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UID:3271@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20130307T140000
DTEND;TZID=Europe/Paris:20130307T150000
DTSTAMP:20200826T075346Z
URL:https://www.i2m.univ-amu.fr/events/j-lefevre-lsis-harmonic-analysis-on
-manifolds-recent-applications-in-neuroimaging-data/
SUMMARY:J. Lefèvre (LSIS): Harmonic analysis on manifolds: recent applicat
ions in neuroimaging data -
DESCRIPTION:Harmonic analysis on manifolds: recent applications in neuroima
ging data By Julien Lefèvre\, LSIS.\n\nThis talk aims at introducing some
mathematical tools of harmonic analysis on non-euclidian domains\\\, typi
cally Riemannian manifolds\\\, and to show illustrative applications for s
urfaces in R^3. In parallel I will refer to a discrete version of this fra
mework by considering graph laplacian.\nFirst\\\, I will present classical
results on eigenfunctions of Laplace-Beltrami operator\\\, sometimes call
ed Manifold harmonics in computer graphics community. These harmonics must
be seen as Fourier modes for an arbitrary domain that can be used for ana
lysis/synthesis of signals living on the manifold. Besides\\\, these modes
reveal important properties related to the underlying geometry which are
related to a famous question raised by Kac "can one hear the shape of a dr
um ?" I will show also how to compute practically eigenfunctions and eigen
vectors with Finite Elements Method in the case of triangulated meshes as
well as unstructured point clouds.\nIn a second part I will focus on possi
ble applications of harmonic analysis for 3D surfaces such as geometric fi
ltering\\\, registration and clustering. Several topics in neuroanatomy wi
ll be addressed such as brain variability or cortical development. At last
I will present some open issues that have emerged from observation of dat
a and that can be formulated in terms of a mathematical conjecture.
CATEGORIES:Séminaire Signal et Apprentissage
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