Statistical Analysis of Shapes of 2D Curves, 3D Curves, and Facial<br/><br/>Surfaces

Tuesday, April 4, 2006 - 4:00pm - 5:00pm
EE/CS 3-180
Anuj Srivastava (Florida State University)
Our previous work developed techniques for computing geodesics on
shape spaces of planar closed curves, first with and later without
restrictions to arc-length parameterizations. Using tangent
principal component analysis (TPCA), we have imposed probability
models on these spaces and have used them in Bayesian shape
estimation and classification of objects in images. Extending
these ideas to 3D problems, I will present a path-straightening
approach for computing geodesics between closed curves in R3. The
basic idea is to define a space of such closed curves, initialize
a path between the given two curves, and iteratively straighten it
using the gradient of an energy whose critical points are
geodesics. This computation of geodesics between 3D curves helps
analyze shapes of facial surfaces as follows. Using level sets of
smooth functions, we represent any surface as an indexed
collection of facial curves. We compare any two facial surfaces by
registering their facial curves, and by comparing shapes of
corresponding curves. Note that these facial curves are not
necessarily planar, and require tools for analyzing shapes of 3D

(This work is in collaboration with E. Klassen, C. Samir, and M.
MSC Code: