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UID:5494@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20130307T140000
DTEND;TZID=Europe/Paris:20130307T150000
DTSTAMP:20241028T220535Z
URL:https://www.i2m.univ-amu.fr/evenements/j-lefevre-lsis-harmonic-analysi
 s-on-manifolds-recent-applications-in-neuroimaging-data/
SUMMARY: (...): J. Lefèvre (LSIS): Harmonic analysis on manifolds: recent 
 applications in neuroimaging data
DESCRIPTION:: Harmonic analysis on manifolds: recent applications in neuroi
 maging data By Julien Lefèvre\, LSIS.\n\nThis talk aims at introducing so
 me mathematical tools of harmonic analysis on non-euclidian domains\, typi
 cally Riemannian manifolds\, and to show illustrative applications for sur
 faces in R^3. In parallel I will refer to a discrete version of this frame
 work by considering graph laplacian.\n\nFirst\, I will present classical r
 esults on eigenfunctions of Laplace-Beltrami operator\, sometimes called M
 anifold harmonics in computer graphics community. These harmonics must be 
 seen as Fourier modes for an arbitrary domain that can be used for analysi
 s/synthesis of signals living on the manifold. Besides\, these modes revea
 l important properties related to the underlying geometry which are relate
 d to a famous question raised by Kac "can one hear the shape of a drum ?" 
 I will show also how to compute practically eigenfunctions and eigenvector
 s with Finite Elements Method in the case of triangulated meshes as well a
 s unstructured point clouds.\nIn a second part I will focus on possible ap
 plications of harmonic analysis for 3D surfaces such as geometric filterin
 g\, registration and clustering. Several topics in neuroanatomy will be ad
 dressed such as brain variability or cortical development. At last I will 
 present some open issues that have emerged from observation of data and th
 at can be formulated in terms of a mathematical conjecture.
CATEGORIES:Séminaire,Signal et Apprentissage
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