# Sobolev active contours as alternatives to higher-order flows

Thursday, March 26, 2009 - 10:00am - 10:45am

EE/CS 3-180

Anthony Yezzi (Georgia Institute of Technology)

We discuss the use of geometric (i.e. formulated exclusively

in terms of a curve's arclength parameter) Sobolev metrics to

devise new gradient flows of curves. We refer to the resulting

evolving contours as Sobolev Active Contours. An interesting

property of Sobolev gradient flows is that they stabilize many

gradient descent processes that are unstable when formulated in

the more traditional L

^{2}sense. Furthermore, the order of the

gradient flow partial differential equation is reduced when

employing the Sobolev metric rather than L

^{2}. This greatly

facilitates numerical implementation methods since higher order

PDE's are replaced by lower order integral-differential PDE's

to minimize the exact same geometric energy functional. The

fourth order L

^{2}gradient flow for the elastic energy of a

curve, for example, is substituted by a second order Sobolev

gradient flow for the same energy. In this talk we give some

background on Sobolev active contours, show some applications

using energy regularizers normally connected with fourth order

flows, and present some recent results in visual tracking.

Joint work with Ganesh Sundaramoorthi, Andrea Mennucci, Guillermo Sapiro, and Stefano Soatto.

MSC Code:

46E39

Keywords: