Detecting building change in bitemporal remote sensing (RS) imagery requires a model to highlight the changes in buildings and ignore the irrelevant changes of other objects and sensing conditions. Buildings have comparatively less diverse textures than other objects and appear as repetitive visual patterns on RS images. In this paper, we propose Gabor Feature Network (GFN) to extract the distinctive repetitive texture features of buildings. Furthermore, we also design Feature Fusion Module (FFM) to fuse the extracted multiscale features from GFN with the features from a Transformer-based encoder to pass on the texture features to different parts of the model. Using GFN and FFM, we design a Transformer-based model, called GabFormer for building change detection. Experimental results on the LEVIR-CD and WHU-CD datasets indicate that GabFormer outperforms other SOTA models and in particular show significant improvement in the generalization capability. Our code is available on https://github.com/Ayana-Inria/GabFormer.

This paper tackles the semantic segmentation of zones affected by forest fires by the introduction of methods fusing multimodal imagery collected from unmanned aerial vehicles (UAVs) and satellite platforms. The multiresolution fusion task is especially challenging in this case because the difference between the involved spatial resolutions is very large – a situation that is normally not addressed by traditional multiresolution schemes. Two novel multiresolution fusion approaches, based on Bayesian and probabilistic graphical fusion models and integrated with a deep fully convolutional network and with the expectation-maximization algorithm, are proposed. The application is to a real case of fire zone mapping and management in the area of Marseille, France.

The availability of multimodal remotely sensed images calls for the development of methods capable to jointly exploit the information deriving from images acquired at different spatial resolutions, frequencies, and bands, taking advantage from their possible complementary features. This letter proposes to address this task in the case of multimission synthetic aperture radar (SAR) images, through a combination of fully convolutional networks (FCNs), hierarchical probabilistic graphical models (PGMs), and decision tree ensembles. The objective is to model the multimodal information collected at multiple spatial resolutions by distinct space missions with SAR payloads through the nonparametric formulation of FCNs and decision trees, and the spatial and multiresolution modeling capabilities of FCNs and hierarchical PGMs. The experimental validation is conducted with multimission SAR imagery acquired at X-, L-, and C-band, respectively, by COSMO-SkyMed, SAOCOM, and Sentinel-1 over Northern Italy. The results suggest the advantages of incorporating multifrequency radar acquisitions to reach accurate classification maps and the multimodal fusion capabilities of the proposed methodology.

This article presents a method for the automatic learning of the potentials of a stochastic model, in particular a conditional random field (CRF), in a non-parametric fashion. The proposed model is based on a neural architecture, in order to leverage the modeling capabilities of deep learning (DL) approaches to directly learn semantic and spatial information from the input data. Specifically, the methodology is based on fully convolutional networks and fully connected neural networks. The idea is to access the multiscale information intrinsically extracted in the intermediate layers of a fully convolutional network through the integration of fully connected neural networks at different scales, while favoring the interpretability of the hidden layers as posterior probabilities. The potentials of the CRF are learned through an additional convolutional layer, whose kernel models the local spatial information considered. The loss function is computed as a linear combination of cross-entropy losses, accounting for the multiscale and the spatial information. To evaluate the capabilities of the proposed approach for the semantic segmentation of remote sensing images, the experimental validation was conducted with the ISPRS 2-D semantic labeling challenge Vaihingen and Potsdam datasets and with the IEEE GRSS data fusion contest Zeebruges dataset. As the ground truths of these benchmark datasets are spatially exhaustive, they have been modified to approximate the spatially sparse ground truths common in real remote sensing applications. The results are significant, as the proposed approach obtains higher average classification accuracies than recent state-of-the-art techniques considered in this article. The code is available athttps://github.com/Ayana-Inria/CRFNet-RS.

We present a real-time multi-object tracker using an enhanced version of the Gaussian mixture probability hypothesis density (GM-PHD) filter to track detections of a state-of-the-art convolutional neural network (CNN). This approach adapts the GM-PHD filter to a real-world scenario to recover target trajectories in remote sensing videos. Our GM-PHD filter uses a measurement-driven birth, considers past tracked objects, and uses CNN information to propose better hypotheses initialization. Additionally, we present a label tracking solution for the GM-PHD filter to improve identity propagation given target path uncertainties. Our results show competitive scores against other trackers while obtaining real-time performance. Code is available at https://github.com/Ayana-Inria/RFS-filters-for-satellite-videos.

The problem of the semantic segmentation of multimodal images is characterized by the challenge of jointly exploiting information deriving from images possibly acquired at different spatial resolutions, frequencies, and bands. This paper proposes to address this task in the case of multimission synthetic aperture radar (SAR) images, through a combination of fully convolutional networks (FCNs), hierarchical probabilistic graphical models (PGMs), and decision tree ensembles. The objective is to model the spatial and multiresolution information contained in multimodal remote sensing images collected by distinct space missions with SAR payloads. The experimental validation is conducted with COSMO-SkyMed and SAOCOM images over Northern Italy. The results show that the proposed methodology is capable to reach accurate classification maps from input multimission SAR imagery.

Identifying and mapping fractures and faults are important in geosciences, especially in earthquake hazard and geological reservoir studies. This mapping can be done manually in optical images of the earth surface, yet it is time consuming and it requires an expertise that may not be available. Building upon a recent prior study, we develop a deep learning approach, based on a variant of a U-Net neural network, and apply it to automate fracture and fault mapping in optical images and topographic data. We show that training the model with a realistic knowledge of fracture and fault uneven distributions and trends, and using a loss function that operates at both pixel and larger scales through the combined use of weighted Binary Cross Entropy and Intersection over Union, greatly improves the predictions, both qualitatively and quantitatively. As we apply the model to a site differing from those used for training, we demonstrate its enhanced generalization capacity.

This paper presents a novel semantic segmentation method of very high resolution remotely sensed images based on fully convolutional networks (FCNs) and feedforward neural networks (FFNNs). The proposed model aims to exploit the intrinsic multiscale information extracted at different convolutional blocks in an FCN by the integration of FFNNs, thus incorporating information at different scales. The purpose is to obtain accurate classification results with realistic data sets characterized by sparse ground truth (GT) data by taking benefit from multiscale and long-range spatial information. The final loss function is computed as a linear combination of the weighted cross-entropy losses of the FFNNs and of the FCN. The modeling of spatial-contextual information is further addressed by the introduction of an additional loss term which allows to integrate spatial information between neighboring pixels. The experimental validation is conducted with the ISPRS 2D Semantic Labeling Challenge data set over the city of Vaihingen, Germany. The results are promising, as the proposed approach obtains higher average classification results than the state-of-the-art techniques considered, especially in the case of scarce, suboptimal GTs.

This paper addresses the semantic segmentation of synthetic aperture radar (SAR) images through the combination of ful-ly convolutional networks (FCN s), hierarchical probabilistic graphical models (PGMs), and decision tree ensembles. The idea is to incorporate long-range spatial information together with the multiresolution information extracted by FCN s, through the multiresolution graph topology on which hierar-chical PGMs can be efficiently formulated. The objective is to obtain accurate classification results with small datasets and reduce problems of spatial inconsistency. The experimental validation is conducted with several COSMO-SkyMed satel-lite images over Northern Italy. The results are significant, as the proposed method obtains more accurate classification results than the standard FCN s considered.

Deep learning (DL) is currently the dominant approach to image classification and segmentation, but the performances of DL methods are remarkably influenced by the quantity and quality of the ground truth (GT) used for training. In this article, a DL method is presented to deal with the semantic segmentation of very-high-resolution (VHR) remote-sensing data in the case of scarce GT. The main idea is to combine a specific type of deep convolutional neural networks (CNNs), namely fully convolutional networks (FCNs), with probabilistic graphical models (PGMs). Our method takes advantage of the intrinsic multiscale behavior of FCNs to deal with multiscale data representations and to connect them to a hierarchical Markov model (e.g., making use of a quadtree). As a consequence, the spatial information present in the data is better exploited, allowing a reduced sensitivity to GT incompleteness to be obtained. The marginal posterior mode (MPM) criterion is used for inference in the proposed framework. To assess the capabilities of the proposed method, the experimental validation is conducted with the ISPRS 2D Semantic Labeling Challenge datasets on the cities of Vaihingen and Potsdam, with some modifications to simulate the spatially sparse GTs that are common in real remote-sensing applications. The results are quite significant, as the proposed approach exhibits a higher producer accuracy than the standard FCNs considered and especially mitigates the impact of scarce GTs on minority classes and small spatial details.

In this paper, a novel method to deal with the semantic segmentation of very high resolution remote sensing data is presented. Recent advances in deep learning (DL), especially convolutional neural networks (CNNs) and fully convolutional networks (FCNs), have shown outstanding performances in this task. However, the map accuracy depends on the quantity and quality of ground truth (GT) used to train them. At the same time, probabilistic graphical models (PGMs) have sparked even more interest in the past few years, because of the ever-growing need for structured predictions. The novel method proposed in this paper combines DL and PGMs to perform remote sensing image classification. FCNs can be exploited to deal with multiscale data through the integration with a hierarchical Markov model. The marginal posterior mode (MPM) criterion for inference is used in the proposed framework. Experimental validation is conducted on the ISPRS 2D Semantic Labeling Challenge Vaihingen dataset. The results are significant, as the proposed method has a higher recall than the standard FCNs considered and allows mitigating the impact of incomplete or suboptimal GT, especially with regard to the discrimination of minoritary classes.

Retinal vessel extraction and segmentation is essential for supporting diagnosis of eye-related diseases. In recent years, deep learning has been applied to vessel segmentation and achieved excellent performance. However, these supervised methods require accurate hand-labeled training data, which may not be available. In this paper, we propose an unsupervised segmentation method based on our previous connected tube marked point process (MPP) model. The vessel network is extracted by the connected-tube MPP model first. Then a new tube-based segmentation method is applied to the extracted tubes. We test this method on STARE and DRIVE databases and the results show that not only do we extract the retina vessel network accurately, but we also achieve high G-means score for vessel segmentation, without using labeled training data.

Road detection in high-resolution satellite images is an important and popular research topic in the field of image processing. In this paper, we propose a novel road extraction and tracking method based on road segmentation results from a convolutional network, providing improved road detection. The proposed method incorporates our previously proposed connected-tube marked point process (MPP) model and a post-tracking algorithm. We present experimental results on the Massachusetts roads dataset to show the performance of our method on road detection in remotely-sensed images.

In this paper, we address the problem of the joint classification of multiple images acquired on the same scene at different spatial resolutions. From an application viewpoint, this problem is of importance in several contexts, including, most remarkably, satellite and aerial imagery. From a methodological perspective, we use a probabilistic graphical approach and adopt a hierarchical Markov mesh framework that we have recently developed and models the spatial-contextual classification of multiresolution and possibly multisensor images. Here, we focus on the methodological properties of this framework. First, we prove the causality of the model, a highly desirable property with respect to the computational cost of the inference. Then, we prove the expression of the marginal posterior mode criterion for this model and discuss the related assumptions. Experimental results with multi-spectral and panchromatic satellite images are also presented.

In this paper, the problem of the classification of multiresolution and multisensor remotely sensed data is addressed by proposing a multiscale Markov mesh model. Multiresolution and multisensor fusion are jointly achieved through an explicitly hierarchical probabilistic graphical classifier, which uses a quadtree structure to model the interactions across different spatial resolutions, and a symmetric Markov mesh random field to deal with contextual information at each scale and favor applicability to very high resolution imagery. Differently from previous hierarchical Markovian approaches, here, data collected by distinct sensors are fused through either the graph topology itself (across its layers) or decision tree ensemble methods (within each layer). The proposed model allows taking benefit of strong analytical properties, most remarkably causality, which make it possible to apply time-efficient non-iterative inference algorithms.

In this paper, we propose a connected-tube model based on a Marked Point Process (MPP) for strip feature extraction in images. This model incorporates a connection prior that favors certain connections between tubes based on their mutual positional relationship. Moreover, this model can easily be combined with other geometric models to form a mixed MPP model for more complex detection tasks. The proposed tube model is applied to fiber detection in microscopy images by combining connected-tube and ellipse models. The ellipse model is used for detecting short fibers, while the longer fibers are detected by tube model. We also test the model on road and building detection in remotely sensed images.

This letter proposes two methods for the supervised classification of multisensor optical and synthetic aperture radar images with possibly different spatial resolutions. Both the methods are formulated within a unique framework based on hierarchical Markov random fields. Distinct quad-trees associated with the individual information sources are defined to jointly address multisensor, multiresolution, and possibly multifrequency fusion, and are integrated with finite mixture models and the marginal posterior mode criterion. Experimental validation is conducted with Pléiades, COSMO-SkyMed, RADARSAT-2, and GeoEye-1 data.

This paper proposes a framework for tracking multiple fluorescent objects in 2D + time video-microscopy. We present a novel batch-processing track-before-detect multiple object tracking approach based on a spatio-temporal marked point process model of ellipses. Our approach takes into account events such as births, deaths, splits and merges of objects which are motivated by the biological and physical considerations. We show the performance of the proposed model on synthetic biological data and a real total internal reflection fluorescence microscopy (TIRF) image sequence.

In this paper, we propose a novel hierarchical method for remote sensing image classification. The proposed approach integrates an explicit hierarchical graph-based classifier, which uses a quad-tree structure to model multiscale interactions, and a third order Markov mesh random field to deal with pixel wise contextual information in the same scale. The choice of a quad-tree and the third order Markov mesh allow taking benefit from their good analytical properties (especially causality) and consequently apply non-iterative algorithms. Indeed, the Markov mesh is used to incorporate spatial information in each scale of the quad-tree while keeping the causality of the hierarchical model.

In this paper, we propose a novel method for the joint classification of both multidate and multiresolution remote sensing imagery, which represents an important and relatively unexplored classification problem. The proposed classifier is based on an explicit hierarchical graph-based model that is sufficiently flexible to address a coregistered time series of images collected at different spatial resolutions. Within this framework, a novel element of the proposed approach is the use of multiple quadtrees in cascade, each associated with the images available at each observation date in the considered time series. For each date, the input images are inserted in a hierarchical structure on the basis of their resolutions, whereas missing levels are filled in with wavelet transforms of the images embedded in finer-resolution levels. This approach is aimed at both exploiting multiscale information, which is known to play a crucial role in high-resolution image analysis, and supporting input images acquired at different resolutions in the input time series. The experimental results are shown for multitemporal and multiresolution optical data.

The accurate statistical modeling of synthetic aperture radar (SAR) images is a crucial problem in the context of effective SAR image processing, interpretation, and application. In this paper, a semi-parametric approach is designed within the framework of finite mixture models based on the generalized Gamma distribution in view of its flexibility and compact form. Specifically, we develop a generalized Gamma mixture model to implement an effective statistical analysis of high-resolution SAR images and prove the identifiability of such mixtures. A low-complexity unsupervised estimation method is derived by combining the proposed histogram-based expectation-conditional maximization algorithm and the Figueiredo-Jain algorithm. This results in a numerical maximum-likelihood (ML) estimator that can simultaneously determine the ML estimates of component parameters and the optimal number of mixture components. Finally, the state-of-the-art performance of this proposed method is verified by experiments with a wide range of high-resolution SAR images.

