Statistical models for deformable templates in image and shape analysis

Allassonnière, Stéphanie; Bigot, Jérémie; Glaunès, Joan Alexis; Maire, Florian; Richard, Frédéric J.P.

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.

Classification : 62H12, 62H30, 62H35
Mots clés : Review paper, Deformable template model, statistical analysis

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