In supervised classification, the learning process typically trains a classifier to optimize the accuracy of classifying data into the classes that appear in the learning set, and only them. While this framework fits many use cases, there are situations where the learning process is knowingly performed using a learning set that only represents the data that have been observed so far among a virtually unconstrained variety of possible samples. It is then crucial to define a classifier which has the ability to reject a sample, i.e., to classify it into a rejection class that has not been yet defined. Although obvious solutions can add this ability a posteriori to a classifier that has been learned classically, a better approach seems to directly account for this requirement in the classifier design. In this paper, we propose an innovative learning strategy for supervised classification that is able, by design, to reject a sample as not belonging to any of the known classes. For that, we rely on modeling each class as the combination of a probability density function (PDF) and a threshold that is computed with respect to the other classes. Several alternatives are proposed and compared in this framework. A comparison with straightforward approaches is also provided.

The confined and crowded environment of developing brains imposes spatial constraints on neuronal cells that have evolved individual and collective strategies to optimize their growth. These include organizing neurons into populations extending their axons to common target territories. How individual axons interact with each other within such populations to optimize innervation is currently unclear and difficult to analyze experimentally in vivo. Here, we developed a stochastic model of 3D axon growth that takes into account spatial environmental constraints, physical interactions between neighboring axons, and branch formation. This general, predictive and robust model, when fed with parameters estimated on real neurons from the Drosophila brain, enabled the study of the mechanistic principles underlying the growth of axonal populations. First, it provided a novel explanation for the diversity of growth and branching patterns observed in vivo within populations of genetically identical neurons. Second, it uncovered that axon branching could be a strategy optimizing the overall growth of axons competing with others in contexts of high axonal density. The flexibility of this framework will make it possible to investigate the rules underlying axon growth and regeneration in the context of various neuronal populations.

The analysis and comparison of tree-like shapes is of great importance since many structures in nature can be described by them. In the field of biomedical imaging, trees have been used to describe structures such as neurons, blood vessels and lung airways. Since it is known that their morphology provides information on their functioning and allows the characterization of pathological states, it is of paramount importance to develop methods to analyze their shape and to quantify differences in structures. At present, there are a number of methods for the comparison of trees. Some only take into account the topology of the trees (such as [1], [2]), while others consider both topological and geometrical information (such as [3], [4]).

In this paper, we use statistical inference and muti-spectral images to quantify the evolution of skin hyper-pigmentation lesions under treatment. We show that statistical inference allows getting change maps of the disease which can be useful for dermatologists to analyze the disease evolution. Indeed, a local change map is obtained by computing the deviation between two multi-spectral images in a region of interest (ROI). Then, we normalize the obtained map and develop a statistical inference framework to quantify the changes. Finally, we propose a criterion that integrates change maps in order to quantify the treatment efficacy on a patient.

In this paper, we introduce a new probabilistic method which integrates building extraction with change detection in remotely sensed image pairs. A global optimization process attempts to find the optimal configuration of buildings, considering the observed data, prior knowledge, and interactions between the neighboring building parts. We present methodological contributions in three key issues: 1) We implement a novel object-change modeling approach based on Multitemporal Marked Point Processes, which simultaneously exploits low-level change information between the time layers and object-level building description to recognize and separate changed and unaltered buildings. 2) To answer the challenges of data heterogeneity in aerial and satellite image repositories, we construct a flexible hierarchical framework which can create various building appearance models from different elementary feature-based modules. 3) To simultaneously ensure the convergence, optimality, and computation complexity constraints raised by the increased data quantity, we adopt the quick Multiple Birth and Death optimization technique for change detection purposes, and propose a novel nonuniform stochastic object birth process which generates relevant objects with higher probability based on low-level image features.

