Unsupervised restoration of hidden nonstationary Markov chains using evidential priors

Lanchantin, Pierre; Pieczynski, Wojciech

doi:10.1109/tsp.2005.851131

Cited by 48 publications

(49 citation statements)

References 18 publications

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“…There are some studies concerning triplet Markov chains [18,28], where general ideas somewhat similar to those discussed in the present paper, have been investigated. However, as Markov fields based processing is quite different from the Markov chains based one, we will concentrate here on Markov fields with no further reference to Markov chains.…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

Unsupervised image segmentation using triplet Markov fields

Benboudjema¹,

Pieczynski²

2005

Computer Vision and Image Understanding

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“…Multi modality tumor segmentation was performed by exploiting the hierarchical property of the HMT, allowing associating the high resolution CT image at the leafs of the tree, and the lower resolution PET image at the next higher scale in the tree. Future work will focus on exploiting this HMT model for PET/MR and PET multi tracer information, in addition to the use of Pairwise Markov Tree (PMT) [1] combined with evidence theory [7]. Validation of the PET/CT segmentation on datasets with histopathological reference will be also presented.…”

Section: B Multi Modal (Pet/ct) Image Segmentationmentioning

confidence: 99%

PET/CT image denoising and segmentation based on a multi observation and a multi scale Markov tree model

2013

2013 IEEE Nuclear Science Symposium and Medical Imaging Conference (2013 NSS/MIC)

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“…The use of standard HMCs in unsupervised segmentation in such a situation (nonstationary hidden process) provides poor results [12]. This is due to the mismatch between the estimated stationary model and the data.…”

Section: Introductionmentioning

confidence: 99%

“…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%

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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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Unsupervised restoration of hidden nonstationary Markov chains using evidential priors

Cited by 48 publications

References 18 publications

Unsupervised image segmentation using triplet Markov fields

Unsupervised image segmentation using triplet Markov fields

PET/CT image denoising and segmentation based on a multi observation and a multi scale Markov tree model

Dempster–Shafer fusion of multisensor signals in nonstationary Markovian context

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