Statistical models for deformable templates in image and shape analysis
[Modèles statistiques d’atlas déformables pour l’analyse d’images et de formes]
Allassonnière, Stéphanie1 ; Bigot, Jérémie2 ; Glaunès, Joan Alexis3 ; Maire, Florian4 ; Richard, Frédéric J.P.5
1 CMAP Ecole Polytechnique Route de Saclay 91128 Palaiseau FRANCE
2 Institut de Mathématiques de Toulouse, CNRS UMR 5219 Université de Toulouse 118 route de Narbonne 31062 Toulouse Cedex 9 FRANCE
3 MAP5 Université Paris Descartes, Sorbonne Paris Cité 45 rue des Saints-Pères 75270 Paris Cedex 06 FRANCE
4 ONERA - The French Aerospace Lab F-91761 Palaiseau FRANCE
5 LATP CNRS UMR 7353 Aix Marseille Université Centre de mathématiques et d’informatique 39 rue Frédéric Joliot 13453 Marseille Cedex FRANCE
Annales mathématiques Blaise Pascal, Tome 20 (2013) no. 1, pp. 1-35.

Les données de grande dimensions sont de plus en plus fréquemment collectées dans de nombreux domaines d’application. Il devient alors particulièrement important d’être capable d’extraire des caractéristiques significatives de ces bases de données. Le modèle d’atlas déformable (Deformable template model) est un outil maintenant répandu pour atteindre ce but. Cet article présente un panorama des aspects statistiques de ce modèle ainsi que ses généralisations. Nous décrivons les différents cadres mathématiques permettant de prendre en compte des types variés de données et de déformations. Nous rappelons les propriétés théoriques de convergence des estimateurs et des algorithmes permettant l’estimation de ces caractéristiques. Nous terminons cet article par la présentation de quelques résultats publiés utilisant des données réelles.

High dimensional data are more and more frequent in many application fields. It becomes particularly important to be able to extract meaningful features from these data sets. Deformable template model is a popular way to achieve this. This paper is a review on the statistical aspects of this model as well as its generalizations. We describe the different mathematical frameworks to handle different data types as well as the deformations. We recall the theoretical convergence properties of the estimators and the numerical algorithm to achieve them. We end with some published examples.

DOI : 10.5802/ambp.320
Classification : 62H12, 62H30, 62H35
Mots-clés : Review paper, Deformable template model, statistical analysis
Allassonnière, Stéphanie 1 ; Bigot, Jérémie 2 ; Glaunès, Joan Alexis 3 ; Maire, Florian 4 ; Richard, Frédéric J.P. 5

1 CMAP Ecole Polytechnique Route de Saclay 91128 Palaiseau FRANCE
2 Institut de Mathématiques de Toulouse, CNRS UMR 5219 Université de Toulouse 118 route de Narbonne 31062 Toulouse Cedex 9 FRANCE
3 MAP5 Université Paris Descartes, Sorbonne Paris Cité 45 rue des Saints-Pères 75270 Paris Cedex 06 FRANCE
4 ONERA - The French Aerospace Lab F-91761 Palaiseau FRANCE
5 LATP CNRS UMR 7353 Aix Marseille Université Centre de mathématiques et d’informatique 39 rue Frédéric Joliot 13453 Marseille Cedex FRANCE 
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Allassonnière, Stéphanie; Bigot, Jérémie; Glaunès, Joan Alexis; Maire, Florian; Richard, Frédéric J.P. Statistical models for deformable templates in image and shape analysis. Annales mathématiques Blaise Pascal, Tome 20 (2013) no. 1, pp. 1-35. doi : 10.5802/ambp.320. http://www.numdam.org/articles/10.5802/ambp.320/

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