Combining local regularity estimation and total variation optimization for scale-free texture segmentation

Texture segmentation constitutes a standard image processing task, crucial to many applications. The present contribution focuses on the particular subset of scale-free textures and its originality resides in the combination of three key ingredients: First, texture characterization relies on the concept of local regularity ; Second, estimation of local regularity is based on new multiscale quantities referred to as wavelet leaders ; Third, segmentation from local regularity faces a fundamental bias variance trade-off: In nature, local regularity estimation shows high variability that impairs the detection of changes, while a posteriori smoothing of regularity estimates precludes from locating correctly changes. Instead, the present contribution proposes several variational problem formulations based on total variation and proximal resolutions that effectively circumvent this trade-off. Estimation and segmentation performance for the proposed procedures are quantified and compared on synthetic as well as on real-world textures

On-the-fly Approximation of Multivariate Total Variation Minimization

In the context of change-point detection, addressed by Total Variation minimization strategies, an efficient on-the-fly algorithm has been designed leading to exact solutions for univariate data. In this contribution, an extension of such an on-the-fly strategy to multivariate data is investigated. The proposed algorithm relies on the local validation of the Karush-Kuhn-Tucker conditions on the dual problem. Showing that the non-local nature of the multivariate setting precludes to obtain an exact on-the-fly solution, we devise an on-the-fly algorithm delivering an approximate solution, whose quality is controlled by a practitioner-tunable parameter, acting as a trade-off between quality and computational cost. Performance assessment shows that high quality solutions are obtained on-the-fly while benefiting of computational costs several orders of magnitude lower than standard iterative procedures. The proposed algorithm thus provides practitioners with an efficient multivariate change-point detection on-the-fly procedure

A Parallel Inertial Proximal Optimization Method

International audienceThe Douglas-Rachford algorithm is a popular iterative method for finding a zero of a sum of two maximal monotone operators defined on a Hilbert space. In this paper, we propose an extension of this algorithm including inertia parameters and develop parallel versions to deal with the case of a sum of an arbitrary number of maximal operators. Based on this algorithm, parallel proximal algorithms are proposed to minimize over a linear subspace of a Hilbert space the sum of a finite number of proper, lower semicontinuous convex functions composed with linear operators. It is shown that particular cases of these methods are the simultaneous direction method of multipliers proposed by Stetzer et al., the parallel proximal algorithm developed by Combettes and Pesquet, and a parallelized version of an algorithm proposed by Attouch and Soueycatt

A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems

Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the non-local variations, jointly for the different components, through various $\ell_{1,p}$ matrix norms with $p \ge 1$. To facilitate the choice of the hyper-parameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for multispectral and hyperspectral images. The results demonstrate the interest of introducing a non-local structure tensor regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods

2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis

This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure, and (ii) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2-D mode decompositions based on non-smooth convex optimization: a "Genuine 2-D" approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D" approach, which constrains separately the extrema of lines, columns, and diagonals. The spectral analysis step is based on Prony annihilation property that is applied on small square patches of the IMFs. The resulting 2-D Prony-Huang transform is validated on simulated and real data.Comment: 24 pages, 7 figure

A Multicomponent proximal algorithm for Empirical Mode Decomposition

International audienceThe Empirical Mode Decomposition (EMD) is known to be a powerful tool adapted to the decomposition of a signal into a collection of intrinsic mode functions (IMF). A key procedure in the extraction of the IMFs is the sifting process whose main drawback is to depend on the choice of an interpolation method and to have no clear convergence guarantees. We propose a convex optimization procedure in order to replace the sifting process in the EMD. The considered method is based on proximal tools, which allow us to deal with a large class of constraints such as quasi-orthogonality or extrema-based constraints

Régularité locale pour l'analyse de texture : le mariage des coefficients dominants et de la minimisation proximale

National audienceDans cette contribution, nous revisitons la question de la caractérisation de textures d’images par analyse des fluctuations de régularité locale en combinant deux éléments nouveaux. D’une part, dans l’estimation de la régularité locale proprement dite, la quantité multirésolution utilisée était classiquement le coefficient d’ondelette, l’accroissement ou l’oscillation. Nous la remplaçons par les coefficients dominants, une déclinaison des coefficients d’ondelettes inventée dans le contexte de l’analyse multifractale et qui apportent robustesse et amélioration dans les performances d’estimation. D’autre part, le post-traitement des estimées est réalisé par la mise en place d’une procédure de segmentation en partition minimale résolue à l’aide d’outils proximaux, ce qui nous permet de gérer efficacement le grand volume de données impliqué. Nous générons des textures synthétiques gaussiennes caractérisées par un changement de régularité locale dans une zone dont la position et la surface sont tirées aléatoirement. Nous mettons en oeuvre systématiquement la combinaison de l’estimation par coefficients dominants et segmentation proximale, illustrons la qualité et l’intérêt de cette approche pour segmenter les textures et quantifions la qualité de la segmentation obtenue en fonction de l’amplitude de l’amplitude du changement de régularité locale et de la surface de la zone modifiée

Bancs de filtres et méthodes proximales pour la restauration d'images

National audienceLes algorithmes proximaux parallèles et les méthodes de directions alternées des multiplicateurs sont devenus populaires pour la résolution de problèmes inverses. En particulier, de nombreux travaux se sont intéressés à la résolution de problèmes de restauration dans un cadre variationnel convexe utilisant des trames. Jusqu'à présent, la plupart de ces méthodes nécessitaient une hypothèse de trames ajustées. Dans ce travail, nous relâchons cette contrainte en considérant des bancs de filtres à reconstruction parfaite non-nécessairement décimés de manière critique. Nous illustrons l'intérêt de telles trames sur un exemple de déconvolution en présence de bruit de Poisson