In this paper, we address the problem of unsupervised change detection on two or more coregistered images of the same object or scene at several time instants. We propose a novel empirical-Bayesian approach that is based on a false discovery rate formulation for statistical inference on local patch-based samples. This alternative error metric allows to efficiently adjust the family-wise error rate in case of the considered large-scale testing problem. The designed change detector operates in an unsupervised manner under the assumption of the limited amount of changes in the analyzed imagery. The detection is based on the use of various statistical features, which enable the detector to address application-specific detection problems provided an appropriate ad hoc feature choice. In particular, we demonstrate the use of the rank-based statistics: Wilcoxon and Cramér-von Mises for image pairs, and multisample Levene statistic for short image sequences. The experiments with remotely sensed radar, dermatological, and still camera surveillance imagery demonstrate accurate performance and flexibility of the proposed method.

This paper presents image-based quantitative evaluation of subtle variations in facial wrinkles for the same subject in response to a dermatological treatment. This is a novel application because the time series images of the same subject over a shorter time period of weeks are analyzed as compared to more prevalent inter-person analysis of facial skin/marks. We propose image features based on Gabor filter bank for an accurate quantitative evaluation of variations in facial wrinkles. Since variations in Gabor features are very small on a time period of weeks, we propose a framework to compare image features in key wrinkle sites only while excluding the noise introduced by non-wrinkle sites. The framework consists of finer registration of images using Large Deformation Diffeomorphic Metric Mapping (LDDMM) and detection of wrinkle sites using Gabor filter bank and morphological image processing. Preliminary experiments show that the framework is useful in calculating variations in Gabor features at detected sites and indicating trends in the response of facial wrinkles to the dermatological treatment.

In this work, we propose a stochastic model for curvilinear structure reconstruction using morphological profiles of path opening operator. We apply the support vector machine classifier to obtain initial probabilities to belong to line network for each pixel. Then, we formulate a stochastic optimization problem that detects line segments corresponding to the latent curvilinear structure in a scene. Experimental results on DNA filament and remote sensing images validate the effectiveness of the proposed algorithm when compared to other recent methods.

This paper addresses the problem of multisensor fusion of COSMO-SkyMed and RADARSAT-2 data together with optical imagery for classification purposes. The proposed method is based on an explicit hierarchical graph-based model that is sufficiently flexible to deal with multisource coregistered images collected at different spatial resolutions by different sensors. An especially novel element of the proposed approach is the use of multiple quad-trees in cascade, each associated with a set of images acquired by different SAR sensors, with the aim to characterize the correlations associated with distinct images from different instruments. Experimental results are shown with COSMO-SkyMed, RADARSAT-2, and Pléiades data1.

In this paper, we present a novel approach based on spatio-temporal marked point processes to detect and track moving objects in a batch of high resolution images. Batch processing techniques are applicable to and desirable for a large class of applications such as offline scene and video analysis, and provide better overall detection and data association accuracy than sequential methods. We develop a new, intuitive energy based model consisting of several terms that take into account both the image evidence and physical constraints such as target dynamics, track persistence and mutual exclusion. We construct a suitable optimization scheme that allows us to find strong local minima of the proposed highly non-convex energy. We test our model on three batches of 25 synthetic biological images with different levels of noise. Our main application however consists of two batches of 14 remotely sensed high resolution optical images of boats which are particularly hard to analyze due to the different angles at which the images were taken and the low temporal frequency.

In this paper, we propose a novel method for the joint classification of multidate, multiresolution and multisensor remote sensing imagery, which represents a vital and fairly unexplored classification problem. The proposed classifier is based on an explicit hierarchical graph-based model sufficiently flexible to deal with multisource coregistered time series of images collected at different spatial resolutions [1]. An especially novel element of the proposed approach is the use of multiple quadtrees in cascade, each associated with each new available image at different dates, with the aim to characterize the temporal correlations associated with distinct images in the input time series. Experimental results are shown with multitemporal and multiresolution Pléiades data.

We propose a new model for wrinkle detection in human faces using a marked point process. In order to detect an arbitrary shape of wrinkles, we represent them as a set of line segments, where each segment is characterized by its length and orientation. We propose a probability density of wrinkle model which exploits local edge profile and geometric properties of wrinkles. To optimize the probability density of wrinkle model, we employ reversible jump Markov chain Monte Carlo sampler with delayed rejection. Experimental results demonstrate that the new algorithm detects facial wrinkles more accurately than a recent state-of-the-art method.

In this paper, we propose a Multilayer Markovian model for change detection in registered aerial image pairs with large time differences. A Three Layer Markov Random Field takes into account information from two different sets of features namely the Modified HOG (Histogram of Oriented Gradients) difference and the Gray-Level (GL) Difference. The third layer is the resultant combination of the two layers. Thus we integrate both the texture level as well as the pixel level information to generate the final result. The proposed model uses pair wise interaction retaining the sub-modularity condition for energy. Hence a global energy optimization can be achieved using a standard min-cut/ max flow algorithm ensuring homogeneity in the connected regions.

Marked point processes have proven their efficiency in solving object extraction problems from high resolution optical images. However, these complex mathematical models are difficult to simulate which usually results in high computation times. A new parallel sampler has been recently developed. Nevertheless, this sampler does not yield good results in the presence of large objects. We propose modifications to the original parallel sampler to cope with such situations. Furthermore, we implement an additional mask to increase the speedup in the case of boat extraction.

In this paper, we propose a novel method to fuse multidate, multiresolution, and multiband remote sensing imagery for multitemporal classification purposes. The proposed method is based on an explicit hierarchical graph-based model that is sufficiently flexible to deal with multisource coregistered time series of images collected at different spatial resolutions. An especially novel element of the proposed approach is the use of multiple quad-trees in cascade, each associated with an image acquired at a different date, with the aim to characterize the temporal correlations associated with distinct images in an input time series. Experimental results are shown with multitemporal and multiresolution Pléiades data1.

In this paper, we develop a novel classification approach for multiresolution, multisensor [optical and synthetic aperture radar (SAR)], and/or multiband images. This challenging image processing problem is of great importance for various remote sensing monitoring applications and has been scarcely addressed so far. To deal with this classification problem, we propose a two-step explicit statistical model. We first design a model for the multivariate joint class-conditional statistics of the coregistered input images at each resolution by resorting to multivariate copulas. Such copulas combine the class-conditional marginal probability density functions (pdfs) of each input channel that are estimated by finite mixtures of well-chosen parametric families. We consider different distribution families for the most common types of remote sensing imagery acquired by optical and SAR sensors. We then plug the estimated joint pdfs into a hierarchical Markovian model based on a quad-tree structure, where each tree-scale corresponds to the different input image resolutions and to corresponding multiscale decimated wavelet transforms, thus preventing a strong resampling of the initial images. To obtain the classification map, we resort to an exact estimator of the marginal posterior mode. We integrate a prior update in this model in order to improve the robustness of the developed classifier against noise and speckle. The resulting classification performance is illustrated on several remote sensing multiresolution data sets, including very high resolution and multisensor images acquired by COSMO-SkyMed and GeoEye-1.

Marked point process models have been successfully used in image analysis for feature extraction purposes in high resolution remotely sensed images. The model is usually based on two types of energy terms: a data term, which reflects the configuration's fidelity with respect to the input image, and a prior term, which reflects some knowledge about the objects to be extracted. In this paper, we deal with the problem of elliptical shape extraction. We propose new energy terms for the extraction of boats in harbors, which is a particularly difficult problem and we show results on high resolution optical images.

In this paper we address the problem of unsupervised change detection on image pairs. We develop a novel patch-based hypothesis testing approach that employs the false discovery rate technique for statistical hypothesis testing. The designed approach can be adopted to specific detection applications via selection of appropriate statistical features. Experiments with still camera imagery demonstrate high performance and flexibility of the proposed method.

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.

This letter addresses the problem of classifying synthetic aperture radar (SAR) images of urban areas by using a supervised Bayesian classification method via a contextual hierarchical approach. We develop a bivariate copula-based statistical model that combines amplitude SAR data and textural information, which is then plugged into a hierarchical Markov random field model. The contribution of this letter is thus the development of a novel hierarchical classification approach that uses a quad-tree model based on wavelet decomposition and an innovative statistical model. The performance of the developed approach is illustrated on a high-resolution satellite SAR image of urban areas.

In this paper, we combine amplitude and texture statistics of the synthetic aperture radar images for the purpose of model-based classification. In a finite mixture model, we bring together the Nakagami densities to model the class amplitudes and a 2-D auto-regressive texture model with t-distributed regression error to model the textures of the classes. A non-stationary multinomial logistic latent class label model is used as a mixture density to obtain spatially smooth class segments. The classification expectation-maximization algorithm is performed to estimate the class parameters and to classify the pixels. We resort to integrated classification likelihood criterion to determine the number of classes in the model. We present our results on the classification of the land covers obtained in both supervised and unsupervised cases processing TerraSAR-X, as well as COSMO-SkyMed data.

Parameter estimation of probability density functions is one of the major steps in the area of statistical image and signal processing. In this paper we explore several properties and limitations of the recently proposed method of logarithmic cumulants (MoLC) parameter estimation approach which is an alternative to the classical maximum likelihood (ML) and method of moments (MoM) approaches. We derive the general sufficient condition for a strong consistency of the MoLC estimates which represents an important asymptotic property of any statistical estimator. This result enables the demonstration of the strong consistency of MoLC estimates for a selection of widely used distribution families originating from (but not restricted to) synthetic aperture radar image processing. We then derive the analytical conditions of applicability of MoLC to samples for the distribution families in our selection. Finally, we conduct various synthetic and real data experiments to assess the comparative properties, applicability and small sample performance of MoLC notably for the generalized gamma and K families of distributions. Supervised image classification experiments are considered for medical ultrasound and remote-sensing SAR imagery. The obtained results suggest that MoLC is a feasible and computationally fast yet not universally applicable alternative to MoM. MoLC becomes especially useful when the direct ML approach turns out to be unfeasible.

This paper considers change detection with multitemporal synthetic aperture radar (SAR) images. A novel statistical approach is developed that formulates the detection of changes between two coregistered SAR images acquired at different dates as a non-parametric local-window hypothesis testing problem. This approach takes into account the simultaneous testing of a large amount of similar hypotheses (i.e., one Wilcoxon test at each pixel of the image), and is based on a likelihood ratio test to obtain a detection map at the pixel level. Some encouraging detection results are obtained on XSAR and very high resolution COSMO-SkyMed images.

We compare the performance of the texture and the amplitude based mixture density models for urban area extraction from high resolution Synthetic Aperture Radar (SAR) images. We use an Auto-Regressive (AR) model with t-distribution error for the textures and a Nakagami density for the amplitudes. We exploit a Multinomial Logistic (MnL) latent class label model as a mixture density to obtain spatially smooth class segments. We combine the Classification EM (CEM) algorithm with the hierarchical agglomeration strategy and a model order selection criterion called Integrated Completed Likelihood (ICL).We test our algorithm on TerraSAR-X data provided by DLR/DFD.

In the framework of the monitoring of structures and infrastructures from environmental disasters, the COSMO-SkyMed constellation has a huge potential, thanks to up to metric spatial resolution, short revisit time, and the day/night all-weather acquisition capability ensured by SAR. This paper focuses on the scientific results of the project “Development and validation of multitemporal image analysis methodologies for multirisk monitoring of critical structures and infrastructures,” funded by the Italian Space Agency. Several change-detection, data-fusion, and feature-extraction techniques, which were developed and experimentally validated in the project for COSMO-SkyMed imagery and for their integration with other data sources (including very high resolution optical data), are described and examples of processing results are discussed.

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.

We combine both amplitude and texture statistics of the Synthetic Aperture Radar (SAR) images using Products of Experts (PoE) approach for classification purpose. We use Nak-agami density to model the class amplitudes. To model the textures of the classes, we exploit a non-Gaussian Markov Random Field (MRF) texture model with t-distributed regression error. Non-stationary Multinomial Logistic (MnL) latent class label model is used as a mixture density to obtain spatially smooth class segments. We perform the Classification Expectation-Maximization (CEM) algorithm to estimate the class parameters and classify the pixels. We obtained some classification results of water, land and urban areas in both supervised and semi-supervised cases on TerraSAR-X data.

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.

We present an automatic approach for modeling buildings from aerial LiDAR data. The method produces accurate, watertight and compact meshes under planar constraints which are especially designed for urban scenes. The LiDAR point cloud is classified through a non-convex energy minimization problem in order to separate the points labeled as building. Roof structures are then extracted from this point subset, and used to control the meshing procedure. Experiments highlight the potential of our method in term of minimal rendering, accuracy and compactness.

In this letter, we address the problem of estimating the amplitude probability density function (pdf) of single-channel synthetic aperture radar (SAR) images. A novel flexible method is developed to solve this problem, extending the recently proposed dictionary-based stochastic expectation maximization approach (developed for a medium-resolution SAR) to very high-resolution (VHR) satellite imagery, and enhanced by introduction of a novel procedure for estimating the number of mixture components, that permits to reduce appreciably its computational complexity. The specific interest is the estimation of heterogeneous statistics, and the developed method is validated in the case of the VHR SAR imagery, acquired by the last-generation satellite SAR systems, TerraSAR-X and COSMO-SkyMed. This VHR imagery allows the appreciation of various ground materials resulting in highly mixed distributions, thus posing a difficult estimation problem that has not been addressed so far. We also conduct an experimental study of the extended dictionary of state-of-the-art SAR-specific pdf models and consider the dictionary refinements.

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.

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.

In this paper we propose a method for classifying the vegetation types in an aerial color infra-red (CIR) image. Different vegetation types do not only differ in color, but also in texture. We study the use of four Haralick features (energy, contrast, entropy, homogeneity) for texture analysis, and then perform the classification using the one-against-all (OAA) multi-class support vector machine (SVM), which is a popular supervised learning technique for classification. The choice of features (along with their corresponding parameters), the choice of the training set, and the choice of the SVM kernel highly affect the performance of the classification. The study was done on several CIR aerial images provided by the French National Forest Inventory (IFN). In this paper, we will show one example on a national forest near Sedan (in France), and compare our result with the IFN map.

Many problems in remote sensing can be modeled as the minimization of the sum of a data term and a prior term. We propose to use a new complex wavelet based prior and an efficient scheme to solve these problems. We show some results on a problem of image reconstruction with noise, irregular sampling and blur. We also show a comparison between two widely used priors in image processing: sparsity and regularity priors.

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.

We propose a new Bayesian method for detecting the regions of object displacements in aerial image pairs. We use a robust but coarse 2-D image registration algorithm. Our main challenge is to eliminate the registration errors from the extracted change map. We introduce a three-layer Markov random field (L(3)MRF) model which integrates information from two different features, and ensures connected homogenous regions in the segmented images. Validation is given on real aerial photos.

In this paper, we present a novel multiscale texture model and a related algorithm for the unsupervised segmentation of color images. Elementary textures are characterized by their spatial interactions with neighboring regions along selected directions. Such interactions are modeled, in turn, by means of a set of Markov chains, one for each direction, whose parameters are collected in a feature vector that synthetically describes the texture. Based on the feature vectors, the texture are then recursively merged, giving rise to larger and more complex textures, which appear at different scales of observation: accordingly, the model is named Hierarchical Multiple Markov Chain (H-MMC). The Texture Fragmentation and Reconstruction (TFR) algorithm, addresses the unsupervised segmentation problem based on the H-MMC model. The "fragmentation" step allows one to find the elementary textures of the model, while the "reconstruction" step defines the hierarchical image segmentation based on a probabilistic measure (texture score) which takes into account both region scale and inter-region interactions. The performance of the proposed method was assessed through the Prague segmentation benchmark, based on mosaics of real natural textures, and also tested on real-world natural and remote sensing images.

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.

We propose a new method to solve a problem of image restoration with many different aspects: reconstruction from irregular samples, deconvolution and denoising. The model we propose is robust to different kind of noises, in particular, impulse and Gaussian noise. We compare our results to the ones obtained in [1] and show that our problem presents some advantages particularly in satellite imaging. At last, we conclude on a discussion about resolution schemes for variational problems' minimization and propose some faster resolution shemes for our problem and the one in [1].

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.

The segmentation of networks is important in several imaging domains, and models incorporating prior shape knowledge are often essential for the automatic performance of this task. Higher-order active contours provide a way to include such knowledge, but their behaviour can vary significantly with parameter values: e.g. the same energy can model networks or a dasiagas of circlespsila. In this paper, we present a stability analysis of a HOAC energy leading to the phase diagram of a long bar. The results, which are confirmed by numerical experiments, enable the selection of parameter values for the modelling of network shapes using the energy. We apply the resulting model to the problem of hydrographic network extraction from VHR satellite images.

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 address the problem of updating road maps in dense urban areas by extracting the main road network from a very high resolution (VHR) satellite image. Our model of the region occupied by the road network in the image is innovative. It incorporates three different types of prior geometric knowledge: generic boundary smoothness constraints, equivalent to a standard active contour prior; knowledge of the geometric properties of road networks (i.e. that they occupy regions composed of long, low-curvature segments joined at junctions), equivalent to a higher-order active contour prior; and knowledge of the road network at an earlier date derived from GIS data, similar to other ‘shape priors’ in the literature. In addition, we represent the road network region as a ‘phase field’, which offers a number of important advantages over other region modelling frameworks. All three types of prior knowledge prove important for overcoming the complexity of geometric ‘noise’ in VHR images. Promising results and a comparison with several other techniques demonstrate the effectiveness of our approach.

A novel model for unsupervised segmentation of texture images is presented. The image to be segmented is first discretized and then a hierarchical finite-state region-based model is automatically coupled with the data by means of a sequential optimization scheme, namely the texture fragmentation and reconstruction (TFR) algorithm. Both intra- and inter-texture interactions are modeled, by means of an underlying hierarchical finite-state model, and eventually the segmentation task is addressed in a completely unsupervised manner. The output is then a nested segmentation, so that the user may decide the scale at which the segmentation has to be provided. TFR is composed of two steps: the former focuses on the estimation of the states at the finest level of the hierarchy, and is associated with an image fragmentation, or over-segmentation; the latter deals with the reconstruction of the hierarchy representing the textural interaction at different scales.

In this paper, we give a probabilistic model for automatic change detection on airborne images taken with moving cameras. To ensure robustness, we adopt an unsupervised coarse matching instead of a precise image registration. The challenge of the proposed model is to eliminate the registration errors, noise and the parallax artifacts caused by the static objects having considerable height (buildings, trees, walls etc.) from the difference image. We describe the background membership of a given image point through two different features, and introduce a novel three-layer Markov random field (MRF) model to ensure connected homogenous regions in the segmented image.

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).

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.

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.

Synthetic aperture radar (SAR) images are inherently affected by a signal dependent noise known as speckle, which is due to the radar wave coherence. In this paper, we propose a novel adaptive despeckling filter and derive a maximum a posteriori (MAP) estimator for the radar cross section (RCS). We first employ a logarithmic transformation to change the multiplicative speckle into additive noise. We model the RCS using the recently introduced heavy-tailed Rayleigh density function, which was derived based on the assumption that the real and imaginary parts of the received complex signal are best described using the alpha-stable family of distribution. We estimate model parameters from noisy observations by means of second-kind statistics theory, which relies on the Mellin transform. Finally, we compare the proposed algorithm with several classical speckle filters applied on actual SAR images. Experimental results show that the homomorphic MAP filter based on the heavy-tailed Rayleigh prior for the RCS is among the best for speckle removal.

In 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.

Confocal laser scanning microscopy is a powerful and increasingly popular technique for 3D imaging of biological specimens. However, the acquired images are degraded by blur from out-of-focus light and Poisson noise due to photon-limited detection. Several deconvolution and/or denoising methods have been proposed to reduce these degradations. Here, we propose a wavelet denoising method, which turns out to be very effective for 3D confocal images. To obtain a translation and rotation invariant algorithm, we have developed the 3D complex wavelet transform introduced by N. Kingsbury. These wavelets allow, moreover, a better directional selectivity of the wavelet coefficients. We show on simulated and real biological data the good performance of this algorithm.

The representation and modelling of regions is an important topic in computer vision. In this paper, we represent a region via a level set of a 'phase field' function. The function is not constrained, e.g. to be a distance function; nevertheless, phase field energies equivalent to classical active contour energies can be defined. They represent an advantageous alternative to other methods: a linear representation space; ease of implementation (a PDE with no reinitialization); neutral initialization; greater topological freedom. We extend the basic phase field model with terms that reproduce 'higher-order active contour' energies, a powerful way of including prior geometric knowledge in the active contour framework via nonlocal interactions between contour points, in addition to the above advantages, the phase field greatly simplifies the analysis and implementation of the higher-order terms. We define a phase field model that favours regions composed of thin arms meeting at junctions, combine this with image terms, and apply the model to the extraction of line networks from remote sensing images

Classification results obtained using wavelet-based texture analysis techniques vary with the choice of mother wavelet used in the methodology. We discuss the use of mother wavelet filters as parameters in a probabilistic approach to texture analysis based on adaptive biorthogonal wavelet packet bases. The optimal choice for the mother wavelet filters is estimated from the data, in addition to the other model parameters. The model is applied to the classification of single texture images and mosaics of Brodatz textures, the results showing improvement over the performance of standard wavelets for a given filter length.

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.

Using the framework of higher-order active contours, we present a new quadratic continuation energy for the extraction of line networks (e.g. road, hydrographic, vascular) in the presence of occlusions. Occlusions create gaps in the data that frequently translate to gaps in the extracted network. The new energy penalizes nearby opposing extremities of the network, and thus favours the closure of the gaps created by occlusions. Nearby opposing extremities are identified using a sophisticated interaction between pairs of points on the contour. This new model allows the extraction of fully connected networks, even though occlusions violate common assumptions about the homogeneity of the interior, and high contrast with the exterior, of the network. We present experimental results on real aerial images that demonstrate the effectiveness of the new model for network extraction tasks.

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.

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.

Although subband histograms of the wavelet coefficients of natural images possess a characteristic leptokurtotic form, this is no longer true for wavelet packet bases adapted to a given texture. Instead, three types of subband statistics are observed: Gaussian, leptokurtotic, and interestingly, in some subbands, multimodal histograms. These subbands are closely linked to the structure of the texture, and guarantee that the most probable image is not flat. Motivated by these observations, we propose a probabilistic model that takes them into account. Adaptive wavelet packet subbands are modelled as Gaussian, generalized Gaussian, or a constrained Gaussian mixture. We use a Bayesian methodology, finding MAP estimates for the adaptive basis, for subband model selection, and for subband model parameters. Results confirm the effectiveness of the proposed approach, and highlight the importance of multimodal subbands for texture discrimination and modelling.

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.

We discuss the use of adaptive biorthogonal wavelet packet bases in a probabilistic approach to texture analysis, thus combining the advantages of biorthogonal wavelets (FIR, linear phase) with those of a coherent texture model. The computation of the probability uses both the primal and dual coefficients of the adapted biorthogonal wavelet packet basis. The computation of the biorthogonal wavelet packet coefficients is done using a lifting scheme, which is very efficient. The model is applied to the classification of mosaics of Brodatz textures, the results showing improvement over the performance of the corresponding orthogonal wavelets.

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 parametric 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, that have been proved to be effective for different land-cover typologies, thus making the choice of a single optimal SAR parametric PDF a hard task. In this paper, an innovative estimation algorithm is described, that faces such a problem by adopting a finite mixture model (FMM) for the amplitude PDF, with mixture components belonging to a given dictionary of SAR-specific PDFs. The 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 (SEM) iterative methodology with the recently developed "method-of-log-cumulants" (MoLC) for parametric PDF estimation. Experimental results on several real SAR images are reported, showing that the proposed method accurately models the statistics of SAR amplitude data.

ENERGY minimization techniques are central to many methods in computer vision and pattern recognition. Stated simply, if a task can be posed as the minimization of an energy measure, which may, for instance, be the negative logarithm of a probability or an entropy, then a variety of optimization methods may be applied to locate the solution. The solution may be a vector of parameters representing the shapes of a curve, a surface, or a volume, it may be a set of symbolic labels representing the semantic or syntactic content of a signal, or it may be a graph representing arrangement or structure. The optimization methods that can be applied to the cost function to recover the solution include gradient descent, simulated annealing, mean-field annealing, evolutionary search, and tabu search, to mention just a few. Many of the classical methods in the fields of computer vision and pattern recognitionmake use of energyminimization techniques. Familiar examples include relaxation labeling, regularization, active contours, and Markov models. More recent examples include the use of graph-cuts, spectral graph theory, and semidefinite programming. Energy minimization techniques have also been pivotal in the development of algorithms for learning, inference, and classification. One of the characteristics of this field is that it draws strongly on recent developments in other disciplines such as mathematics, statistics, operations research, biology, and economics. Moreover, the basic methodology is being developed at a great rate in these related disciplines. In this respect, energy minimization is different from other widely used techniques such as geometry or probability, where the basic methods have been available in the mathematics literature for well over 100 years. It is probably fair to say that the problems of optimization and, in particular, combinatorial optimization, are ones of a computational nature and have hence only emerged over the past few decades. Our own involvement in this field has been, in part, through a biennial series of workshops (EMMVCPR) that commenced in 1997 and which have been aimed at providing a focus for research in this area. From the interest shown in these workshops and the number of papers on the topic appearing in the main conferences (CVPR, ECCV, ICCV), it seemed to us that a special edition of IEEE Transactions on Pattern Analysis and Machine Intelligence would be both timely and valuable to the community. The call for papers was issued in mid-2001 and we received 50 papers by the deadline on 1 May 2002. Each paper was reviewed by at least three reviewers according to the standard TPAMI reviewing procedure. This meant that we needed the assistance of some 150 reviewers. By late October 2002, we had first reviews for all of the papers and met in Venice to make initial decisions. Based on the reviews, and giving authors the chance to revise their papers in the light of reviewers comments, we selected the six papers that appear in the current special section, together with three papers that will appear in a subsequent special section. The papers span a diverse set of methods and applications. The techniques covered include semidefinite programming, Markov models, and simulated annealing, while the problems addressed include deformable models, shape-from-shading, and clustering. The first regular paper in this special section is “Binary Partitioning, Perceptual Grouping, and Restoration with Semidefinite Programming” by J. Keuchel, C. Schnorr, C. Schellewald, and D. Cremers. The authors describe a new optimization method based on semidefinite programming relaxations. The method is applied to the computer vision problems of unsupervised partitioning, figure-ground discrimination, and binary restoration. The interesting feature of the proposed method is that it does not require any parameter tuning. Moreover, apart from the symmetry condition, no assumptions aremade concerning the objective criterion. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 25, NO. 11, NOVEMBER 2003 1361

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.

The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem, which can be regularized within a Bayesian context by using an a priori model of the reconstructed solution. Since real satellite data show spatially variant characteristics, we propose here to use an inhomogeneous model. We use the maximum likelihood estimator (MLE) to estimate its parameters and we show that the MLE computed on the corrupted image is not suitable for image deconvolution because it is not robust to noise. We then show that the estimation is correct only if it is made from the original image. Since this image is unknown, we need to compute an approximation of sufficiently good quality to provide useful estimation results. Such an approximation is provided by a wavelet-based deconvolution algorithm. Thus, a hybrid method is first used to estimate the space-variant parameters from this image and then to compute the regularized solution. The obtained results on high resolution satellite images simultaneously exhibit sharp edges, correctly restored textures, and a high SNR in homogeneous areas, since the proposed technique adapts to the local characteristics of the data.

Synthetic aperture radar (SAR) imagery has found important applications due to its clear advantages over optical satellite imagery one of them being able to operate in various weather conditions. However, due to the physics of the radar imaging process, SAR images contain unwanted artifacts in the form of a granular look which is called speckle. The assumptions of the classical SAR image generation model lead to a Rayleigh distribution model for the histogram of the SAR image. However, some experimental data such as images of urban areas show impulsive characteristics that correspond to underlying heavy-tailed distributions, which are clearly non-Rayleigh. Some alternative distributions have been suggested such as the Weibull, log-normal, and the k-distribution which had success in varying degrees depending on the application. Recently, an alternative model namely the alpha-stable distribution has been suggested for modeling radar clutter. In this paper, we show that the amplitude distribution of the complex wave, the real and the imaginery components of which are assumed to be distributed by the alpha-stable distribution, is a generalization of the Rayleigh distribution. We demonstrate that the amplitude distribution is a mixture of Rayleighs as is the k-distribution in accordance with earlier work on modeling SAR images which showed that almost all successful SAR image models could be expressed as mixtures of Rayleighs. We also present parameter estimation techniques based on negative order moments for the new model. Finally, we test the performance of the model on urban images and compare with other models such as Rayleigh, Weibull, and the k-distribution.

Remote sensing imagery plays an important role in many fields. It has become an invaluable tool for diverse applications ranging from cartography to ecosystem management. In many of the images processed in these types of applications, semantic entities in the scene are correlated with textures in the image. In this paper, we propose a new method of analysing such textures based on adaptive probabilistic models of wavelet packets. Our approach adapts to the principal periodicities present in the textures, and can capture long-range correlations while preserving the independence of the wavelet packet coefficients. This technique has been applied to several remote sensing images, the results of which are presented. 1

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).

Two main issues arise when working in the area of texture segmentation: the need to describe the texture accurately by capturing its underlying structure, and the need to perform analyses on the boundaries of textures. Herein, we tackle these problems within a consistent probabilistic framework. Starting from a probability distribution on the space of infinite images, we generate a distribution on arbitrary finite regions by marginalization. For a Gaussian distribution, the computational requirement of diagonalization and the modelling requirement of adaptivity together lead naturally to adaptive wavelet packet models that capture the 'significant amplitude features' in the Fourier domain. Undecimated versions of the wavelet packet transform are used to diagonalize the Gaussian distribution efficiently, albeit approximately. We describe the implementation and application of this approach and present results obtained on several Brodatz texture mosaics.

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).

In this paper we propose a new algorithm to estimate the parameters of the noise related to the sensor and the impulse response of the optical system, from a blurred and noisy satellite or aerial image. The noise is supposed to be white, Gaussian and stationary. The blurring kernel has a parametric form and is modeled in such a way as to take into account the physics of the system (the atmosphere, the optics and the sensor). The observed scene is described by a fractal model, taking into account the scale invariance properties of natural images. The estimation is performed automatically by maximizing a marginalized likelihood, which is achieved by a deterministic algorithm whose complexity is limited to O (N), where N is the number of pixels.

In this paper we present a new deconvolution method, able to deal with noninvertible blurring functions. To avoid noise amplification, a prior model of the image to be reconstructed is used within a Bayesian framework. We use a spatially adaptive prior defined with a complex wavelet transform in order to preserve shift invariance and to better restore variously oriented features. The unknown image is estimated by an EM technique, whose E step is a Landweber update iteration, and the M step consists of denoising the image, which is achieved by wavelet coefficient thresholding. The new algorithm has been applied to high resolution satellite and aerial data, showing better performance than existing techniques when the blurring process is not invertible, like motion blur for instance.

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.

In this paper, we have derived analytic expressions for the phase correlation of downsampled images. We have shown that for downsampled images the signal power in the phase correlation is not concentrated in a single peak, but rather in several coherent peaks mostly adjacent to each other. These coherent peaks correspond to the polyphase transform of a filtered unit impulse centered at the point of registration. The analytic results provide a closed-form solution to subpixel translation estimation, and are used for detailed error analysis. Excellent results have been obtained for subpixel translation estimation of images of different nature and across different spectral bands.

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.

In this paper, we propose to use a hidden Markov tree modeling of the complex wavelet packet transform, to capture the inter-scale dependencies of natural images. First, the observed image, blurred and noisy, is deconvolved without regularization. Then its transform is denoised within a Bayesian framework using the proposed model, whose parameters are estimated by an EM technique. The total complexity of this new deblurring algorithm remains O(N).

The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem. Donoho (1994) has proposed to deconvolve the image without regularization and to denoise the result in a wavelet basis by thresholding the transformed coefficients. We have developed a new filtering method, consisting of using a complex wavelet packet basis. Herein, the thresholding functions associated to the proposed method are automatically estimated. The estimation is performed within a Bayesian framework, by modeling the subbands using generalized Gaussian distributions, and by applying the maximum a posteriori (MAP) estimator on each coefficient. Compared to real wavelet-packet-based algorithms, the proposed method is shift invariant, provides good directionality properties and remains of complexity O(N).

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.

The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem, which can be regularized within a Bayesian context by using an a priori model of the reconstructed solution. Since real satellite data show spatially variant characteristics, we propose to use an inhomogeneous model. We use the maximum likelihood estimator (MLE) to estimate its parameters. We demonstrate that the MLE computed on the corrupted image is not suitable for image deconvolution, because it is not robust to noise. Then we show that the estimation is correct only if it is made from the original image. As this image is unknown, we need to compute an approximation of sufficiently good quality to provide useful estimation results. Such an approximation is provided by a wavelet-based deconvolution algorithm. Thus, an hybrid method is first used to estimate the space-variant parameters from this image and second to compute the regularized solution. The obtained results on high resolution satellite images simultaneously exhibit sharp edges, correctly restored textures and a high SNR in homogeneous areas, since the proposed technique adapts to the local characteristics of the data.

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 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. 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.

Herein, we present a variational model devoted to image classification coupled with an edge-preserving regularization process. 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 compound of homogeneous regions with regularized boundaries. The soundness of this 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.

Shape information is useful for road detection to improve the correctness and smoothness of the results. Within the frame of dynamic programming, the proposed method stores in an auxiliary image the global direction V(M) followed in the current shortest path. The potential is a function of this image, so that pixels prolongating the current shortest path are favored. The auxiliary image is updated recursively at the same time as the energy, during the optimization. A variant of this method stores in the auxiliary image the center of the circle tangent to the current shortest path. Another application presented herein computes the average of the potential instead of its sum. The optimality principle is not verified anymore with the auxiliary functions but they give smoother results without increasing the complexity. Furthermore, several improvements w.r.t. the scanning allow gains of up to 50% for the computational time.

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).

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 introduce a method of isolating and extracting a certain class of local singular behaviours of signals/images which in turn leads to a method of pointwise noise estimation and suppression. The underlying motivation is to decompose functions directly in terms of components which would naturally represent different orders of regular or singular behaviours defined by the local Holder exponents. We have shown that such a decomposition can lead to a factorization of the spectrum of the singular portion of the signal in terms of the spectrum of the original signal and that of a denoising filter.

This paper presents a method for indexing and retrieval of multimedia data through texture segmentation, using the Wold decomposition. The texture field is assumed to be a realisation of a regular homogeneous random field. On the basis of a 2-D Wold-like decomposition, the field is represented as the sum of a purely indeterministic component, a harmonic component and a countable number of evanescent fields. A new rigorous distance measure between textures is derived, using Wold parameters. Adopting the MRF framework, we construct a segmentation procedure using the Wold parameters.

This paper focuses on hyperparameter estimation of a variational model for image deconvolution. Using the generalized maximum likelihood (GML) estimator, the estimation problem is reduced to the ML estimation in the case of perfectly observed data. A method based on stochastic gradient is then developed for the estimation of both linear and nonlinear hyperparameters.

This paper presents a method for indexing and retrieval of multimedia data. The proposed indexing and retrieval strategy is based on the usage of textural information contained in the data imagery components as the indexing keys. On the basis of a 2-D Wold-like decomposition, the texture field is represented as the sum of purely indeterministic, harmonic, and evanescent fields. A new rigorous distance measure between textures which employs their estimated parametric models, is developed. This distance measure is then applied to retrieve multimedia records that contain images with textured segments which are similar to those in a given image. Evaluation of this distance measure is computationally efficient, and hence highly suitable for data base retrieval applications.

We investigate the problem of the reconstruction of a continuous-time function f(x)/spl isin//spl Hscr/ from the responses of m linear shift-invariant systems sampled at 1/m the reconstruction rate, extending Papoulis' (1977) generalized sampling theory in two important respects. First, we allow for arbitrary (non-bandlimited) input signals (typ. /spl Hscr/=L/sub 2/). Second, we use a more general specification of the reconstruction subspace V(/spl phi/), so that the output of the system can take the form of a bandlimited function, a spline, or a wavelet expansion. The system that we describe yields an approximation f/spl isin/V(/spl phi/) that is consistent with the input f(x) in the sense that it produces exactly the same measurements. We show that this solution can be computed by multivariate filtering. We also characterize the stability of the system (condition number). Finally, we illustrate the theory by presenting a new example of interlaced sampling using splines.

Multi-channel super-resolution is a means of recovering high frequency information by trading off the temporal bandwidth. Almost all the methods proposed in the literature are based on optimizing a cost function. But since the problem is usually ill-posed, one needs to impose some regularity constraints. However, regularity constraints tend to attenuate the high frequency contents of the data (usually present in the form of discontinuities). This inherent contradiction between regularization and super-resolution has not been addressed in the literature, despite the availability of off the shelf tools. W have investigated this issue in the context of adaptive regularization, using /spl phi/-functions (convex, non-convex, bounded, unbounded).

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.

A method of registering images at subpixel accuracy has been proposed, which does not resort to interpolation. The method is based on the phase correlation method and is remarkably robust to correlated noise and uniform variations of luminance. We have shown that the cross power spectrum of two images, containing subpixel shifts, is a polyphase decomposition of a Dirac delta function. By estimating the sum of polyphase components one can then determine sub-pixel shifts along each axis.

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* 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. The authors present herein a mathematical formalization of the F* algorithm, which allows them 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).

Using a probabilistic interpretation of an n dimensional extension of Papoulis's Generalized Sampling Theorem, an iterative algorithm has been devised for 3D reconstruction of a Lambertian surface at subpixel accuracy. The problem has been formulated as an optimization one in a Bayesian framework. The latter allows for introducing a priori information on the solution, using Markov Random Fields (MRF). The estimated 3D features of the surface are the albedo and the height which are obtained simultaneously using a set of low resolution images. keywords: 3D Super resolution, Generalized Sampling Expansion, Low level image processing, Markov Random Fields (MRF).

This paper deals with the problem of unsupervised Bayesian segmentation of images modeled by Markov random fields (MRF). If the model parameters are known then we have various methods to solve the segmentation problem (simulated annealing, ICM, etc...). However, when they are not known, the problem becomes more difficult. One has to estimate the hidden label field parameters from the available image only. Our approach consists of a recent iterative method of estimation, called iterative conditional estimation (ICE), applied to a monogrid Markovian image segmentation model. The method has been tested on synthetic and real satellite images.

The paper deals with the problem of unsupervised classification of images modeled by Markov random fields (MRF). If the model parameters are known then we have various methods to solve the segmentation problem (simulated annealing, ICM, etc...). However, when they are not known, the problem becomes more difficult. One has to estimate the hidden label field parameters from the only observable image. Our approach consists of extending a recent iterative method of estimation, called iterative conditional estimation (ICE) to a hierarchical Markovian model. The idea resembles the estimation-maximization (EM) algorithm as we recursively look at the maximum a posteriori (MAP) estimate of the label field given the estimated parameters then we look at the maximum likelihood (ML) estimate of the parameters given a tentative labeling obtained at the previous step. We propose unsupervised image classification algorithms using a hierarchical model. The only parameter supposed to be known is the number of regions, all the other parameters are estimated. The presented algorithms have been implemented on a Connection Machine CM200. Comparative tests have been done on noisy synthetic and real images (remote sensing).>

Using a set of low resolution images it is possible to reconstruct high resolution information by merging low resolution data on a finer grid. A 3D super-resolution algorithm is proposed, based on a probabilistic interpretation of the n-dimensional version of Papoulis' (1977) generalized sampling theorem. The algorithm is devised for recovering the albedo and the height map of a Lambertian surface in a Bayesian framework, using Markov random fields for modeling the a priori knowledge.

Deterministic pseudo-annealing (DPA) is a new deterministic optimization method for finding the maximum a posteriori (MAP) labeling in a Markov random field, in which the probability of a tentative labeling is extended to a merit function on continuous labelings. This function is made convex by changing its definition domain. This unambiguous maximization problem is solved, and the solution is followed down to the original domain, yielding a good, if suboptimal, solution to the original labeling assignment problem. The performance of DPA is analyzed on randomly weighted graphs.

Given a set of low resolution camera images, it is possible to reconstruct high resolution luminance and depth information, specially if the relative displacements of the image frames are known. We propose iterative algorithms for recovering hash resolution albedo and depth maps that require no a priori knowledge of the scene, and therefore do not depend on other methods, as regards boundary and initial conditions. The problem of surface reconstruction has been formulated as one of expectation maximization (EM) and has been tackled in a probabilistic framework using Markov random fields (MRF). As for the depth map, our method directly recovers surface heights without refering to surface orientations, while increasing the resolution by camera jittering. Conventional statistical models have been coupled with geometrical techniques to construct a general model of the world and the imaging process.>

Dynamic programming is one of the main methods of line detection. It defines a cost, which depends on local information, and performs a summation-minimization process in a graph or in the image. In particular, Fischler et al. (1981) presented an algorithm called F*, which achieves important results (convergence, robustness, rapidity). In previous works, we proposed a mathematical formalization of the F*, which allowed us to extend the cost to cliques of more than two points to take into account the contrast, and to include curvature information in the cost by using neighborhoods of size larger than one. In the present paper, we propose a method for computing this cost automatically for a wide range of images, from the probability distribution in the neighborhood of sample segments. We apply the resulting potentials on SPOT images.>

Describes an algorithm which restores images of incomplete contours using a Markovian model. In order to complete the boundaries, a criterion is defined and introduced in an energy function, which has to be optimized. A deterministic relaxation algorithm ICM ("iterated conditional mode") is implemented to minimize this energy function. It generates a configuration in which the contours are reconstructed. Several examples of real image restoration have been tested on a SIMD computer (Connection Machine CM 200). This algorithm allows one to fill up large gaps and to get a better contour grouping.

As it is well known, optimization of the energy function of Markov random fields is very expensive. Hierarchical models have usually much more communication per pixel than monogrid ones. This is why classical annealing schemes are too slow, even on a parallel machine, to minimize the energy associated with such a model. However, taking benefit of the pyramidal structure of the model, we can define a new annealing scheme: the multitemperature annealing (MTA), which consists of associating higher temperatures to coarser levels, in order to be less sensitive to local minima at coarser grids. The convergence to the global optimum is proved by a generalisation of the annealing theorem of Geman and Geman (1984). We have applied the algorithm to image classification and tested it on synthetic and real images.

The authors consider multiscale Markov random field (MRF) models. It is well known that multigrid methods can improve significantly the convergence rate and the quality of the final results of iterative relaxation techniques. A hierarchical model is proposed, which consists of a label pyramid and a whole observation field. The parameters of the coarse grid can be derived by simple computation from the finest grid. In the label pyramid, a new local interaction is introduced between two neighbor grids. This model gives a relaxation algorithm which can be run in parallel on the entire pyramid. The model allows propagation of local interactions more efficiently, giving estimates closer to the global optimum for deterministic as well as for stochastic relaxation schemes. It can also be seen as a way to incorporate cliques with far apart sites for a reasonable price.>

The authors 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 developed by F.C. Jeng and J.W. Woods (1990), 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. A deterministic relaxation method based on mean field annealing with a compound Gauss-Markov random (CGMRF) field model is proposed. The authors 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. The relationship between this technique and two other methods is considered. Edge detection and image estimation results on several noisy images are included.

A pseudo-stochastic variation of the Metropolis dynamics for combinatorial optimization in image classification using Markov random fields is presented. At high temperature, the behavior of the algorithm is similar to the stochastic ones. However, if the temperature is less than a certain threshold, it becomes deterministic. The length of the pseudo-stochastic phase is controlled by a constant threshold used in the modified dynamics. The algorithm yields an approximate but usually good solution to the optimization problem. The algorithm runs on a connection machine. It is applied to the standard pixel classification problem; objective and subjective comparisons with other algorithms have been made.>

A new iterative algorithm for edge intensity image enhancement is proposed. It uses local cooperation-inhibition processes to produce an edge image in which the most relevant contours have reached maximal activation, and small gaps and junctions have been filled in. Implementation on a massively parallel machine has provided high speed performances, and results of experimentations with real scene images are presented. The algorithm is robust in complex edge image context, and is perfectly stable under any number of iterations.>

This paper describes the development of an intelligent imaging system (UKIS) to be used in hazardous or disordered environments. The main purpose of this system is to build a 3D map of the environment using observations of multiple sensors to increase system performance (i.e. resolution, accuracy) and reduce uncertainty. Imaging in UKIS will be based on sensor data fusion in combination with sensor specific and environmental knowledge. Such knowledge can range from the characteristics of the sensors, the algorithms used to a complete blueprint of the environment. This paper describes the main ideas that are used for the development of such a system. Concepts like logical sensors, multi-sensor fusion, world modeling and knowledge-based systems are integrated for the development of an intelligent sensing system.>

A composed Gauss-Markov random field (CGMRF) model is used with mean field approximation for edge detection and image restoration. A set of iterative equations is presented for the mean values of the intensity field and both horizontal and vertical line processes. It is shown that if the CGMRF is isotropic, the same equations as those of Geiger and Girosi (1989) are obtained. How the proposed method is related to the graduated nonconvexity technique using CGMRF is shown. From an implementation point of view, the emphasis is on the use of an optimal step-descent method to get a robust algorithm. Edge detection and image restoration results from a noisy image are presented.>

Two alternative ARMA (autoregressive moving average) estimators are compared both theoretically and through simulation analysis. The first is a dual algorithm that estimates the MA and the AR components as the solution of two linear and independent systems of equations. For the second estimator, the AR coefficients result from a system of linear equations, while the MA component is obtained from a fast filtering algorithm initialized with the previous AR estimated coefficients.>

The authors study the asymptotic error variance of the ARMA (autoregressive moving-average) parameters. The ARMA estimation method involves a two-step procedure: first, the AR parameters are estimated using the Burg algorithm and the time-varying components of a Kalman filter gain. Then the MA parameters are obtained using a fast identification algorithm derived from Chandrasekhar equations. The authors report on results obtained for some very simple examples: ARMA