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This work presents a framework for automatic feature extraction from images using stochastic geometry. Features in images are modeled as realizations of a spatial point process of geometrical shapes. This framework allows the incorporation of a priori knowledge on the spatial repartition of features. More specifically, we present a model based on the superposition of a process of segments and a process of rectangles. The former is dedicated to the detection of linear networks of discontinuities, whereas the latter aims at segmenting homogeneous areas. An energy is defined, favoring connections of segments, alignments of rectangles, and a relevant interaction between both types of objects. The estimation is performed by minimizing the energy using a simulated annealing algorithm. The proposed model is applied to the analysis of Digital Elevation Models (DEMs). These images are raster data representing the altimetry of a dense urban area. We present results on real data provided by the French National Geographic Institute (IGN) consisting in low-quality DEMs of various types. Index Terms--Image processing, Poisson point process, stochastic geometry, dense urban area, Digital Elevation Models, land register, building detection, MCMC, RJMCMC, simulated annealing.

A novel homomorphic statistical maximum a posteriori (MAP) filter for speckle noise removal in synthetic aperture radar (SAR) images is presented, based on the heavy-tailed Rayleigh model for the amplitude of the radar cross section (RCS). The developed despeckling filter is applied to simulated and real speckle images, and results reveal that this filter is among the best for speckle removal.

A distinct parametric estimation technique for synthetic aperture radar (SAR) amplitude data that assumes a Generalized Gaussian (GG) model for complex SAR backscattered signals is described. The tests show that the method-of-log cumulants (MoLC) estimates are acceptable, consistent, and the amplitude probability density function (PDF) is better than other proposed models.

In remotely sensed data analysis, a crucial problem is represented by the need to develop accurate models for the statistics of the pixel intensities. This paper deals with the problem of probability density function (pdf) estimation in the context of synthetic aperture radar (SAR) amplitude data analysis. Several theoretical and heuristic models for the pdfs of SAR data have been proposed in the literature, which have been proved to be effective for different land-cover typologies, thus making the choice of a single optimal parametric pdf a hard task, especially when dealing with heterogeneous SAR data. In this paper, an innovative estimation algorithm is described, which faces such a problem by adopting a finite mixture model for the amplitude pdf, with mixture components belonging to a given dictionary of SAR-specific pdfs. The proposed method automatically integrates the procedures of selection of the optimal model for each component, of parameter estimation, and of optimization of the number of components by combining the stochastic expectation-maximization iterative methodology with the recently developed 'method-of-log-cumulants' for parametric pdf estimation in the case of nonnegative random variables. Experimental results on several real SAR images are reported, showing that the proposed method accurately models the statistics of SAR amplitude data. Index Terms--Finite mixture models (FMMs), parametric estimation, probability density function (pdf) estimation, stochastic expectation maximization (SEM), synthetic aperture radar (SAR) images.

This paper addresses the problem of unsupervised extraction of line networks (for example, road or hydrographic networks) from remotely sensed images. We model the target line network by an object process, where the objects correspond to interacting line segments. The prior model, called "Quality Candy," is designed to exploit as fully as possible the topological properties of the network under consideration, while the radiometric properties of the network are modeled using a data term based on statistical tests. Two techniques are used to compute this term: one is more accurate, the other more efficient. A calibration technique is used to choose the model parameters. Optimization is done via simulated annealing using a Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm. We accelerate convergence of the algorithm by using appropriate proposal kernels. The results obtained on satellite and aerial images are quantitatively evaluated with respect to manual extractions. A comparison with the results obtained using a previous model, called the "Candy" model, shows the interest of adding quality coefficients with respect to interactions in the prior density. The relevance of using an offline computation of the data potential is shown, in particular, when a proposal kernel based on this computation is added in the RJMCMC algorithm. Index Terms--Stochastic processes, Monte Carlo, simulated annealing, edge and feature detection, remote sensing.

Most remote sensing images exhibit a clear hierarchical structure which can be taken into account by defining a suitable model for the unknown segmentation map. To this end, one can resort to the tree-structured Markov random field (MRF) model, which describes a K-ary field by means of a sequence of binary MRFs, each one corresponding to a node in the tree. Here we propose to use the tree-structured MRF model for supervised segmentation. The prior knowledge on the number of classes and their statistical features allows us to generalize the model so that the binary MRFs associated with the nodes can be adapted freely, together with their local parameters, to better fit the data. In addition, it allows us to define a suitable likelihood term to be coupled with the TS-MRF prior so as to obtain a precise global model of the image. Given the complete model, a recursive supervised segmentation algorithm is easily defined. Experiments on a test SPOT image prove the superior performance of the proposed algorithm with respect to other comparable MRF-based or variational algorithms. Index Terms--Hierarchical fields, image classification, image segmentation, Markov random fields (MRFs), regression trees, structured images.

Texture analysis has been widely investigated in the monospectral and multispectral imagery domains. At the same time, new image sensors with a large number of bands (more than ten) have been designed. They are able to provide images with both fine spectral and spatial sampling, and are called hyperspectral images. The aim of this work is to perform a joint texture analysis in both discrete spaces. To achieve this goal, we propose a probabilistic vector texture model, using a Gauss-Markov random field (MRF). The MRF parameters allow the characterization of different hyperspectral textures. A possible application of this work is the classification of urban areas. These areas are not well characterized by radiometry alone, and so we use the MRF parameters as new features in a maximum-likelihood classification algorithm. The results obtained on Airborne Visible/Infrared Imaging Spectrometer hyperspectral images demonstrate that a better classification is achieved when texture information is included in the analysis. Index Terms--Classification, hyperspectral image processing, Markov random fields (MRFs), texture features.

An automatic image deblurring algorithm based on an adaptive Gaussian model giving good deconvolution results on high resolution satellite data is proposed. Results of the hybrid method called complex wavelet packet thresholding (COWPATH) on high resolution satellite images exhibits sharp edges, restored textures and a high SNR in homogeneous areas adapting to the local characteristics of the data.

A study on the development of a generalization of the classical Rayleigh models for synthetic aperture radar (SAR) images namely the alpha-stable distribution, which is a popular heavytailed noise Rayleigh-mixture model for radar clutter, is presented. It is used in modeling SAR speckle and belongs to the family of spherically invariant random processes (SIRP).

Analytic expressions for the phase correlation of downsampled images are obtained. It is shown that the signal power in the phase correlation is not concentrated in one peak, but rather, occurs in several peaks, usually adjacent to each other.

We consider the problem of the reconstruction of a continuous-time function f(x) [element of] H from the samples of the responses of m linear shift-invariant systems sampled at 1/m the reconstruction rate. We extend Papoulis' generalized sampling theory in two important respects. First, our class of admissible input signals (typ. H = [L.sub.2]) is considerably larger than the subspace of band-limited functions. Second, we use a more general specification of the reconstruction subspace V([Phi]), so that the output of the system can take the form of a band-limited function, a spline, or a wavelet expansion. Since we have enlarged the class of admissible input functions, we have to give up Shannon and Papoulis' principle of an exact reconstruction. Instead, we seek an approximation [Mathematical Expression Omitted] that is consistent in the sense that it produces exactly the same measurements as the input of the system. This leads to a generalization of Papoulis' sampling theorem and a practical reconstruction algorithm that takes the form of a multivariate filter. In particular, we show that the corresponding system acts as a projector from H onto V([Phi]). We then propose two complementary polyphase and modulation domain interpretations of our solution. The polyphase representation leads to a simple understanding of our reconstruction algorithm in terms of a perfect reconstruction filter bank. The modulation analysis, on the other hand, is useful in providing the connection with Papoulis' earlier results for the band-limited case. Finally, we illustrate the general applicability of our theory by presenting new examples of interlaced and derivative sampling using splines.

A stability and performance analysis on generalized sampling was conducted to determine the stability of the algorithm and the strength of the system against noise. Result showed that generalized sampling provides a means for recovering an unknown input function from sample responses. Furthermore, the generalized sampling solution is equivalent to the optimal minimum error approximation.

Markovian approaches to early vision processes need a huge amount of computing power. These algorithms can usually be implemented on parallel computing structures. With the Cellular Neural Networks (CNN), a new image processing tool is coming into consideration. Its VLSI implementation takes place on a single analog chip containing several thousands of cells. Herein we use the CNN UM architecture for statistical image segmentation. The Modified Metropolis Dynamics (MMD) method can be implemented into the raw analog architecture of the CNN. We are able to implement a (pseudo) random field generator using one layer (one memory/cell) of the CNN. We can introduce the whole pseudostochastic segmentation process in the CNN architecture using 8 memories/cell. We use simple arithmetic functions (addition, multiplication), equality-test between neighboring pixels and very simple nonlinear output functions (step, jigsaw). With this architecture, a real VLSI CNN chip can execute a pseudostochastic relaxation algorithm of about 100 iterations in about 1 ms. In the proposed solution the segmentation is unsupervised. We have developed a pixel-level statistical estimation model. The CNN turns the original image into a smooth one. Then we have two gray-level values for every pixel: the original and the smoothed one. These two values are used for estimating the probability distribution of region label at a given pixel. Using the conventional first-order Markov Random Field (MRF) model, some misclassification errors remained at the region boundaries, because of the estimation difficulties in case of low SNR. By using a greater neighborhood, this problem has been avoided. In our CNN experiments, we used a simulation system with a fixed-point integer precision of 16 bits. Our results show that even in the case of the very constrained conditions of value-representations (the interval is (-64, +64), the accuracy is 0.002) can result in an effective and acceptable segmentation.

The detection of lines in satellite images has drawn a lot of attention within the last 15 years. Problems of resolution, noise, and image understanding are involved, and one of the best methods developed so far is the [F.sup.*] algorithm of Fischler, which achieves robustness, rightness, and rapidity. Like other methods of dynamic programming, it consists of defining a cost which depends on local information; then a summation-minimization process in the image is performed. We present herein a mathematical formalization of the [F.sup.*] algorithm, which allows us to extend the cost both to cliques of more than two points (to deal with the contrast), and to neighborhoods of size larger than one (to take into account the curvature). Thus, all the needed information (contrast, grey-level, curvature) is synthesized in a unique cost function defined on the digital original image. This cost is used to detect roads and valleys in satellite images (SPOT). Index Terms - Line detection, energy minimization, dynamic programming, curvature, satellite images.

In this paper, we consider the problem of edge detection and image estimation in nonstationary images corrupted by additive Gaussian noise. The noise-free image is represented using the compound Gauss-Markov random field of Jeng and Woods and the problem of image estimation and edge detection is posed as a maximum a posteriori estimation problem. Since the a posteriori probability function is nonconvex, computationally intensive stochastic relaxation algorithms are normally required. We proposed a deterministic relaxation method based on mean field annealing with a compound Gauss-Markov random (CGMRF) field model. We present a set of iterative equations for the mean values of the intensity and both horizontal and vertical line processes with or without taking into account some interaction between them. We show the relationship between this technique and two other methods, that described by Geiger and Girosi and the one proposed by Simchony et al. Finally, we present edge detection and image estimation results on several noisy images.

Deterministic pseudo-annealing (DPA) solves the maximum a posteriori problem in a Markov random field by extending the tentative labeling probability. A merit function and continuous relaxation labeling are used for this extension. The method is deterministic and allows a high degree of parallelism. A change in the definition domain of DPA produces a convex probability function. Randomly weighted graphs are used to evaluate DPA.

Herein, we present a variational model devoted to image classification coupled with an edge-preserving regularization process. The discrete nature of classification (i.e., to attribute a label to each pixel) has led to the development of many probabilistic image classification models, but rarely to variational ones. In the last decade, the variational approach has proven its efficiency in the field of edge-preserving restoration. In this paper, we add a classification capability which contributes to provide images composed of homogeneous regions with regularized boundaries, a region being defined as a set of pixels belonging to the same class. The soundness of our model is based on the works developed on the phase transition theory in mechanics. The proposed algorithm is fast, easy to implement, and efficient. We compare our results on both synthetic and satellite images with the ones obtained by a stochastic model using a Potts regularization. Index Terms--Variational model, classification, labeling, phase transition theory, edge-preserving regularization, minimization, satellite images.

An algorithm for performing maximum likelihood estimation of Markovian prior parameters is proposed based on recent developments in statistics. With the use of importance sampling, the proposed algorithm minimizes the need to generate samples and, therefore, practical in terms of computation time. The algorithm was demonstrated on three Markov random fields models. The computation of segmentations was based on the estimated parameters.