It has been shown that the Cramer-Rao bound (CRB) can be helpful to characterize vegetation and ground height estimations based on the homogenous random volume over ground (RVoG) model and polarimetric interferometric SAR techniques. However, this model is a function of 20 unknown parameters, which makes the performance analysis a tedious task. We show that the group invariance property of the RVoG model can greatly reduce the complexity of the analysis since the CRB of the vegetation and ground heights only depends on four unknown parameters instead of 20. Furthermore, for the considered situations analyzed in this letter, only three of these four parameters have a nonnegligible influence and can be interpreted as contrast parameters.

Analyzing the precision of vegetation height estimation with compact (i.e., single transmit instead of dual transmit) polarimetric interferometric synthetic aperture radar (PolInSAR) with the homogeneous random volume over ground model can help justify the use of this type of radar rather than using the full PolInSAR. However, since compact PolInSAR provides less information than full PolInSAR, a loss of precision in the vegetation height estimation is expected, which can depend on the single transmit polarization. The adaptation of the Cramer-Rao bound (CRB) derived for full PolInSAR in our earlier work to compact PolInSAR measurement provides a general methodology to characterize this loss of precision. Indeed, the CRB is a lower bound of the variance of unbiased estimators that does not depend on the choice of a particular estimation method. We illustrate this methodology for P-band measurements with three synthetic examples chosen for their variability of polarimetric responses. For these examples, it is shown that there can exist a large set of transmit polarizations for which the loss of precision described by the CRB is small (smaller than a factor 2) although there also exist transmit polarizations for which the loss can be large (about a factor 100). This loss of precision is compared with the large dependency of the precision to the vegetation height estimation that can be observed with the vegetation height (more than a factor 100 in the precision described by the CRB) when all the other parameters of the vegetation, ground, and radar system are constant.

The random volume over ground model, which is based on a simple description of the electromagnetic wave interaction with a vegetated media, allows one to define techniques to estimate the vegetation height from the polarimetric interferometric synthetic aperture radar observations. We discuss this issue with the Cramer-Rao lower bound (CRLB) which provides a minimal bound of the variance independently of the estimation if it is unbiased. The usefulness of this approach is illustrated on three different examples. The first example deals with the influence of a priori knowledge of some physical parameters. We show that reducing the number of unknown physical parameters does not necessarily improve the CRLB. The second example focus on the efficiency of the Cloude et al. height estimator. On the considered data, this estimator reaches the CRLB when the standard deviation equals approximately one meter. In the third example we optimize the radar baseline.

The framework of this paper is focused on semiautomatic fast recognition of areas of interest for fast and user-interactive synthetic aperture radar (SAR) image interpretation for which only a unique intensity SAR image is available. The goal is to label regions into classes significant to a given application in an image, as rapidly as possible. A semiautomated “rough” classification is proposed. It defines the information extraction as a two-level procedure. The technique is based on a first partition image into homogeneous regions using the approach proposed by GallandThen, discrimination characteristics are determined in each homogeneous region. This allows one to automatically obtain a first segmentation of the image into semantic regions of interest. Finally, this segmentation can be easily modified by a user in a limited computational time. At this level, they are considered as “objects,” to identify which typical class of ground it can be attached to. Among a large set of tested measures, we have selected the most pertinent ones for the considered SAR images. In fact, we will see that to obtain an accurate measures estimation, measures need to be estimated inside a neighborhood as homogeneously as possible. This can be achieved with a reasonable confidence in the proposed approach due to the homogeneity properties of the segmentation technique applied. In this paper, we focus on linear structures, urban structures, agricultural parcels, and forest areas extraction in SAR images.

We analyze the application of Shannon entropy and Bhattacharyya distance for the characterization of polarimetric interferometric synthetic aperture radar (PolInSAR) images. We discuss the relevance of the decomposition of the Shannon entropy of a homogeneous region into the sum of three physically meaningful terms that depend respectively on intensity, polarimetry, and interferometry. We also discuss an analogous decomposition property for the Bhattacharyya distance, which is an efficient measure of the contrast between two regions. We illustrate the application of this approach for analyzing different contributions in the information content of PolInSAR images.

A new and fast unsupervised technique for segmentation of high-resolution synthetic aperture radar (SAR) images into homogeneous regions is proposed. This technique is based on Fisher probability density functions (pdfs) of the intensity fluctuations and on an image model that consists of a patchwork of homogeneous regions with polygonal boundaries. The segmentation is obtained by minimizing the stochastic complexity of the image. Different strategies for the pdf parameter estimation are analyzed, and a fast and robust technique is proposed. Finally, the relevance of the proposed approach is demonstrated on high-resolution SAR images.