In this paper, we introduce a novel probabilistic approach to handle occlusions and perspective effects. The proposed method is an object based method embedded in a marked point process framework. We apply it for the size estimation of a penguin colony, where we model a penguin colony as an unknown number of 3D objects. The main idea of the proposed approach is to sample some candidate configurations consisting of 3D objects lying in the real plane. A Gibbs energy is define on the configuration space. These configurations are projected onto the image plane to define the data term, to which some prior information is added. The configurations are modified until convergence using the multiple birth and death optimization algorithm and by measuring the similarity between the projected image of the configuration and the real image. During optimization, the proposed configuration is modeled by a mixed graph which represents all dependencies between the objects, including interaction between neighbor objects and parent-child dependency for occluded objects. We tested our model on synthetic image, and real images.

In this paper, we present a faster version of the newly proposed Multiple Birth and Cut (MBC) algorithm. MBC is an optimization method applied to the energy minimization of an object based model, defined by a marked point process. We show that, by proposing good candidates in the birth step of this algorithm, the speed of convergence is increased. The algorithm starts by generating a dense configuration in a special organization, the best candidates are selected using the belief propagation algorithm. Next, this candidate configuration is combined with the current configuration using binary graph cuts as presented in the original version of the MBC algorithm. We tested the performance of our algorithm on the particular problem of counting flamingos in a colony, and show that it is much faster with the modified birth step.

Clinical evaluation of skin treatments consists of two steps. First, the degree of the disease is measured clinically on a group of patients by dermatologists. Then, a statistical test is used on obtained set of measures to determine the treatment efficacy. In this paper, a method is proposed to automatically measure the severity of skin hyperpigmentation. After a classification step, an objective function is designed in order to obtain an optimal linear combination of bands defining the severity criterion. Then a hypothesis test is deployed on this combination to quantify treatment efficacy.

In this paper, we compare two different approaches for semiautomatic detection of skin hyper-pigmentation on multi-spectral images. These two methods are support vector machine (SVM) and blind source separation. To apply SVM, a dimension reduction method adapted to data classification is proposed. It allows to improve the quality of SVM classification as well as to have reasonable computation time. For the blind source separation approach we show that, using independent component analysis, it is possible to extract a relevant cartography of skin pigmentation.

In this paper we introduce a probabilistic approach of building extraction in remotely sensed images. To cope with data heterogeneity we construct a flexible hierarchical framework which can create various building appearance models from different elementary feature based modules. A global optimization process attempts to find the optimal configuration of buildings, considering simultaneously the observed data, prior knowledge, and interactions between the neighboring building parts. The proposed method is evaluated on various aerial image sets containing more than 500 buildings, and the results are matched against two state-of-the-art techniques.

We present a new approach for building reconstruction from a single Digital Surface Model (DSM). It treats buildings as an assemblage of simple urban structures extracted from a library of 3D parametric blocks (like a LEGO set). First, the 2D-supports of the urban structures are extracted either interactively or automatically. Then, 3D-blocks are placed on the 2D-supports using a Gibbs model which controls both the block assemblage and the fitting to data. A Bayesian decision finds the optimal configuration of 3D-blocks using a Markov Chain Monte Carlo sampler associated with original proposition kernels. This method has been validated on multiple data set in a wide-resolution interval such as 0.7 m satellite and 0.1 m aerial DSMs, and provides 3D representations on complex buildings and dense urban areas with various levels of detail.

This paper presents a new stochastic marked point process for describing images in terms of a finite library of geometric objects. Image analysis based on conventional marked point processes has already produced convincing results but at the expense of parameter tuning, computing time, and model specificity. Our more general multimarked point process has simpler parametric setting, yields notably shorter computing times, and can be applied to a variety of applications. Both linear and areal primitives extracted from a library of geometric objects are matched to a given image using a probabilistic Gibbs model, and a Jump-Diffusion process is performed to search for the optimal object configuration. Experiments with remotely sensed images and natural textures show that the proposed approach has good potential. We conclude with a discussion about the insertion of more complex object interactions in the model by studying the compromise between model complexity and efficiency.

We present a new approach to extract predefined objects, such as trees and oil tanks for instance, from high resolution SAR images. We consider a stochastic approach based on an object process also called marked point process. The objects represent trees or oil tanks which are modeled by disks in the image. We first define a Gibbs density that takes into account both prior information and the data. The energy we define is composed of two terms, one is a prior, penalizing overlaps between objects, and the other is a data term, which measures the suitability of an object in the SAR image. The problem is then reduced to an energy minimization problem. We sample the process to extract the configuration of objects minimizing the energy by a fast birth-and-death dynamics, leading to the total number of objects (trees or oil tanks in our case). This approach is much faster than manual counts and does not need any preprocessing or supervision of a user.

The present work concerns the analysis of dynamic scenes from earth observation images. We are interested in building a map which, on one hand locates places of change, on the other hand, reconstructs a unique visual information of the non-change areas. We show in this paper that such a problem can naturally be takled with conditional mixed-state random field modeling (mixed-state CRF), where the ¿mixed state¿ refers to the symbolic or continous nature of the unknown variable. The maximum a posteriori (MAP) estimation of the CRF is, through the Hammersley-Clifford theorem, turned into an energy minimisation problem. We tested the model on several Quickbird images and illustrate the quality of the results.

In this paper we introduce a new probabilistic method which integrates building extraction with change detection in remotely sensed image pairs. A global optimization process attempts to find the optimal configuration of buildings, considering the observed data, prior knowledge, and interactions between the neighboring building parts. The accuracy is ensured by a Bayesian object model verification, meanwhile the computational cost is significantly decreased by a non-uniform stochastic object birth process, which proposes relevant objects with higher probability based on low-level image features.

The advent of a new generation of synthetic aperture radar (SAR) satellites, such as Advanced SAR/Environmental Satellite (C-band), Phased Array Type L-band Synthetic Aperture Radar/Advanced Land Observing Satellite (L-band), and TerraSAR-X (X-band), offers advanced potentials for the detection of urban tissue. In this letter, we analyze and compare the performance of multiple types of SAR images in terms of band frequency, polarization, incidence angle, and spatial resolution for the purpose of operational urban areas delineation. As a reference for comparison, we use a proven method for extracting textural features based on a Gaussian Markov Random Field (GMRF) model. The results of urban areas delineation are quantitatively analyzed allowing performing intrasensor and intersensors comparisons. Sensitivity of the GMRF model with respect to texture window size and to spatial resolutions of SAR images is also investigated. Intrasensor comparison shows that polarization and incidence angle play a significant role in the potential of the GMRF model for the extraction of urban areas from SAR images. Intersensors comparison evidences the better performances of X-band images, acquired at 1-m spatial resolution, when resampled to resolutions of 5 and 10 m.

We present a new approach for building reconstruction from a single Digital Elevation Model (DEM). It treats buildings as an assemblage of simple urban structures extracted from a library of 3D parametric blocks (like a LEGOregset). This method works on various data resolutions such as 0.7 m satellite and 0.1 m aerial DEMs and allows us to obtain 3D representations with various levels of detail. First, the 2D supports of the urban structures are extracted either interactively or automatically. Then, 3D blocks are placed on the 2D supports using a Gibbs model. A Bayesian decision finds the optimal configuration of 3D blocks using a RJMCMC sampler. Experimental results on complex buildings and dense urban areas are presented using data at various resolutions.

Here we present a new approach to automatically detect and count breeding greater flamingos (Phoenicopterus Roseus) on aerial photographs of their colonies. We consider a stochastic approach based on object processes also called marked point processes. The objects represent flamingos which are defined as ellipses. We formulate a Gibbs density, associated with the marked point process of ellipses, which is defined w.r.t a Poisson measure. Thus, the issue is reduced to an energy minimization, where the energy is composed of a regularization term (prior density), which introduces some constraints on the objects and their interactions, and a data term, which links the objects to the features to be extracted in the image. Then, we sample the process to extract the configuration of objects minimizing the energy by a new and fast birth-and-death dynamics, leading to the total number of birds. This approach gives counts with good precision compared to manual counts. Additionally, this approach does not need image pre-processing or supervision of the extraction by an operator thus considerably reducing the overall processing time required to get the estimate.

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, while the latter aims at segmenting homogeneous areas. An energy is defined, favoring connections of segments, alignments of rectangles, as well as 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 IGN (French National Geographic Institute) consisting in low quality DEMs of various types.

