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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Graph Methods for Manifold-valued Data - Daniel Te
nbrinck (Universität Münster)
DTSTART;TZID=Europe/London:20171020T100000
DTEND;TZID=Europe/London:20171020T110000
UID:TALK89491AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/89491
DESCRIPTION:Next to traditional processing tasks there exist r
eal applications in which measured data are not in
a Euclidean vector space but rather are given on
a Riemannian manifold. This is the case\, e.g.\, w
hen dealing with Interferometric Synthetic Apertur
e Radar (InSAR) data consisting of phase values or
data obtained in Diffusion Tensor Magnetic Resona
nce Imaging (DT-MRI). In this talk we present a f
ramework for processing discrete manifold-valued d
ata\, for which the underlying (sampling) topology
is modeled by a graph. We introduce the notion of
a manifold-valued derivative on a graph and based
on this deduce a family of manifold-valued graph
operators. In particular\, we introduce the graph
p-Laplacian and graph infinity-Laplacian for manif
old-valued data. We discuss a simple numerical sch
eme to compute a solution to the corresponding par
abolic PDEs and apply this algorithm to different
manifold-valued data\, illustrating the diversity
and flexibility of the proposed framework in denoi
sing and inpainting applications. This is joint w
ork with Dr. Ronny Bergmann (TU Kaiserslautern).
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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