Mohamed El Yazid Boudaren

Unsupervised Segmentation of Random Discrete Data Hidden With Switching Noise Distributions

Hidden Markov models are very robust and have been widely used in a wide range of application fields; however, they can prove some limitations for data restoration under some complex situations. These latter include cases when the data to be recovered are nonstationary. The recent triplet Markov models have overcome such difficulty thanks to their rich formalism, that allows considering more complex data structures while keeping the computational complexity of the different algorithms linear to the data size. In this letter, we propose a new triplet Markov chain that allows the unsupervised restoration of random discrete data hidden with switching noise distributions. We also provide genuine parameters estimation and MPM restoration algorithms. The new model is validated through experiments conducted on synthetic data and on real images, whose results show its interest with respect to the standard hidden Markov chain.

Dempster-Shafer fusion of evidential pairwise Markov fields

Hidden Markov fields (HMFs) have been successfully used in many areas to take spatial information into account. In such models, the hidden process of interest X is a Markov field, that is to be estimated from an observable process Y. The possibility of such estimation is due to the fact that the conditional distribution of the hidden process with respect to the observed one remains Markovian. The latter property remains valid when the pairwise process ( X , Y ) is Markov and such models, called pairwise Markov fields (PMFs), have been shown to offer larger modeling capabilities while exhibiting similar processing cost. Further extensions lead to a family of more general models called triplet Markov fields (TMFs) in which the triplet ( U , X , Y ) is Markov where U is an underlying process that may have different meanings according to the application. A link has also been established between these models and the theory of evidence, opening new possibilities of achieving Dempster-Shafer fusion in Markov fields context. The aim of this paper is to propose a unifying general formalism allowing all conventional modeling and processing possibilities regarding information imprecision, sensor unreliability and data fusion in Markov fields context. The generality of the proposed formalism is shown theoretically through some illustrative examples dealing with image segmentation, and experimentally on hand-drawn and SAR images. We propose an original formalism unifying a large family of Markov fields.The proposed family of models is closed with respect to DS fusion rule.Our modeling handles information imprecision, sensor unreliability and data fusion.Dempster-Shafer fusion is performed by simply adding the corresponding Markov energies.A particular model from the new family is applied to image segmentation.

Unified Representation of Sets of Heterogeneous Markov Transition Matrices

Markov chains are very efficient models and have been extensively applied in a wide range of fields covering queuing theory, signal processing, performance evaluation, time series, and finance. For discrete finite first-order Markov chains, which are among the most used models of this family, the transition matrix can be seen as the model parameter, since it encompasses the set of probabilities governing the system state. Estimating such a matrix is, however, not an easy task due to possible opposing expert reports or variability of conditions under which the estimation process is carried out. In this paper, we propose an original approach to infer a consensus transition matrix, defined in accordance with the theory of evidence, from a family of data samples or transition matrices. To validate our method, experiments are conducted on nonstationary label images and daily rainfall data. The obtained results confirm the interest of the proposed evidential modeling with respect to the standard Bayesian one.

Dempster–Shafer Fusion of Evidential Pairwise Markov Chains

Hidden Markov models have been extended in many directions, leading to pairwise Markov models, triplet Markov models, or discriminative random fields, all of which have been successfully applied in many fields covering signal and image processing. The Dempster-Shafer theory of evidence has also shown its interest in a wide range of situations involving reasoning under uncertainty and/or information fusion. There are, however, only few works dealing with both of these modeling tools simultaneously. The aim of this paper, which falls under this category of works, is to propose a general evidential Markov model offering wide modeling and processing possibilities regarding information imprecision, sensor unreliability, and data fusion. The main interest of the proposed model relies in the possibility of achieving, easily, the Dempster-Shafer fusion without destroying the Markovianity.

Unsupervised segmentation of non stationary data hidden with non stationary noise

Classical hidden Markov chains (HMC) can be inefficient in the unsupervised segmentation of non stationary data. To overcome such involvedness, the more elaborated triplet Markov chains (TMC) resort to using an auxiliary underlying process to model the behavior switches within the hidden states process. However, so far, only this latter was considered non stationary. The aim of this paper is to extend the results of a recently proposed TMC by considering both hidden states and noise non stationary. To show the efficiency of the proposed model, we provide results of non stationary synthetic and real images restoration.

Unsupervised Segmentation of SAR Images Using Gaussian Mixture-Hidden Evidential Markov Fields

Hidden Markov fields have been extensively applied in the field of synthetic aperture radar (SAR) image processing, mainly for segmentation and change detection. In such models, the hidden process of interest X is assumed to be a Markov field that is to be searched from an observable process Y. The possibility of such estimation lies, however, on several assumptions that turn out to be unsuitable for many natural systems. These models have then been extended in many directions, leading to triplet Markov fields among other extensions. A link has then been established between these models and the theory of evidence, opening new possibilities of uncertainty modeling and information fusion. The aim of this letter is to further generalize the hidden evidential Markov field (EMF) to consider more general forms of noise with application to unsupervised segmentation of SAR images. For parameters estimation, we use iterative conditional estimation, whereas maximization is performed through iterative conditional mode. The performance of the proposed model is assessed against the original EMF on real SAR images.

Phasic Triplet Markov Chains.

Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data.

Load Balancing Heuristic for Tasks Scheduling in Cloud Environment.

Distributed systems, a priori intended for applications by connecting distributed entities, have evolved into supercomputing to run a single application. Currently, Cloud Computing has arisen as a new trend in the world of IT (Information Technology). Cloud computing is an architecture in full development and has become a new computing model for running scientific applications. In this context, resource allocation is one of the most challenging problems. Indeed, assigning optimally the available resources to the needed cloud applications is known to be an NP complete problem. In this paper, we propose a new task scheduling strategy for resource allocation that minimizes the completion time (makespan) in cloud computing environment. To show the interest of the proposed solution, experiments are conducted on a simulated

Unsupervised Segmentation of Nonstationary Data using Triplet Markov Chains.

An important issue in statistical image and signal segmentation consists in estimating the hidden variables of interest. For this purpose, various Bayesian estimation algorithms have been developed, particularly in the framework of hidden Markov chains, thanks to their efficient theory that allows one to recover the hidden variables from the observed ones even for large data. However, such models fail to handle nonstationary data in the unsupervised context. In this paper, we show how the recent triplet Markov chains, which are strictly more general models with comparable computational complexity, can be used to overcome this limit through two different ways: (i) in a Bayesian context by considering the switches of the hidden variables regime depending on an additional Markov process; and, (ii) by introducing Dempster-Shafer theory to model the lack of precision of the hidden process prior distributions, which is the origin of data nonstationarity. Furthermore, this study analyzes both approaches in order to determine which one is better-suited for nonstationary data. Experimental results are shown for sampled data and noised images.

Evidential Correlated Gaussian Mixture Markov Model for Pixel Labeling Problem

Hidden Markov Fields (HMF) have been widely used in various problems of image processing. In such models, the hidden process of interest \( X \) is assumed to be a Markov field that must be estimated from an observable process \( Y \). Classic HMFs have been recently extended to a very general model called “evidential pairwise Markov field” (EPMF). Extending its recent particular case able to deal with non-Gaussian noise, we propose an original variant able to deal with non-Gaussian and correlated noise. Experiments conducted on simulated and real data show the interest of the new approach in an unsupervised context.