Séminaire Brillouin: Sciences Géométriques de l'Information

11 Octobre 2012

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Catégorie : Journée d étude

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Orateur: Alain Trouvé (ENS CACHAN, CMLA)

Titre : Coding shape information from a shape space point of view.

Résumé : In different setting ranging from image processing to medical or biological imaging, various kind of geometrical objects, called hereafter generically as shapes, are emerging and need to be described and processed as infinite dimensional variables. The basic idea of shape space is to put the focus on building proper structure on shapes considered as an ensemble of objects that should be organised as an infinite dimensional smooth manifold. This talk will give a quick overview of what has been be done in this direction through the use of action of groups of diffeomorphisms and mainly right invariant distances. We will show that simple ideas coming from Riemannian geometry can be recast in the shape setting providing a range of practical tools as well as challenging questions in geometry, probability and statistics.

Orateur : Stanley Durrleman (ICM et INRIA)

Titre : Anatomy and statistics.

Résumé : Group studies in neuroimaging raise the need for statistical methods to find (in)variants in large data sets of anatomical structures. In this talk, we will present a generic statistical framework that can deal with 3D structural images as well as shapes segmented from images such as white matter fiber tracts, meshes of the cortical structures, sulcal ribbons, etc. The mean is given as a typical anatomical configuration that captures the geometric invariants within the studied population. The variance is described by typical deformations of the mean configuration. The framework relies on the metric of large diffeomorphic deformations in an adaptive finite-dimensional setting. Extension of this framework for the analysis of longitudinal shape data sets will be also presented. The talk will be illustrated by various examples taken from neuroanatomical studies.