We present a new algorithm which merges discontinuities in 3-D images of tubular structures presenting undesirable gaps. The application of the proposed method is mainly associated to large 3-D images of microvascular networks. In order to recover the real network topology, we need to fill the gaps between the closest discontinuous vessels. The algorithm presented in this paper aims at achieving this goal. This algorithm is based on the skeletonization of the segmented network followed by a tensor voting method. It permits to merge the most common kinds of discontinuities found in microvascular networks. It is robust, easy to use, and relatively fast. The microvascular network images were obtained using synchrotron tomography imaging at the European Synchrotron Radiation Facility. These images exhibit samples of intracortical networks. Representative results are illustrated.

In this paper, we present an automatic method for the 3D building reconstruction from satellite images. The proposed approach consists in reconstructing buildings by assembling simple urban structures extracted from a grammar of 3D parametric models, as a "LEGO" game. First, the building footprints are extracted through sequences of quadrilaterals: it allows to define the problem as a causal process. Then, the 3D reconstruction stage is realized through a Hidden Markov Model and the optimal sequences of 3D parametric objects are found using the Viterbi algorithm.

In this paper, satellite-based remote sensing techniques are used for assessing the damage after a forest fire. Here, burnt land mapping is based on a single after-fire satellite image (SPOT 5). Both support vector machines (SVM) and traditional classification algorithms such as the K-nearest neighbours or the K-means are used to discriminate burnt from unburnt areas. An automatic method combining K-means and SVM is presented and its performances are compared to more classical methods. Maps produced by the different classifiers are also compared to official ground truth provided by the French Space Agency (CNES).

Ant colony optimization (ACO) has been proposed as a promising tool for regularization in image classification. The algorithm is applied here in a different way than the classical transposition of the graph color affectation problem. The ants collect information through the image, from one pixel to the others. The choice of the path is a function of the pixel label, favoring paths within the same image segment. We show that this corresponds to an automatic adaptation of the neighborhood to the segment form, and that it outperforms the fixed-form neighborhood used in classical Markov random field regularization techniques. The performance of this new approach is illustrated on a simulated image and on actual remote sensing images.

We propose to apply a marked point process to detect a galaxy filament network. From the "quality candy" model, initially developed for road network extraction in remotely sensed images, we adapt the data term to the filament detection. The optimization is realized by a simulated annealing using a reversible jump Markov Chain Monte Carlo algorithm. Results are presented on a numerical simulation and on an astronomical survey

We propose a parametric model for automatic 3D reconstruction of urban areas from high resolution satellite data. An automatic building extraction method based on marked point processes is used to provide rectangular building footprints. Based on a parametric model with rectangular ground footprint, the proposed method is developed using a Bayesian approach : we search for the best configuration of parametric models with respect to both a priori knowledge of models and their interactions, and a likelihood which fits models to the DEM. A simulated annealing is used to find the configuration which maximizes the a posteriori density of the Bayesian expression

In this work, we propose a new model based on stochastic geometry for extracting features from images. This type of model allows the incorporation of a prior knowledge on the interactions between features within the extraction process. We focus on the specific problem of automatic building extraction from digital elevation models (DEMs). The model we propose is based on two interacting spatial point processes, the former being a process of rectangles, the latter a process of segments. An energy associated with the resulting process is defined. This energy consists in five main parts. We first define two energy data terms to make the rectangles fit the homogeneous areas and the segments fit meaningful discontinuities. Two prior terms favoring respectively the alignment of rectangles and the connection of segments are incorporated. The last part of the energy is an interaction term that makes the two types of objects cooperate. We present results on real data provided by the IGN (French Geographic Institute)

We present an automatic 3D city model of dense urban areas from HR satellite data. The proposed method is developed using a structural approach: we construct complex buildings by merging simple parametric models with rectangular ground footprint. To do so, an automatic building extraction method based on marked point processes is used to provide rectangular building footprints. A collection of 3D parametric models is defined in order to be fixed onto these building footprints. A Bayesian framework including both prior knowledge of models and their interactions, and a likelihood fitting them to the digital elevation model, is then used. A simulated annealing scheme allows to find the configuration which maximizes the posterior density of the Bayesian expression.

