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 L2 sense. Furthermore, the order of the
gradient flow partial differential equation is reduced when
employing the Sobolev metric rather than L2. 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 L2 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.

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