SAR Amplitude Probability Density Function Estimation Based on a Generalized Gaussian Model

International audienceIn the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed “method-of-log-cumulants” (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena

A markovian approach to unsupervised change detection with multiresolution and multimodality SAR data

In the framework of synthetic aperture radar (SAR) systems, current satellite missions make it possible to acquire images at very high and multiple spatial resolutions with short revisit times. This scenario conveys a remarkable potential in applications to, for instance, environmental monitoring and natural disaster recovery. In this context, data fusion and change detection methodologies play major roles. This paper proposes an unsupervised change detection algorithmfor the challenging case of multimodal SAR data collected by sensors operating atmultiple spatial resolutions. The method is based on Markovian probabilistic graphical models, graph cuts, linear mixtures, generalized Gaussian distributions, Gram-Charlier approximations, maximum likelihood and minimum mean squared error estimation. It benefits from the SAR images acquired at multiple spatial resolutions and with possibly different modalities on the considered acquisition times to generate an output change map at the finest observed resolution. This is accomplished by modeling the statistics of the data at the various spatial scales through appropriate generalized Gaussian distributions and by iteratively estimating a set of virtual images that are defined on the pixel grid at the finest resolution and would be collected if all the sensors could work at that resolution. A Markov random field framework is adopted to address the detection problem by defining an appropriate multimodal energy function that is minimized using graph cuts

A goal-driven unsupervised image segmentation method combining graph-based processing and Markov random fields

Image segmentation is the process of partitioning a digital image into a set of homogeneous regions (according to some homogeneity criterion) to facilitate a subsequent higher-level analysis. In this context, the present paper proposes an unsupervised and graph-based method of image segmentation, which is driven by an application goal, namely, the generation of image segments associated with a user-defined and application-specific goal. A graph, together with a random grid of source elements, is defined on top of the input image. From each source satisfying a goal-driven predicate, called seed, a propagation algorithm assigns a cost to each pixel on the basis of similarity and topological connectivity, measuring the degree of association with the reference seed. Then, the set of most significant regions is automatically extracted and used to estimate a statistical model for each region. Finally, the segmentation problem is expressed in a Bayesian framework in terms of probabilistic Markov random field (MRF) graphical modeling. An ad hoc energy function is defined based on parametric models, a seed-specific spatial feature, a background-specific potential, and local-contextual information. This energy function is minimized through graph cuts and, more specifically, the alpha-beta swap algorithm, yielding the final goal-driven segmentation based on the maximum a posteriori (MAP) decision rule. The proposed method does not require deep a priori knowledge (e.g., labelled datasets), as it only requires the choice of a goal-driven predicate and a suited parametric model for the data. In the experimental validation with both magnetic resonance (MR) and synthetic aperture radar (SAR) images, the method demonstrates robustness, versatility, and applicability to different domains, thus allowing for further analyses guided by the generated product

Modeling the statistics of high resolution SAR images

In the context of remotely sensed data analysis, a crucial problem is represented by the need to develop accurate models for the statistics of pixel intensities. In this work, we develop a parametric finite mixture model for modelling the statistics of intensities in high resolution Synthetic Aperture Radar (SAR) images. Along with the models we design an efficient parameter estimation scheme by integrating the Stochastic Expectation Maximization scheme and the Method of log-cumulants with an automatic technique to select, for each mixture component, an optimal parametric model taken from a predefined dictionary of parametric probability density functions (pdf). In particular, the proposed dictionary consists of eight most efficient state-of-the-art SAR-specific pdfs: Nakagami, log-normal, generalized Gaussian Rayleigh, Heavy-tailed Rayleigh, Weibull, K-root, Fisher and generalized Gamma. The experiment results with a set of several real SAR (COSMO-SkyMed) images demonstrate the high accuracy of the designed algorithm, both from the viewpoint of a visual comparison of the histograms, and from the viewpoint of quantitive measures such as correlation coefficient (always above 99,5%) . We stress, in particular, that the method proves to be effective on all the considered images, remaining accurate for multimodal and highly heterogeneous images

Unsupervised Image Regression for Heterogeneous Change Detection

Change detection (CD) in heterogeneous multitemporal satellite images is an emerging and challenging topic in remote sensing. In particular, one of the main challenges is to tackle the problem in an unsupervised manner. In this paper, we propose an unsupervised framework for bitemporal heterogeneous CD based on the comparison of affinity matrices and image regression. First, our method quantifies the similarity of affinity matrices computed from colocated image patches in the two images. This is done to automatically identify pixels that are likely to be unchanged. With the identified pixels as pseudotraining data, we learn a transformation to map the first image to the domain of the other image and vice versa. Four regression methods are selected to carry out the transformation: Gaussian process regression, support vector regression, random forest regression (RFR), and a recently proposed kernel regression method called homogeneous pixel transformation. To evaluate the potentials and limitations of our framework and also the benefits and disadvantages of each regression method, we perform experiments on two real data sets. The results indicate that the comparison of the affinity matrices can already be considered a CD method by itself. However, image regression is shown to improve the results obtained by the previous step alone and produces accurate CD maps despite of the heterogeneity of the multitemporal input data. Notably, the RFR approach excels by achieving similar accuracy as the other methods, but with a significantly lower computational cost and with fast and robust tuning of hyperparameters

Nouvelle Méthode en Cascade pour la Classification Hiérarchique Multi-Temporelle ou Multi-Capteur d'Images Satellitaires Haute Résolution

International audienceThis paper describes a method dedicated to multi-resolution, multi-date and eventually multi-sensor classification based on explicit statistical modeling through hierarchical Markov random field modeling based on quad-tree. The proposed approach consists of a supervised Bayesian classifier that combines a joint class-conditional statistical model for pixelwise information and a hierarchical Markov random field for spatio-temporal and multiresolution contextual information fusion based on the Marginal Posterior Mode (MPM). The aim is to recursively maximize the posterior marginal at each pixel, which associates the most probable class label given the entire input information. Within this framework, an interesting novel element of the proposed approach is the use of multiple quadtrees in cascade, each associated with a new image in the available set in order to characterize the correlations associated with distinct images in the data set.Ce papier présente un modèle de classification multi-résolution, multi-date et éventuellement multi-capteur fondé sur une modélisation statistique explicite au travers d'un modèle hiérarchique de champs de Markov construit sur une structure quad-arbre. L'approche proposée consiste en un classifieur bayésien supervisé qui combine un modèle statistique condi-tionnel par classe et un champ de Markov hiérarchique fusionnant l'information spatio-temporelle et multi-résolution. La méthode proposée intégre des informations pixel par pixel à la même résolution. Cela en se basant sur le critère des Modes Marginales a Posteriori (MPM en anglais), qui vise à affecter à chaque pixel l'étiquette optimale en maximisant récursivement la probabilité marginale a posteriori, étant donné l'ensemble des observations multi-temporelles ou multi-capteur. Une des originalités de l'approche proposée est l'utilisation en cascade de plusieurs quad-arbres, chacun étant associé à une nouvelle image disponible, en vue de caractériser les corrélations associées à des images distinctes