We present a textural kernel for "support vector machines" classification applied to remote sensing problems. SVMs constitute a method of supervised classification well adapted to deal with data of high dimension, such as images. We introduce kernel functions in order to favor the distinction between our class of interest and the other classes: it gives information of similarity. In our case this similarity is based on radiometric and textural characteristics. One of the main difficulties is to elaborate textural parameters which are relevant and characterize as well as possible the joint distribution of a set of connected pixels. We apply this method to remote sensing problems: the detection of forest fires and the extraction of urban areas in high resolution images.

This work presents a framework to extract tree crowns from remotely sensed data, especially in plantation images, using stochastic geometry. We aim at finding the tree top positions, and the tree crown diameter distribution. Our approach consists in considering that these images are some realizations of a marked point process. First we model the tree plantation as a configuration of an unknown number of ellipses. Then, a Bayesian energy is defined, containing both a prior energy which incorporates the prior knowledge of the plantation geometric properties, and a likelihood which fits the objects to the data. Eventually, we estimate the global minimum of this energy using reversible jump Markov Chain Monte Carlo dynamics and a simulated annealing scheme. We present results on optical aerial images of poplars provided by IFN.

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.

This paper presents a two-step algorithm to perform an unsupervised extraction of line networks from satellite images, within a stochastic geometry framework. First, we propose a new operator, providing a measure of the possibility of linear structure presence on each image pixel. Second, we propose a Bayesian model in order to extract the line network from the operator output. The prior model, a Markov object process, incorporates the topological properties of the network through interactions between objects, while the line operator answers are taken into account in the likelihood. Optimization is realized by simulated annealing using a reversible jump Monte Carlo Markov chain algorithm. An application to hydrographic network extraction is presented.

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.

This paper is concerned with the detection of multiple small brain lesions from magnetic resonance imaging (MRI) data. A model based on the marked point process framework is designed to detect Virchow-Robin spaces (VRSs). These tubular shaped spaces are due to retraction of the brain parenchyma from its supplying arteries. VRS are described by simple geometrical objects that are introduced as small tubular structures. Their radiometric properties are embedded in a data term. A prior model includes interactions describing the clustering property of VRS. A Reversible Jump Markov Chain Monte Carlo algorithm (RJMCMC) optimizes the proposed model, obtained by multiplying the prior and the data model. Example results are shown on T1-weighted MRI datasets of elderly subjects.

To extract buildings from digital elevation models, we define a point process whose points represent buildings. We then define a density for this point process which is split into two parts, consisting in an "internal field" that allows us to model the prior knowledge we have on patterns of buildings in urban areas and an "external field" that makes the point process fit the data. We then use a metropolis Hastings Green sampler coupled with a simulated annealing that gives the configuration of buildings minimizing the energy we have defined. We present results on real data provided by the French Mapping Institute (IGN).

In this paper, we rely on the theory of marked point processes to perform an unsupervised road network extraction from optical and radar images. A road network is modeled by a Markov object process, where the objects correspond to interacting line segments. The prior model, called "quality candy" model, is constructed so as to exploit as far as possible the geometric constraints of this type of line network. Data properties are taken into account in the density of the process through a data term based on statistical tests. Optimization is realized by simulated annealing using a RJM-CMC algorithm. Some experimental results are provided on aerial and satellite images (optical and radar data).

We propose a method for the synthesis of urban areas based on a description of objects in the scene. Using Digital Elevation Models (DEM) and aerial pictures, we extract the objects in the scene and model them by simple geometric shapes. The extraction process is described for three groups of objects: buildings, roofs and trees. The reconstruction of buildings is based on a statistical approach developed within the Ariana project in which a marked point process is defined, whose points represent buildings. The marked point process is determined by two elements: a prior using interactions between points to model the knowledge we have about urban areas, and a data model to enforce coherence with respect to the DEM. For the treatment of the roofs, we adopt a strategy which consists of detecting intersection lines between roof planes. The ridges are extracted from the DEM by means of image filtering, morphological operations and a Hough transform. For the extraction of trees, we compare colour information from aerial images and height information from the DEM to select the zones of high vegetation corresponding to trees. Then, mathematical morphology techniques are used to refine the selected zones. Finally, the zones are filled according to a randomized algorithm with circles of fixed radius that model individual trees. Furthermore, in order to evaluate the previous techniques and to experiment with this object-oriented approach in image synthesis, we have developed a graphical tool allowing 3D rendering of urban scenes with the possibility to move around the scene and to interact with the environment. Tests have been conducted on DEMs of the city of Amiens kindly provided by the French Mapping Institute (IGN).

Shape from shading is an ill-posed inverse problem for which there is no completely satisfactory solution in the existing literature. In this paper, we address shape from shading as an energy minimization problem. We first show that the deterministic approach provides efficient algorithms in terms of CPU time, but reaches its limits since the energy associated with shape from shading can contain multiple deep local minima. We derive an alternative stochastic approach using simulated annealing. The obtained results strongly outperform the results of the deterministic approach. The shortcoming is an extreme slowness of the optimization. Therefore, we propose a hybrid approach which combines the deterministic and stochastic approaches in a multiresolution framework.

We consider the problem of multi-channel image classification. We take into account not only the radiometric information but also some textural information. The proposed algorithm is a particular case of a fission-fusion scheme. The fission step consists of defining some textural parameters and extracting them from the different channels. The fusion between the texture channels and the original radiometric channels is performed in a second step. We consider a supervised scheme in which some training areas are given. These training areas allow us to define the class parameters and to drive the fusion process. Some results are given on SIR-C images.

This work aims at detecting buildings in digital aerial photographs. We model a set of buildings by a configuration of objects. We define a point process on the set of configurations, which could be divided into two parts: the first one is a prior model on the configurations which uses interactions between objects. The second one is a data model which enforces the coherence with the images. Thus we obtain a distribution /spl pi/ which has to be maximized. In order to achieve this maximum, we use a Monte Carlo Markov Chain simulation-a Metropolis-Hastings-Green algorithm-mixed with simulated annealing. Then we test this method on both synthetic and real data.

We propose a local registration method for cartographic road networks on SPOT satellite images based on Markov random fields (MRF) on graphs. Since the cartographic and image data are obtained from exogeneous sources, the noises degrading these data are of a different nature. This phenomenon can create important differences between the data. In addition, cartographers sometimes introduce distortions, called generalization, in the road map in order to emphasize some details of the road (like the bends of a mountain road). Our algorithm aims at correcting the error due to noise and generalization, hence increasing the accuracy of the road map. The proposed method consists of translating the cartographic data into a graph model, and then defining a MRF to fit the graph on the image.

We present a fully unsupervised clustering algorithm in order to overcome the problem of a priori defining the number of clusters. We propose to optimize an objective function which is the sum of two terms. The first one is a generalization of intra-cluster distance within the framework of fuzzy sets. The second one is an entropy term. Our clustering algorithm has been applied to the problem of clustering both remote sensing data and medical images.

We investigate two Markov object processes to model line networks. The first one is based on region interactions whereas the interactions of the second one are defined w.r.t. the segment intersection points. We use a Metropolis-Hastings-Green scheme to simulate both models.

We propose to analyze the texture through Markov random fields (MRF) in order to extract urban areas from high resolved satellite images. We thus define a new chain-based model derived from classical Gaussian MRF. This model which takes into account directions allows us to discriminate between oriented objects that often lead to false alarms. The texture parameters are conditional local variances estimated through a speedy heuristic method. The estimated parameters are then clustered with a new algorithm that does not require any a priori number of clusters. We ran our algorithm on optical satellite images with several ground resolution (SPOT3 and SPOT5) and on radar satellite images (ERS).

