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SUMMARY:The geometry of the Riemannian manifold of Landmark points\, with 
 applications to Medical Imaging - Micheli\, M (University of California\, 
 Los Angeles)
DTSTART:20110826T104500Z
DTEND:20110826T113000Z
UID:TALK32508@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In the past few years there has been a growing interest\, in d
 iverse scientific communities\, in endowing Shape Spaces with Riemannian m
 etrics\, so to be able to measure similarities between shapes and perform 
 statistical analysis on data sets (e.g. for object recognition\, target de
 tection and tracking\, classification\, and automated medical diagnostics)
 .\n\nThe knowledge of curvature on a Riemannian manifold is essential in t
 hat it allows one to infer about the existence of conjugate points\, the b
 ehavior of geodesic curves\, the well-posedness of the problem of computin
 g the implicit mean (and higher statistical moments) of samples on the man
 ifold\, and more. In shape analysis such issues are of fundamental importa
 nce since they allow one to build templates\, i.e. shape classes that repr
 esent typical situations in different applications (e.g. in the field of c
 omputational anatomy).\n\nThe actual differential geometry of Shape Spaces
  has started to emerge only very recently: in this talk we will explore th
 e sectional curvature for the Shape Space of landmark points\, endowed wit
 h the Riemannian metric induced by the action of a diffeomorphism group.\n
 Applications to Medical Imaging will be discussed and numerical results wi
 ll be shown.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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