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SUMMARY:Discrete Varifolds\, Point Clouds\, and Surface Approximation - Si
 mon Masnou (Université de Lyon)
DTSTART:20151126T150000Z
DTEND:20151126T160000Z
UID:TALK58050@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:There are many models for the discrete approximations of a sur
 face: point clouds\, triangulated surfaces\, pixel or voxel approximations
 \, etc. We claim that it is possible to study these various approximations
  in a common setting using the notion of varifolds. Varifolds are tools fr
 om geometric measure theory which were introduced by Almgren in the contex
 t of Plateau's problem. They carry both spatial and tangential information
 s\, and they have nice properties in a variational context : compactness\,
  continuity of mass\, multiplicity information\, control of regularity\, a
 nd a generalized notion of mean curvature. The aforementioned approximatio
 ns can be associated with "discrete varifolds". The talk will be devoted t
 o approximation properties of such discrete varifolds\, to a notion of app
 roximated mean curvature for these objects\, and to the convergence proper
 ties of this approximated curvature. Numerical evaluations on various 2D a
 nd 3D point clouds will illustrate these notions. \nThis is joint work wit
 h Blanche Buet and Gian Paolo Leonardi.
LOCATION:MR 14\, CMS
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