Wojciech Pieczynski

Unsupervised classification of radar images using hidden Markov chains and hidden Markov random fields

Due to the enormous quantity of radar images acquired by satellites and through shuttle missions, there is an evident need for efficient automatic analysis tools. This paper describes unsupervised classification of radar images in the framework of hidden Markov models and generalized mixture estimation. Hidden Markov chain models, applied to a Hilbert-Peano scan of the image, constitute a fast and robust alternative to hidden Markov random field models for spatial regularization of image analysis problems, even though the latter provide a finer and more intuitive modeling of spatial relationships. We here compare the two approaches and show that they can be combined in a way that conserves their respective advantages. We also describe how the distribution families and parameters of classes with constant or textured radar reflectivity can be determined through generalized mixture estimation. Sample results obtained on real and simulated radar images are presented.

Parameter estimation in hidden fuzzy Markov random fields and image segmentation

This paper proposes a new unsupervised fuzzy Bayesian image segmentation method using a recent model using hidden fuzzy Markov fields. The originality of this model is to use Dirac and Lebesgue measures simultaneously at the class field level, which allows the coexistence of hard and fuzzy pixels in a same picture. We propose to solve the main problem of parameter estimation by using of a recent general method of estimation in the case of hidden data, called iterative conditional estimation (ICE), which has been successfully applied in classical segmentation based on hidden Markov fields. The first part of our work involves estimating the parameters defining the Markovian distribution of the noise-free fuzzy picture. We then combine this algorithm with the ICE method in order to estimate all the parameters of the fuzzy picture corrupted with noise. Last, we combine the parameter estimation step with two segmentation methods, resulting in two unsupervised statistical fuzzy segmentation methods. The efficiency of the proposed methods is tested numerically on synthetic images and a fuzzy segmentation of a real image of clouds is studied.

Pairwise Markov chains

We propose a model called a pairwise Markov chain (PMC), which generalizes the classical hidden Markov chain (HMC) model. The generalization, which allows one to model more complex situations, in particular implies that in PMC the hidden process is not necessarily a Markov process. However, PMC allows one to use the classical Bayesian restoration methods like maximum a posteriori (MAP), or maximal posterior mode (MPM). So, akin to HMC, PMC allows one to restore hidden stochastic processes, with numerous applications to signal and image processing, such as speech recognition, image segmentation, and symbol detection or classification, among others. Furthermore, we propose an original method of parameter estimation, which generalizes the classical iterative conditional estimation (ICE) valid for a classical hidden Markov chain model, and whose extension to possibly non-Gaussian and correlated noise is briefly treated. Some preliminary experiments validate the interest of the new model.

Signal and image segmentation using pairwise Markov chains

The aim of this paper is to apply the recent pairwise Markov chain model, which generalizes the hidden Markov chain one, to the unsupervised restoration of hidden data. The main novelty is an original parameter estimation method that is valid in a general setting, where the form of the possibly correlated noise is not known. Several experimental results are presented in both Gaussian and generalized mixture contexts. They show the advantages of the pairwise Markov chain model with respect to the classical hidden Markov chain one for supervised and unsupervised restorations.

Unsupervised segmentation of randomly switching data hidden with non-Gaussian correlated noise

Hidden Markov chains (HMC) are a very powerful tool in hidden data restoration and are currently used to solve a wide range of problems. However, when these data are not stationary, estimating the parameters, which are required for unsupervised processing, poses a problem. Moreover, taking into account correlated non-Gaussian noise is difficult without model approximations. The aim of this paper is to propose a simultaneous solution to both of these problems using triplet Markov chains (TMC) and copulas. The interest of the proposed models and related processing is validated by different experiments some of which are related to semi-supervised and unsupervised image segmentation.

Unsupervised signal restoration using hidden Markov chains with copulas

This paper deals with the statistical restoration of hidden discrete signals, extending the classical methodology based on hidden Markov chains. The aim is to take into account the hidden signal and complex relationships between the noises which can be from different parametric models, non-independent, and of class-varying nature. We discuss some possibilities of managing it using copulas. Further, we propose a parameter estimation method and apply resulting unsupervised restoration methods in variety of situations. It is also validated by experiments performed in supervised and unsupervised context.

Kalman filtering using pairwise Gaussian models

An important problem in signal processing consists in recursively estimating an unobservable process x={x/sub n/}/sub n/spl isin/IN/ from an observed process y={y/sub n/}/sub n/spl isin/IN/. This is done classically in the framework of hidden Markov models (HMM). In the linear Gaussian case, the classical recursive solution is given by the well-known Kalman filter. We consider pairwise Gaussian models by assuming that the pair (x, y) is Markovian and Gaussian. We show that this model is strictly more general than the HMM, and yet still enables Kalman-like filtering.

Fusion of textural statistics using a similarity measure: application to texture recognition and segmentation

Features computed as statistics (e.g. histograms) of local filter responses have been reported as the most powerful descriptors for texture classification and segmentation. The selection of the filter banks remains however a crucial issue, as well as determining a relevant combination of these descriptors. To cope with selection and fusion issues, we propose a novel approach relying on the definition of the texture-based similarity measure as a weighted sum of the Kullback–Leibler measures between empirical feature statistics. Within a supervised framework, the weighting factors are estimated according to the maximization of a margin-based criterion. This weighting scheme can also be considered as a filter selection method: texture filter response distributions are ranked according to the associated weighting factors so that the problem of selecting a subset of filters reduces to picking the first features only. An application of this similarity measure to texture recognition is reported. We also investigate its use for texture segmentation within a Bayesian Markov Random Field (MRF)-based framework. Experiments carried out on Brodatz textures and sonar images show that the proposed weighting method improves the classification and the segmentation rates while relying on a parsimonious texture representation.

Copula-based Stochastic Kernels for Abrupt Change Detection

This paper shows how to obtain a binary change map from similarity measures of the local statistics of images before and after a disaster. The decision process is achieved by the use of a zz-SVM in which a stochastic kernel has been defined. Stochastic kernel includes two similarity measures, based on the local statistics, to detect changes from the images: 1) A distance between maginal probability density functions (pdfs) and 2) the mutual information between the two observations. Distance between marginal pdfs is evaluated by using a series expansion of the Kullbak-Leibler distance. It is achieved by estimating cumulants up to order 4 from a sliding window of fixed size. Mutual information is estimated through a parametric model that is issued from the copulas theory. It is based on rank statistics and yields an analytic expression, that depends on the parameter of the copula only, to be evaluated to obtain the mutual information. Preliminary results are shown on a pair of Radarsat images acquire before and after a lava flow. A ground truth allows to show the accuracy of the stochastic kernels and the SVM decision.

Unsupervised change detection in SAR images using a multicomponent HMC model

In this work, we propose to use the Hidden Markov Chain (HMC) model for fully automatic change detection in a temporal set of Synthetic Aperture Radar (SAR) images. First, it is shown that this model can be used as an alternative to the Hidden Markov Random Field (HMRF) model in the image differencing context. We then propose a novel approach, called joint characterization, whose principle is to consider that the ‘before’ and ‘after’ images are a unique realization of a bi-dimensional process. Parameters estimation is performed from a multicomponent extension of the HMC model and thematic change can be detected according to the joint statistics of the classes in the images. Preliminary experiments show promising results.