Multisensor triplet Markov fields and theory of evidence

Pieczynski, Wojciech; Benboudjema, Dalila

doi:10.1016/j.imavis.2005.09.012

Cited by 28 publications

(12 citation statements)

References 31 publications

(39 reference statements)

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“…Such a fusion destroys Markovianity; however, its result remains workable because it is formally a TMF model. These cases are only mentioned here and will be not treated further in this paper (see [29] for more details).…”

Section: Three Interpretations Of Tmfmentioning

confidence: 99%

Unsupervised image segmentation using triplet Markov fields

Benboudjema¹,

Pieczynski²

2005

Computer Vision and Image Understanding

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Hidden Markov fields (HMF) models are widely applied to various problems arising in image processing. In these models, the hidden process of interest X is a Markov field and must be estimated from its observable noisy version Y. The success of HMF is mainly due to the fact that the conditional probability distribution of the hidden process with respect to the observed one remains Markovian, which facilitates different processing strategies such as Bayesian restoration. HMF have been recently generalized to ''pairwise'' Markov fields (PMF), which offer similar processing advantages and superior modeling capabilities. In PMF one directly assumes the Markovianity of the pair (X, Y). Afterwards, ''triplet'' Markov fields (TMF), in which the distribution of the pair (X, Y) is the marginal distribution of a Markov field (X, U, Y), where U is an auxiliary process, have been proposed and still allow restoration processing. The aim of this paper is to propose a new parameter estimation method adapted to TMF, and to study the corresponding unsupervised image segmentation methods. The latter are validated via experiments and real image processing.

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Section: Three Interpretations Of Tmfmentioning

confidence: 99%

Unsupervised image segmentation using triplet Markov fields

Benboudjema¹,

Pieczynski²

2005

Computer Vision and Image Understanding

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“…The use of the DSTE in the context of Markov models is quite recent and is undoubtedly very promising [35,62]. A link with TMC [57] and TMF [59] has also been been established. Finally, "evidential filters" based on evidential measures have been proposed recently [29,54].…”

Section: Theory Of Evidencementioning

confidence: 99%

New trends in Markov models and related learning to restore data

Forbes¹,

Pieczynski²

2009

2009 IEEE International Workshop on Machine Learning for Signal Processing

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We present recent approaches that extend standard Markov models and increase their modelling power. These capabilities are illustrated in the cited published works and more recently in the contributions to the Special Session on Markov models of the IEEE International Workshop on Machine Learning for Signal Processing, 2009. However, the review is not exhaustive and major older works may be missing.

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“…The Dempster-Shafer theory of evidence [12][13][14][15][16][17][18][19][20][21][22][23] overcomes these drawbacks; thanks to the rich triplet Markov chains' (TMC) formalism. In fact, the computation of posterior distribution p x ð jyÞ, crucial for Bayesian restoration, can be seen as the DS fusion of the prior knowledge given by p x ð Þ ¼ p x 1 ð Þ Q N n¼2 p x n ð jx nÀ1 Þ with the observation knowledge given by q x ð Þ / p y ð jxÞ ¼ Π N n¼1 p y n ð jx n Þ .…”

Section: Introductionmentioning

confidence: 99%

Dempster–Shafer fusion of multisensor signals in nonstationary Markovian context

Boudaren

Monfrini

Pieczynski

et al. 2012

EURASIP J. Adv. Signal Process.

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The latest developments in Markov models' theory and their corresponding computational techniques have opened new rooms for image and signal modeling. In particular, the use of Dempster-Shafer theory of evidence within Markov models has brought some keys to several challenging difficulties that the conventional hidden Markov models cannot handle. These difficulties are concerned mainly with two situations: multisensor data, where the use of the Dempster-Shafer fusion is unworkable; and nonstationary data, due to the mismatch between the estimated stationary model and the actual data. For each of the two situations, the Dempster-Shafer combination rule has been applied, thanks to the triplet Markov models' formalism, to overcome the drawbacks of the standard Bayesian models. However, so far, both situations have not been considered in the same time. In this article, we propose an evidential Markov chain that uses the Dempster-Shafer combination rule to bring the effect of contextual information into segmentation of multisensor nonstationary data. We also provide the Expectation-Maximization parameters' estimation and the maximum posterior marginal's restoration procedures. To validate the proposed model, experiments are conducted on some synthetic multisensor data and noised images. The obtained segmentation results are then compared to those obtained with conventional approaches to bring out the efficiency of the present model.

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Multisensor triplet Markov fields and theory of evidence

Cited by 28 publications

References 31 publications

Unsupervised image segmentation using triplet Markov fields

Unsupervised image segmentation using triplet Markov fields

New trends in Markov models and related learning to restore data

Dempster–Shafer fusion of multisensor signals in nonstationary Markovian context

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