# 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.

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:

60K35

Keywords: