# 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

curve.

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

Daoudi)

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

curve.

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

Daoudi)

MSC Code:

60K35

Keywords: