Images captured under low-light conditions pose significant limitations in many applications. Removing the illumination effects and enhancing the quality of such images is crucial. In this paper, we introduce a low-light image enhancement variational method based on the Retinex decomposition into illumination, reflectance, and noise. Our model integrates a novel nonlocal gradient-type fidelity term designed to preserve structural details. Additionally, we propose an automatic gamma correction module. Since the noise is explicitly addressed, no post-processing is required for denoising. Experimental results show that our method compares favorably with state-of-the-art deep learning-based approaches.

The authors present a method for the enhancement of backlit images, i.e. images in which the main source of light is behind the photography subject. These images contain, simultaneously, very dark and very bright regions. In this situation, a single tone mapping function is unable to enhance the whole image. They propose the use of several such tone mappings, some of them enhancing the dark regions while others enhancing the bright regions, and then the combination of all these results using an image fusion algorithm. Qualitative and quantitative results confirm the validity of the proposed method.

Common satellite imagery products consist of a panchromatic image at high spatial resolution and several misregistered spectral bands at lower resolution. Pansharpening is the fusion process by which a high-resolution multispectral image is inferred. We propose a variational model for which pan-sharpening is defined as an optimization problem minimizing a cost function with nonlocal regularization. We incorporate a new term preserving the radiometric ratio between the panchromatic and each spectral band. The resulting model is channel-decoupled, thus permitting the application to misregistered spectral data. The experimental results illustrate the superiority of the proposed method to preserve spatial details, reduce color artifacts, and avoid aliasing.

Even after two decades, the total variation (TV) remains one of the most popular regularizations for image processing problems and has sparked a tremendous amount of research, particularly on moving from scalar to vector-valued functions. In this paper, we consider the gradient of a color image as a three-dimensional matrix or tensor with dimensions corresponding to the spatial extent, the intensity differences between neighboring pixels, and the spectral channels. The smoothness of this tensor is then measured by taking different norms along the different dimensions. Depending on the types of these norms, one obtains very different properties of the regularization, leading to novel models for color images. We call this class of regularizations collaborative total variation (CTV). On the theoretical side, we characterize the dual norm, the subdifferential, and the proximal mapping of the proposed regularizers. We further prove, with the help of the generalized concept of singular vectors, that an $\ell^{\infty}$ channel coupling makes the most prior assumptions and has the greatest potential to reduce color artifacts. Our practical contributions consist of an extensive experimental section, where we compare the performance of a large number of collaborative TV methods for inverse problems such as denoising, deblurring, and inpainting.

Enhancement algorithms are absolutely necessary for the visualization of both shadowed and bright image regions. Defining algorithms that permit to visualize them simultaneously without altering the image content is therefore extremely relevant for remote sensing applications. In this paper, we present the results of two successive benchmarks which tested the performance of the state-of-the-art contrast enhancement and tone-mapping algorithms applied to satellite images. Experts from the French Space Agency Centre National d'Etudes Spatiales (CNES), Service Régional de Traitement d'Image et de Télédétection (SERTIT), and two European universities assessed the quality and fidelity of the results of several state-of-the-art enhancement algorithms on the excerpts from seven images (five Pleiades and two simulated 30-cm images). The first benchmark permitted to tighten the procedure and the selection of the test images for the second one, and to make a first selection of concurrent algorithms. The second benchmark not only included the best algorithms selected by the first benchmark but also added even more competitors in the tone-mapping class. The results of both benchmarks were coherent. They point a particular retinex-based algorithm as the best compromise between the competitive requirements of a contrast enhancement in dark regions and a preservation of detail in bright parts.

In this paper, we propose a new dual algorithm for the minimization of discrete nonconvex functionals, called half-linear regularization. Our approach alternates the calculation of a explicit weight with the minimization of a convex functional with respect to the solution. This minimization corresponds to the weighted total variation which is solved via the well-known Chambolle's algorithm. Finally, we present experimental results by applying it to some image restoration problems as denoising and deconvolution.

