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34
Signal and Image Segmentation Using Pairwise Markov Chains
, 2003
"... 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, valid in a general setting where the form of the possibly correlated n ..."
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Cited by 35 (21 self)
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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, 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 classical hidden Markov chain one for supervised and unsupervised restorations.
Multisensor triplet Markov chains and theory of evidence
 International Journal of Approximate Reasoning
, 2006
"... Hidden Markov chains (HMC) are widely applied in various problems occurring in different areas like Biosciences, Climatology, Communications, Ecology, Econometrics and Finances, Image or Signal processing. In such models, the hidden process of interest X is a Markov chain, which must be estimated fr ..."
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Cited by 23 (10 self)
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Hidden Markov chains (HMC) are widely applied in various problems occurring in different areas like Biosciences, Climatology, Communications, Ecology, Econometrics and Finances, Image or Signal processing. In such models, the hidden process of interest X is a Markov chain, which must be estimated from an observable Y, interpretable as being a noisy version of X. The success of HMC is mainly due to the fact that the conditional probability distribution of the hidden process with respect to the observed process remains Markov, which makes possible different processing strategies such as Bayesian restoration. HMC have been recently generalized to ‘‘Pairwise’ ’ Markov chains (PMC) and ‘‘Triplet’ ’ Markov chains (TMC), which offer similar processing advantages and superior modeling capabilities. In PMC, one directly assumes the Markovianity of the pair (X, Y) and in TMC, the distribution of the pair (X, Y) is the marginal distribution of a Markov process (X, U, Y), where U is an auxiliary process, possibly contrived. Otherwise, the Dempster–Shafer fusion can offer interesting extensions of the calculation of the ‘‘a posteriori’ ’ distribution of the hidden data. The aim of this paper is to present different possibilities of using the Dempster–Shafer fusion in the context of different multisensor Markov models. We show that the posterior distribution remains calculable in different general situations and present some examples of their applications in remote sensing area.
Unsupervised Non Stationary Image Segmentation Using Triplet Markov Chains
 In Advanced Concepts for Intelligent Vision Systems (ACVIS 04
, 2004
"... This work deals with the unsupervised Bayesian hidden Markov chain restoration extended to the non stationary case. Unsupervised restoration based on "ExpectationMaximization " (EM) or "Stochastic EM" (SEM) estimates considering the "Hidden Markov Chain" (HMC) model is quite efficient when the hidde ..."
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Cited by 19 (7 self)
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This work deals with the unsupervised Bayesian hidden Markov chain restoration extended to the non stationary case. Unsupervised restoration based on "ExpectationMaximization " (EM) or "Stochastic EM" (SEM) estimates considering the "Hidden Markov Chain" (HMC) model is quite efficient when the hidden chain is stationary. However, when the latter is not stationary, the unsupervised restoration results can be poor, due to a bad match between the real and estimated models. In this paper we present a more appropriate model for non stationary HMC, via recent Triplet Markov Chains (TMC) model. Using TMC, we show that the classical restoration results can be significantly improved in the case of non stationary data. The latter improvement is performed in an unsupervised way using a SEM parameter estimation method. Some application examples to unsupervised image segmentation are also provided.
Contextsensitive hidden Markov models for modeling longrange dependencies in symbol sequences
 IEEE Trans. Signal Processing
, 2006
"... The hidden Markov model (HMM) has been widely used in signal processing and digital communication applications. It is wellknown for its efficiency in modeling shortterm dependencies between adjacent symbols. However, it cannot be used for modeling longrange interactions between symbols that are d ..."
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Cited by 12 (8 self)
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The hidden Markov model (HMM) has been widely used in signal processing and digital communication applications. It is wellknown for its efficiency in modeling shortterm dependencies between adjacent symbols. However, it cannot be used for modeling longrange interactions between symbols that are distant from each other. In this paper, we introduce the concept of contextsensitive HMM. The proposed model is capable of modeling strong pairwise correlations between distant symbols. Based on this model, we propose dynamic programming algorithms that can be used for finding the optimal state sequence and for computing the probability of an observed symbol string. Furthermore, we also introduce a parameter reestimation algorithm, which can be used for optimizing the model parameters based on the given training sequences. 1
Image and Signal Restoration using Pairwise Markov Trees
 in Proceedings of the 2003 IEEE Workshop on Statistical Signal Processing
, 2003
"... This work deals with the statistical restoration of a hidden signal using Pairwise Markov Trees (PMT). PMT have been introduced recently in the case of a discrete hidden signal. We first show that PMT can perform better than the classical Hidden Markov Trees (HMT) when applied to unsupervised image ..."
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Cited by 10 (4 self)
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This work deals with the statistical restoration of a hidden signal using Pairwise Markov Trees (PMT). PMT have been introduced recently in the case of a discrete hidden signal. We first show that PMT can perform better than the classical Hidden Markov Trees (HMT) when applied to unsupervised image segmentation. We next consider a PMT in a linear Gaussian model with continuous hidden data, and we give formulas of an original extension of the classical Kalman filter.
Kalman filtering for triplet Markov chains : Applications and extensions
 in Proceedings of the International Conference on Acoustics, Speech and Signal Processing (ICASSP 05
, 2005
"... Abstract—Let � a � sx be a hidden process, � a � sx an observed process, and � a � sx some additional process. We assume that � a @ � � �A is a (socalled “Triplet”) vector Markov chain (TMC). We first show that the linear TMC model encompasses and generalizes, among other models, the classical st ..."
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Cited by 10 (4 self)
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Abstract—Let � a � sx be a hidden process, � a � sx an observed process, and � a � sx some additional process. We assume that � a @ � � �A is a (socalled “Triplet”) vector Markov chain (TMC). We first show that the linear TMC model encompasses and generalizes, among other models, the classical statespace systems with colored process and/or measurement noise(s). We next propose restoration Kalmanlike filters for arbitrary linear Gaussian (LG) TMC. Index Terms—Bayesian signal restoration, hidden Markov chains, Kalman filtering, Markovian models, triplet Markov chains.
Statistical image segmentation using Triplet Markov fields
 SPIE’s International Symposium on Remote Sensing
, 2002
"... Hidden Markov fields (HMF) are widely used in image processing. In such models, the hidden random field of interest S s s X X = ) ( is a Markov field, and the distribution of the observed random field S s s Y Y = ) ( (conditional on X ) is given by s s x y p x y p ) ( ) ( . The posterior dist ..."
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Cited by 7 (4 self)
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Hidden Markov fields (HMF) are widely used in image processing. In such models, the hidden random field of interest S s s X X = ) ( is a Markov field, and the distribution of the observed random field S s s Y Y = ) ( (conditional on X ) is given by s s x y p x y p ) ( ) ( . The posterior distribution ) ( y x p is then a Markov distribution, which affords different Bayesian processing. However, when dealing with the segmentation of images containing numerous classes with different textures, the simple form of the distribution ) ( x y p above is insufficient and has to be replaced by a Markov field distribution. This poses problems, because taking ) ( x y p Markovian implies that the posterior distribution ) ( y x p , whose Markovianity is needed to use Bayesian techniques, may no longer be a Markov distribution, and so different model approximations must be made to remedy this. This drawback disappears when considering directly the Markovianity of ) , ( Y X ; in these recent "Pairwise Markov Fields (PMF) models, both ) ( x y p and ) ( y x p are then Markovian, the first one allowing us to model textures, and the second one allowing us to use Bayesian restoration without model approximations.
Unsupervised Segmentation of Hidden Semi Markov Non Stationary Chains
"... Abstract. In the classical hidden Markov chain (HMC) model we have a hidden chain X, which is a Markov one and an observed chain Y. HMC are widely used; however, in some situations they have to be replaced by the more general “hidden semiMarkov chains ” (HSMC), which are particular “triplet Markov ..."
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Cited by 7 (1 self)
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Abstract. In the classical hidden Markov chain (HMC) model we have a hidden chain X, which is a Markov one and an observed chain Y. HMC are widely used; however, in some situations they have to be replaced by the more general “hidden semiMarkov chains ” (HSMC), which are particular “triplet Markov chains ” (TMC) T = ( X, U, Y) , where the auxiliary chain U models the semiMarkovianity of X. Otherwise, non stationary classical HMC can also be modeled by a triplet Markov stationary chain with, as a consequence, the possibility of parameters ' estimation. The aim of this paper is to use simultaneously both properties. We
Unsupervised Signal Restoration Using Copulas And Pairwise Markov Chains
, 2003
"... This work deals with the statistical restoration of hidden discrete signals. The problem we deal with is how to take into account, in recent pairwise and triplet Markov chain context, complex noises that can be nonGaussian, correlated, and of classvarying nature. We propose to solve this modeling ..."
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Cited by 6 (4 self)
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This work deals with the statistical restoration of hidden discrete signals. The problem we deal with is how to take into account, in recent pairwise and triplet Markov chain context, complex noises that can be nonGaussian, correlated, and of classvarying nature. We propose to solve this modeling problem using Copulas. The interest of the new modeling is validated by experiments performed in supervised and unsupervised context. In the latter, all parameters are estimated from the only observed data by an original method.