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SUMMARY:Discrete geodesic calculus in shape space - Martin Rumpf\, Institu
 te for Numerical Simulation\, University of Bonn
DTSTART:20111117T150000Z
DTEND:20111117T160000Z
UID:TALK33714@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:Based on a local approximation of the Riemannian distance on a
  manifold by a computationally cheap dissimilarity measure a time discrete
  geodesic calculus is developed and applications to shape space are explor
 ed.\nThereby\, the dissimilarity measure is derived from a spring type ene
 rgy whose Hessian reproduces the underlying Riemannian metric. Using this 
 measure to define length and energy on discrete paths on the manifold a di
 screte analog of classical geodesic calculus can be developed. \nThe notio
 n of discrete geodesics defined as energy minimizing paths gives rise to  
 discrete logarithmic and exponential maps and enables to introduce a time 
 discrete parallel transport as well.\nThe relation of this time discrete t
 o the actual\, time continuous Riemannian calculus is explored and the new
  concept is applied to a shape space in which shapes are considered as bou
 ndary contours of  physical objects consisting of viscous material. The fl
 exibility and computational efficiency of the approach is demonstrated for
  topology preserving morphing\, the interplay of paths in shape space and 
 local shape variations as associated generators\, the extrapolation of pat
 hs\, and the transfer of geometric features. 
LOCATION:MR14\, CMS
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