Diffeomorphisms and active contours

Monday, October 5, 2009 - 11:30am - 12:00pm
Lind 305
Laurent Younes (Johns Hopkins University)
Keywords: Shape evolution; Shape spaces; Active contours; Riemannian metrics on diffeomorphisms

We present a geometric flow approach to the segmentation of two- three- dimensional shapes
by minimizing a cost function similar to the ones used with geometric active contours or to the
Chan-Vese approach. Our goal, well-adapted to many shape segmentation problems, including
those arising from medical images, is to ensure that the evolving contour or surface remains
smooth and diffeomorphic to its initial position over time.

This is formulated as a variational problem in a group of diffeomorphisms equipped with a
right-invariant Riemannian metric. A resulting gradient descent algorithm is used, with an
interesting variant that constrains the velocity in shape space to belong in a finite dimensional
space determined by time-dependent control points.

Experimental results with 2D and 3D shapes will be presented.

MSC Code: