Markov Models in Image Processing. Modèles de Markov en Traitement D’images

Markov Models in Image Processing

Modèles de Markov en Traitement D’images

Wojciech Pieczynski

GET/INT, Département CITI, CNRS UMR 5157, 9, rue Charles Fourier, 91000 Evry, France

Page: 
255-277
|
Received: 
23 September 2002
|
Accepted: 
N/A
|
Published: 
30 September 2003
| Citation

OPEN ACCESS

Abstract: 

The aim of this paper is to present some aspects of Markov model based statistical image processing. After a brief review of statistical processing in image segmentation, classical Markov models (fields, chains, and trees) used in image processing are developed. Bayesian methods of segmentation are then described and different general parameter estimation methods are presented. More recent models and processing techniques, such as Pairwise and Triplet Markov models, Dempster-Shafer fusion in a Markov context, and generalized mixture estimation, are then discussed. We conclude with a nonexhaustive desciption of candidate extensions to multidimensional, multisensor, and multiresolution imagery. Connections with general graphical models are also highlighted.

Résumé

L’objet de l’article est de présenter divers aspects des traitements statistiques des images utilisant des modèles de Markov. En choisissant pour cadre la segmentation statistique nous rappelons brièvement la nature et l’intérêt des traitements probabilistes et présentons les modèles de Markov cachés classiques : champs, chaînes, et arbres. Les méthodes bayésiennes de segmentation sont décrites, ainsi que les grandes familles des méthodes d’apprentissage. Quelques modèles ou méthodes de traitements plus récents comme les modèles de Markov Couple et Triplet, la fusion de Dempster-Shafer dans le contexte markovien, ou l’estimation des mélanges généralisés sont également présentés. Nous terminons par une liste non exhaustive des divers prolongements des méthodes et modèles vers l’imagerie multidimensionnelle, multisenseurs, multirésolution. Des liens avec les modèles graphiques généraux sont également brièvement décrits.

Keywords: 

Markov fields, Markov chains, Markov trees, Bayesian image segmentation, Expectation-Maximization, Iterative Conditional Estimation, Fuzzy segmentation, Dempster-Shafer fusion, theory of evidence, pairwise Markov models, triplet Markov models.

Mots clés 

Champs de Markov, chaînes de Markov, arbres de Markov, segmentation bayésienne d’images, EspéranceMaximisation, Estimation conditionnelle itérative, segmentation floue, fusion Dempster-Shafer, théorie de l’évidence, Markov couple, Markov triplet.

1. Introduction
2. Modèle Probabiliste et Classification Bayésienne
3. Modèles de Markov Cachés
4. Modèles de Markov Couple
5. Apprentissage des Modèles de Markov
6. Extensions
7. Conclusions et Perspectives
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