In this work we propose to analyze the formal properties of the center/surround versions of Retinex. Our main goal is to clarify what the “best” surround should be. Two conditions are sound or necessary from an image theoretical viewpoint: scale invariance and integrability. Then, we present a new kernel, which finds an acceptable compromise between these two conditions. This new kernel is compared with different kernels obtained from some center-surround methods.

Pansharpening refers to the fusion process of inferring a high-resolution multispectral image from a high-resolution panchromatic image and a low-resolution multispectral one. In this paper we propose a new variational method for pansharpening which incorporates a nonlocal regularization term and two fidelity terms, one describing the relation between the panchromatic image and the high-resolution spectral channels and the other one preserving the colors from the low-resolution modality. The nonlocal term is based on the image self-similarity principle applied to the panchromatic image. The existence and uniqueness of minimizer for the described functional is proved in a suitable space of weighted integrable functions. Although quite successful in terms of relative error, state-of-the-art pansharpening methods introduce relevant color artifacts. These spectral distortions can be significantly reduced by involving the image self-similarity. Extensive comparisons with state-of-the-art algorithms are performed.

In 1964 Edwin H. Land formulated the Retinex theory, the first attempt to simulate and explain how the human visual system perceives color. His theory and an extension, the "reset Retinex" were further formalized by Land and McCann. Several Retinex algorithms have been developed ever since. These color constancy algorithms modify the RGB values at each pixel to give an estimate of the color sensation without a priori information on the illumination. Unfortunately, the Retinex Land-McCann original algorithm is both complex and not fully specified. Indeed, this algorithm computes at each pixel an average of a very large set of paths on the image. For this reason, Retinex has received several interpretations and implementations which, among other aims, attempt to tune down its excessive complexity. In this paper, it is proved that if the paths are assumed to be symmetric random walks, the Retinex solutions satisfy a discrete screened Poisson equation. This formalization yields an exact and fast implementation using only two FFTs. Several experiments on color images illustrate the effectiveness of the Retinex original theory.

Demosaicking is the process by which from a matrix of colored pixels measuring only one color component per pixel, red, green, or blue, one can infer a whole color information at each pixel. This inference requires a deep understanding of the interaction between colors, and the involvement of image local geometry. Although quite successful in making such inferences with very small relative error, state-of-the-art demosaicking methods fail when the local geometry cannot be inferred from the neighboring pixels. In such a case, which occurs when thin structures or fine periodic patterns were present in the original, state-of-the-art methods can create disturbing artifacts, known as zipper effect, blur, and color spots. The aim of this paper is to show that these artifacts can be avoided by involving the image self-similarity to infer missing colors. Detailed experiments show that a satisfactory solution can be found, even for the most critical cases. Extensive comparisons with state-of-the-art algorithms will be performed on two different classic image databases.

Presents a method, based on curve evolution, for the reconstruction of a 3D curve from two different projections. Given two views of some 3D curve, we propose to recover the curve minimizing an energy functional. Following the work on geodesic active contour by Caselles et al. (1997), we then transform the problem of minimizing the functional into a problem of geodesic computation in a Riemann space. The Euler-Lagrange equation of this new functional is derived and its associated PDE is solved using the level set formulation scheme. The motivation of this work is the application to the 3D reconstruction of a vessel from a biplane angiography.

We discuss possible algorithms for interpolating data given in a set of curves and/or points in the plane. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The absolute minimal Lipschitz extension model (AMLE) is singled out and studied in more detail. We show experiments suggesting a possible application, the restoration of images with poor dynamic range.

We discuss possible algorithms for interpolating data given in a set of curves and/or points in the plane. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The absolute minimal Lipschitz extension model (AMLE) is singled out and studied in more detail. We show experiments suggesting a possible application, the restoration of images with poor dynamic range.

A geometric approach for 3D object segmentation and representation is presented. The segmentation is obtained by deformable surfaces moving towards the objects to be detected in the 3D image. The model is based on curvature motion and the computation of surfaces with minimal areas, better known as minimal surfaces. The space where the surfaces are computed is induced from the 3D image (volumetric data) in which the objects are to be detected. The model links between classical deformable surfaces obtained via energy minimization, and intrinsic ones derived from curvature based flows. The new approach is stable, robust, and automatically handles changes in the surface topology during the deformation.