Texture Reconstruction Guided by a High-Resolution Patch.

In this paper, we aim at super-resolving a low-resolution texture under the assumption that a high-resolution patch of the texture is available. To do so, we propose a variational method that combines two approaches that are texture synthesis and image reconstruction. The resulting objective function holds a nonconvex energy that involves a quadratic distance to the low-resolution image, a histogram-based distance to the high-resolution patch, and a nonlocal regularization that links the missing pixels with the patch pixels. As for the histogram-based measure, we use a sum of Wasserstein distances between the histograms of some linear transformations of the textures. The resulting optimization problem is efficiently solved with a primal-dual proximal method. Experiments show that our method leads to a significant improvement, both visually and numerically, with respect to the state-of-the-art algorithms for solving similar problems.

Image Zoom Completion.

We consider the problem of recovering a high-resolution image from a pair consisting of a complete low-resolution image and a high-resolution but incomplete one. We refer to this task as the image zoom completion problem. After discussing possible contexts in which this setting may arise, we introduce a nonlocal regularization strategy, giving full details concerning the numerical optimization of the corresponding energy and discussing its benefits and shortcomings. We also derive two total variation-based algorithms and evaluate the performance of the proposed methods on a set of natural and textured images. We compare the results and get with those obtained with two recent state-of-the-art single-image super-resolution algorithms.

Adaptive regularization of the NL-means: application to image and video denoising.

Image denoising is a central problem in image processing and it is often a necessary step prior to higher level analysis such as segmentation, reconstruction, or super-resolution. The nonlocal means (NL-means) perform denoising by exploiting the natural redundancy of patterns inside an image; they perform a weighted average of pixels whose neighborhoods (patches) are close to each other. This reduces significantly the noise while preserving most of the image content. While it performs well on flat areas and textures, it suffers from two opposite drawbacks: it might over-smooth low-contrasted areas or leave a residual noise around edges and singular structures. Denoising can also be performed by total variation minimization-the Rudin, Osher and Fatemi model-which leads to restore regular images, but it is prone to over-smooth textures, staircasing effects, and contrast losses. We introduce in this paper a variational approach that corrects the over-smoothing and reduces the residual noise of the NL-means by adaptively regularizing nonlocal methods with the total variation. The proposed regularized NL-means algorithm combines these methods and reduces both of their respective defaults by minimizing an adaptive total variation with a nonlocal data fidelity term. Besides, this model adapts to different noise statistics and a fast solution can be obtained in the general case of the exponential family. We develop this model for image denoising and we adapt it to video denoising with 3D patches.

Indexing of satellite images with different resolutions by wavelet features.

Space agencies are rapidly building up massive image databases. A particularity of these databases is that they are made of images with different, but known, resolutions. In this paper, we introduce a new scheme allowing us to compare and index images with different resolutions. This scheme relies on a simplified acquisition model of satellite images and uses continuous wavelet decompositions. We establish a correspondence between scales which permits us to compare wavelet decompositions of images having different resolutions. We validate the approach through several matching and classification experiments, and we show that taking the acquisition process into account yields better results than just using scaling properties of wavelet features.

Resolution-independent characteristic scale dedicated to satellite images.

We study the problem of finding the characteristic scale of a given satellite image. This feature is defined so that it does not depend on the spatial resolution of the image. This is a different problem than achieving scale invariance, as often studied in the literature. Our approach is based on the use of a linear scale space and the total variation (TV). The critical scale is defined as the one at which the normalized TV reaches its maximum. It is shown experimentally, both on synthetic and real data, that the computed characteristic scale is resolution independent.

Wavelet-based level set evolution for classification of textured images.

We present a supervised classification model based on a variational approach. This model is specifically devoted to textured images. We want to get a partition of an image, composed of texture regions separated by regular interfaces. Each kind of texture defines a class. We use a wavelet packet transform to analyze the textures, characterized by their energy distribution in each sub-band. In order to have an image segmentation according to the classes, we model the regions and their interfaces by level set functions. We define a functional on these level sets whose minimizers define the optimal classification according to texture. A system of coupled PDEs is deduced from the functional. By solving this system, each region evolves according to its wavelet coefficients and interacts with the neighbor regions in order to obtain a partition with regular contours. Experiments are shown on synthetic and real images.