We propose a new approach for evaluating the contribution of the different channels of polarimetric and interferometric synthetic aperture radar (PolInSAR) images. For that purpose, we demonstrate that the Bhattacharyya distance between the probability density functions of neighboring regions in the image provides an efficient scalar contrast measure. We show that the analysis of this contrast measure allows one to precisely characterize the contribution of each channel for different system configurations, including intensity, polarimetric, and interferometric images. We illustrate this approach using a real synthetic aperture radar image to compare several polarimetric system architectures. Since PolInSAR imaging configurations can correspond to complex and expensive systems, the proposed method can be helpful in system imaging optimization.

The framework of this study is focused on semiautomatic fast recognition of areas of interest for SAR images. The intended goal is to label regions in an image as fastly as possible, into classes significant for a given application. The proposed approach defines the information extraction as a two- level procedure. First, a segmentation technique is applied to obtain an image partition in homogeneous regions, this property being of a crucial interest for the rest of the process. Then, several measures are computed over regions, considered at this level as "objects", in order to identify at which typical class of land-cover they can be attached. Among a large set of measures experimented, we will point out the most pertinent ones for the considered SAR images. In this paper, we focus more on "forest"/"field" areas extraction in SAR images, and show that the discrimination results obtained here are more precise than in a "classical" purely raster classification process. The proposed approach can be extended to discriminate other classes from high resolution SAR images.

An original application of the weighted deflection is proposed for radar target classification by quadratic filters. An explicit formulation of optimal filters is derived. We analyse the impact of the weighting parameter on real data recognition, and show that performances are better when the deflection coincides with the Fisher ratio.

In this paper, we show that polarimetric and interferometric SAR (PolInSAR) images can be efficiently partitioned into homogeneous regions with a statistical technique based on minimization of a parameter-free criterion. This technique consists of finding a polygonal partition of the image that minimizes the stochastic complexity, assuming that the image is made of a tessellation of statistically homogeneous regions. The obtained results demonstrate that a global partition in statistically homogeneous regions of PolInSAR images can provide better results than a partition based on a single characteristic such as polarimetry or interferometry only.

We analyze the generalization of a parametric segmentation technique adapted to Gamma-distributed synthetic aperture radar (SAR) images to nonparametric noise models. This approach is based on a polygonal grid which can have an arbitrary topology and whose number of regions and regularity of its boundaries are obtained by minimizing the stochastic complexity of a quantified version on Q levels of the image. It thus leads to a criterion without parameters to be tuned by the user and adapted to different noise models. We analyze the influence of the quantization scheme and of the optimization procedure on the quality of the partitioning. We then compare the performance of the proposed approach to the parametric one on synthetic images. Finally, we show results obtained on real images and compared with a standard segmentation algorithm of SAR images

We present a generalization of a new statistical technique of image partitioning into homogeneous regions to cases where the family of the probability laws of the gray-level fluctuations is a priori unknown. For that purpose, the probability laws are described with step functions whose parameters are estimated. This approach is based on a polygonal grid which can have an arbitrary topology and whose number of regions and regularity of its boundaries are obtained by minimizing the stochastic complexity of the image. We demonstrate that efficient homogeneous image partitioning can be obtained when no parametric model of the probability laws of the gray levels is used and that this approach leads to a criterion without parameter to be tuned by the user. The efficiency of this technique is compared to a statistical parametric technique on a synthetic image and is compared to a standard unsupervised segmentation method on real optical images.

We propose a nonparametric statistical snake technique that is based on the minimization of the stochastic complexity (minimum description length principle). The probability distributions of the gray levels in the different regions of the image are described with step functions with parameters that are estimated. The segmentation is thus obtained by minimizing a criterion that does not include any parameter to be tuned by the user. We illustrate the robustness of this technique on various types of images with level set and polygonal contour models. The efficiency of this approach is also analyzed in comparison with parametric statistical techniques.

In this paper, we focus on the segmentation of objects not necessarily simply connected using level set snakes and we present a nonparametric statistical approach based on the minimum stochastic complexity principle. This approach allows one to get a criterion to be optimized with no free parameter to be tuned by the user. We thus propose to estimate the probability law of the gray levels of the object and the background of the image with a step function whose order is automatically determinated. We show that coupling the probability law estimation and the segmentation steps leads to good results on various types of images. We illustrate the robustness of the proposed nonparametric statistical snake on different examples and we show on synthetic images that the segmentation results are equivalent to those obtained with a parametric statistical technique, although the technique is nonparametric and without ad hoc parameter in the optimized criterion.

We present a new algorithm for oil spill segmentation in synthetic aperture radar (SAR) images, using the minimum description length (MDL) principle and a polygonal active grid. This algorithm is based on two steps: a first partitioning step into homogeneous regions and a second classification step with an automatic MDL thresholding. The obtained method allows one to segment the different candidate oil spills in an image automatically and in a few seconds.

