BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Geometric Structures for Statistics on Shapes and Deformations in 
 Computational Anatomy
DTSTART:20131009T171500
DTEND:20131009T180000
DTSTAMP:20260407T175747Z
UID:88eea9bfb1c081f2079abf04f15e5436358a2fff259a2db7d3f27faa
CATEGORIES:Conferences - Seminars
DESCRIPTION:Xavier Pennec (INRIA Sophia Antipolis)\nHamiltonian Dynamics S
 eminar\nAbstract: Computational anatomy is an emerging discipline at the i
 nterface of geometry\, statistics\, image analysis and medicine that aims 
 at analysing and modelling the biological variability of the organs shapes
  at the population level. The goal is to model the mean anatomy and its no
 rmal variation among a population and to discover morphological difference
 s between normal and pathological populations. For instance\, the analysis
  of population-wise structural brain changes with aging in Alzheimer's dis
 ease requires first the analysis of longitudinal morphological changes for
  a specific subject. This can be evaluated through the non-rigid registrat
 ion. Second\, To perform a longitudinal group-wise analysis\, the subject-
 specific longitudinal trajectories need to be transported in a common refe
 rence (using some parallel transport).\nTo reach this goal\, one needs to 
 design a consistent statistical framework on manifolds and Lie groups. The
  geometric structure considered so far was that of metric and more special
 ly Riemannian geometry. Roughly speaking\, the main steps are to redefine 
 the mean as the minimizer of an intrinsic quantity: the Riemannian squared
  distance to the data points. When the Fréchet mean is determined\, one c
 an pull back the distribution on the tangent space at the mean to define h
 igher order moments like the covariance matrix.\nIn the context of medical
  shape analysis\, the powerful framework of Riemannian (right) invariant m
 etric on groups of diffeomorphisms (aka LDDMM) has often been investigated
  for such analyses in computational anatomy. In parallel\, efficient image
  registration methods and discrete parallel transport methods based on dif
 feomorphisms parameterized by stationary velocity fields (SVF) (DARTEL\, l
 og-demons\, Schild's ladder etc) have been developed with a great success 
 from the practical point of view but with less theoretical support.\nIn th
 is talk\, I will detail the Riemannian framework for geometric statistics 
 and partially extend if to affine connection spaces and more particularly 
 to Lie groups provided with the canonical Cartan-Schouten connection (a no
 n-metric connection). In finite dimension\, this provides strong theoretic
 al bases for the use of one-parameter subgroups. The generalization to inf
 inite dimensions would grounds the SVF-framework. From the practical point
  of view\, we show that it leads to quite simple and very efficient models
  of atrophy of the brain in Alzheimer's disease.
LOCATION:A A3 31 http://plan.epfl.ch/?room=MA%20A3%2031
STATUS:CONFIRMED
END:VEVENT
END:VCALENDAR