The problem of extracting information from an image which corresponds to early stage processing in vision is addressed. We propose a new approach (the MPI approach) which simultaneously provides a restored image, a segmented image and a map which reflects the local scale for representing the information. Embedded in a Bayesian framework, this approach is based on an information prior, a pixon model and two Markovian priors. This model based approach is oriented to detect and analyze small parabolic patches in a noisy environment. The number of clusters and their parameters are not required for the segmentation process. The MPI approach is applied to the analysis of statistical parametric maps obtained from fMRI experiments.

Recent developments in statistics now allow maximum likelihood estimators for the parameters of Markov random fields (MRFs) to be constructed. We detail the theory required, and present an algorithm that is easily implemented and practical in terms of computation time. We demonstrate this algorithm on three MRF models--the standard Potts model, an inhomogeneous variation of the Potts model, and a long-range interaction model, better adapted to modeling real-world images. We estimate the parameters from a synthetic and a real image, and then resynthesize the models to demonstrate which features of the image have been captured by the model. Segmentations are computed based on the estimated parameters and conclusions drawn.

In this paper, we tackle the problem of estimating textural parameters. We do not consider the problem of texture synthesis, but the problem of extracting textural features for tasks such as image segmentation. We take into account nonstationarities occurring in the local mean. We focus on Gaussian Markov random fields for which two estimation methods are proposed, and applied in a nonstationary framework. The first one consists of extracting conditional probabilities and performing a least square approximation. This method is applied to a nonstationary framework, dealing with the piecewise constant local mean. This framework is adapted to practical tasks when discriminating several textures on a single image. The blurring effect affecting edges between two different textures is thus reduced. The second proposed method is based on renormalization theory. Statistics involved only concern variances of Gaussian laws, leading to Cramer-Rao estimators. This method is thus especially robust with respect to the size of sampling. Moreover, nonstationarities of the local mean do not affect results. We then demonstrate that the estimated parameters allow texture discrimination for remote sensing data. The first proposed estimation method is applied to extract urban areas from SPOT images. Since discontinuities of the local mean are taken into account, we obtain an accurate urban areas delineation. Finally, we apply the renormalization based on method to segment ice in polar regions from AVHRR data.

We address the problem of unsupervised clustering using a Bayesian framework. The entropy is considered to define a priori and enables one to overcome the problem of defining a priori the number of clusters and an initialization of their centers. A deterministic algorithm derived from the standard k-means algorithm is proposed and compared with simulated annealing algorithms. The robustness of the proposed method is shown on a magnetic resonance images database containing 65 volumetric (3D) images.

Functional magnetic resonance images (fMRI's) provide high-resolution datasets which allow researchers to obtain accurate delineation and sensitive detection of activation areas involved in cognitive processes. To preserve the resolution of this noninvasive technique, refined methods are required in the analysis of the data. In this paper, we first discuss the widely used methods based on a statistical parameter map (SPM) analysis exposing the different shortcomings of this approach when considering high-resolution data. First, the often used Gaussian filtering results in a blurring effect and in delocalization of the activated area. Secondly, the SPM approach only considers false alarms due to noise but not rejections of activated voxels. We propose to embed the fMRI analysis problem into a Bayesian framework consisting of two steps: i) data restoration and ii) data analysis. We, therefore, propose two Markov random fields (MRF's) to solve these two problems. Results on three protocols (visual, motor and word recognition) are shown for two SPM approaches and compared with the proposed MRF approach.

Developments in Markov chain Monte Carlo procedures have made it possible to perform fully Bayesian image segmentation. By this we mean that all the parameters are treated identically, be they the segmentation labels, the class parameters or the Markov random field prior parameters. We perform the analysis by sampling from the posterior distribution of all the parameters. Sampling from the MRF parameters has traditionally been considered if not intractable then at least computationally prohibitive. In the statistics literature there are descriptions of experiments showing that the MRF parameters may be sampled by approximating the partition function. These experiments are all, however, on 'toy' problems; for the typical size of image encountered in engineering applications the phase transition behaviour of the models becomes a major limiting factor in the estimation of the partition function. Nevertheless, we show that, with some care, fully Bayesian segmentation can be performed on realistic sized images. We also compare the fully Bayesian approach with the approximate pseudolikelihood method.