matching algorithm in which we enforce the match diversity by limiting the selection of the same superpixels. A fusion framework is designed to transfer the matched colors, and we demonstrate the improvement obtained over exact matching results. Finally, we show that SCT is visually competitive compared to state-of-the-art methods.

Nicolas Papadakis, Julien Rabin

We investigate in this work a versatile convex framework for multiple image segmentation, relying on the regularized optimal mass transport theory. In this setting, several transport cost functions are considered and used to match statistical distributions of features. In practice, global multidimensional histograms are estimated from the segmented image regions, and are compared to referring models that are either fixed histograms given a priori, or directly inferred in the non-supervised case. The different convex problems studied are solved efficiently using primal-dual algorithms. The proposed approach is generic and enables multi-phase segmentation as well as co-segmentation of multiple images.

Sira Ferradans, Nicolas Papadakis, Gabriel Peyré et al.

This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two features are crucial for image processing tasks, which necessitate to take into account families of multimodal histograms, with large mass variation across modes. The corresponding relaxed and regularized transportation problem is the solution of a convex optimization problem. Depending on the regularization used, this minimization can be solved using standard linear programming methods or first order proximal splitting schemes. The resulting transportation plan can be used as a color transfer map, which is robust to mass variation across images color palettes. Furthermore, the regularization of the transport plan helps to remove colorization artifacts due to noise amplification. We also extend this framework to the computation of barycenters of distributions. The barycenter is the solution of an optimization problem, which is separately convex with respect to the barycenter and the transportation plans, but not jointly convex. A block coordinate descent scheme converges to a stationary point of the energy. We show that the resulting algorithm can be used for color normalization across several images. The relaxed and regularized barycenter defines a common color palette for those images. Applying color transfer toward this average palette performs a color normalization of the input images.