&lt;title&gt;Statistical image segmentation using triplet Markov fields&lt;/title&gt;

Pieczynski, Wojciech; Benboudjema, Dalila; Lanchantin, Pierre

doi:10.1117/12.463182

Cited by 46 publications

(10 citation statements)

References 24 publications

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“…In this paper, we have dealt with the recent triplet Markov fields (TMF [27]) model, which is more general than the classical hidden Markov fields (HMF) model and still allows one to recover, via some Bayesian methods, the hidden signal. We proposed two kinds of results:…”

Section: Discussionmentioning

confidence: 99%

“…Another possibility is to use the general ''Iterative Conditional Estimation'' (ICE [25]) method, which has given good results in different classical HMF situations [4,7,10,16,22,23,30], and in more complex Markov models with a Dempster-Shafer fusion [2] or fuzzy hidden fields [31]. Moreover, first applications of ICE in a simple TMF context also gave promising results [27]. ICE resembles EM, and some relationships are specified in [8]; however, it is more flexible and seems better suited to the Markov field context.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…Both p (y|x) and p (x|y) are then Markovian, the former ensuring possibilities of modeling textures without approximations, and the latter allowing Bayesian processing, similar to those provided by HMF. PMF have then been generalized to ''triplet'' Markov fields (TMF), in which the distribution of the pair Z = (X, Y) is the marginal distribution of a Markov field T = (X, U, Y), where U = (U s ) s2S is an auxiliary random field [27]. Once the space K of possible values of each U s is simple enough, TMF still allow one to estimate the unobservable X = x from the observed Y = y.…”

Section: Introductionmentioning

confidence: 99%

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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: Discussionmentioning

confidence: 99%

Section: Parameter Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Unsupervised image segmentation using triplet Markov fields

Benboudjema¹,

Pieczynski²

2005

Computer Vision and Image Understanding

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“…In this model we assume directly the Markovianity of ( ) Y X , . Afterwards, triplet Markov fields (TMF) which are the generalization of the PMF, have been proposed [7]. In such model, the distribution of the couple ( )…”

Section: A Nonstationary Triplet Markov Fieldmentioning

confidence: 99%

Unsupervised segmentation of SAR images using Triplet Markov fields and fisher noise distributions

Benboudjema

Tupin

Pieczynski³

et al. 2007

2007 IEEE International Geoscience and Remote Sensing Symposium

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Abstract-This paper deals with SAR data segmentation in an unsupervised way. The model we propose is a combination of the nonstationary triplet Markov field recently introduced and the Fisher distributions. The first one allows modeling the different stationarities present in a given image. The second one has the advantage that is well adapted to this kind of data. We present an original technique based on Iterative Conditional Estimation method, to estimate the parameters of the model we propose. Application examples on simulated data and real SAR images are presented as well.

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“…Besag [3] applied them in the context of binary image restoration and Derin [8] and Gimelfarb and coworkers [12] analyzed texture in the context of a Markov random field using learned priors based on gray level co-occurrences. Work has continued through new applications such as texture segmentation [20] or through extension of the basic model, for example by considering higher-order cliques [23].…”

Section: Introductionmentioning

confidence: 99%

Statistical Priors for Efficient Combinatorial Optimization Via Graph Cuts

Cremers

Grady

2006

Computer Vision – ECCV 2006

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Abstract. Bayesian inference provides a powerful framework to optimally integrate statistically learned prior knowledge into numerous computer vision algorithms. While the Bayesian approach has been successfully applied in the Markov random field literature, the resulting combinatorial optimization problems have been commonly treated with rather inefficient and inexact general purpose optimization methods such as Simulated Annealing. An efficient method to compute the global optima of certain classes of cost functions defined on binary-valued variables is given by graph min-cuts. In this paper, we propose to reconsider the problem of statistical learning for Bayesian inference in the context of efficient optimization schemes. Specifically, we address the question: Which prior information may be learned while retaining the ability to apply Graph Cut optimization? We provide a framework to learn and impose prior knowledge on the distribution of pairs and triplets of labels. As an illustration, we demonstrate that one can optimally restore binary textures from very noisy images with runtimes on the order of a second while imposing hundreds of statistically learned constraints per pixel.

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<title>Statistical image segmentation using triplet Markov fields</title>

Cited by 46 publications

References 24 publications

Unsupervised image segmentation using triplet Markov fields

Unsupervised image segmentation using triplet Markov fields

Unsupervised segmentation of SAR images using Triplet Markov fields and fisher noise distributions

Statistical Priors for Efficient Combinatorial Optimization Via Graph Cuts

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