We consider polarimetric images formed with coherent waves, such as in laser-illuminated imagery or synthetic aperture radar. A definition of the contrast between regions with different polarimetric properties in such images is proposed, and it is shown that the performances of maximum likelihood-based detection and segmentation algorithms are bijective functions of this contrast parameter. This makes it possible to characterize the performance of such algorithms by simply specifying the value of the contrast parameter.

We analyze level set implementation of region snakes based on the maximum likelihood method for different noise models that belong to the exponential family. We show that this approach can improve segmentation results in noisy images and we demonstrate that the regularization term can be efficiently determined using an information theory-based approach, i.e., the minimum description length principle. The criterion to be optimized has no free parameter to be tuned by the user and the obtained segmentation technique is adapted to nonsimply connected objects.

We describe a general framework to design optimal image processing algorithms for polarimetric images formed with coherent radiations, which can be optical or microwave. Starting from the classical speckle model for coherent signals, we show that a wide class of algorithms to perform such tasks as detection, localization and segmentation depend on a simple statistics, which is the determinant of the coherency matrix estimated on a given region of the image. We use this property to design computationally efficient techniques for target/edge detection and image segmentation using statistical active contours and the minimum description length principle.

We present a new minimum description length (MDL) approach based on a deformable partition--a polygonal grid--for automatic segmentation of a speckled image composed of several homogeneous regions. The image segmentation thus consists in the estimation of the polygonal grid, or, more precisely, its number of regions, its number of nodes and the location of its nodes. These estimations are performed by minimizing a unique MDL criterion which takes into account the probabilistic properties of speckle fluctuations and a measure of the stochastic complexity of the polygonal grid. This approach then leads to a global MDL criterion without an undetermined parameter since no other regularization term than the stochastic complexity of the polygonal grid is necessary and noise parameters can be estimated with maximum likelihood-like approaches. The performance of this technique is illustrated on synthetic and real synthetic aperture radar images of agricultural regions and the influence of different terms of the model is analyzed.

We address the problem of target segmentation and detection in coherent active polarimetric images. We consider polarimetric imagers which illuminate the scene with a laser beam and which measure how this light is depolarized by the scene. Since they are formed with coherent light, these "depolarization" images are perturbed by strong speckle-like noise, and by the spatial nonuniformity of the illumination beam. We design image processing algorithms which are adapted to the original statistical properties of these images. We address object segmentation using statistical active contours and target detection using maximum-likelihood (ML) algorithms. We show that the proposed algorithms perform well on both simulated and real-world images.

The likelihood ratio edge detector is an efficient filter for the segmentation of synthetic aperture radar (SAR) images. We show that this filter provides biased location of the edge, when the window does not have the same orientation as the edge. A phenomenological model is proposed to characterize this bias. We then introduce an efficient technique to refine edge location: the statistical active contour. The combination of these two methods permits to achieve accurate and regularized edge location.

The likelihood ratio edge detector is an efficient filter for the segmentation of SAR images. The authors show that this filter provides biased location of the edge if it is not an "ideal" step edge of known orientation. A simple model enables the authors to interpret this observation and to evaluate the bias.

Algorithms for object segmentation are crucial in many image processing applications. During past years, active contour models (snakes) have been widely used for finding the contours of objects. This segmentation strategy is classically edge-based in the sense that the snake is driven to fit the maximum of an edge map of the scene. We propose a region snake approach and we determine fast algorithms for the segmentation of an object in an image. The algorithms developed in a maximum likelihood approach are based on the calculation of the statistics of the inner and the outer regions (defined by the snake). It has thus been possible to develop optimal algorithms adapted to the random fields which describe the gray levels in the input image if we assume that their probability density function family are known. We demonstrate that this approach is still efficient when no boundary's edge exists in the image. We also show that one can obtain fast algorithms by transforming the summations over a region, for the calculation of the statistics, into summations along the boundary of the region. Finally, we will provide numerical simulation results for different physical situations in order to illustrate the efficiency of this approach.

The optimal detection and location of a target in a scene in presence of non-additive noise is studied. The optimal processors in the maximum likelihood sense are determined for different white or correlated noise statistics. It is shown that the required computations are mainly correlations, and that there is no need of iterative methods.

In this paper, we address the problem of robustness in multilayer perceptrons. We present the main theoretical results in the case of linear neural networks with one hidden layer in order to go beyond the empirical study we previously made. We show that the robustness can greatly be improved and that even without decreasing performance in normal use. Finally, we show how this behavior, clearly demonstrated in the linear case, is an approximation of the behavior of nonlinear networks.