Statistics of Shape: Simple Statistics on Interesting Spaces

Wednesday, April 5, 2006 - 1:30pm - 2:30pm
EE/CS 3-180
Sarang Joshi (University of North Carolina, Chapel Hill)
A primary goal of Computational Anatomy is the statistical
analysis of anatomical variability. A
natural question that arises is how dose one define the image of an Average
Anatomy given a collection of anatomical images. Such
an average image must represent the intrinsic geometric anatomical variability
present. Large Deformation Diffeomorphic
transformations have been shown to accommodate the geometric variability but
performing statistics of Diffeomorphic transformations remains a challenge. Standard
techniques for computing statistical descriptions such as mean and principal component
analysis only work for data lying in a Euclidean vector space. In this talk, using
the Riemannian metric theory the ideas of mean and covariance estimation will
be extended to non-linear curved spaces, in particular for finite dimensional Lie-Groups
and the space of Diffeomorphisms transformations. The covariance estimation problem on
Riemannian manifolds is posed as a metric estimation problem. Algorithms for estimating the Average
Anatomical image as well as for estimating the second order geometrical variability
will be presented.
MSC Code: