A number of active contour models have been proposed which unify the
curve and surface evolution framework with classical energy
minimization techniques for segmentation, such as the use of
snakes. The essential idea is to evolve a curve (in 2D) or a surface
(in 3D) under constraints from image forces so that it clings to
features of interest in an intensity image. In this talk I provide a
theoretical motivation for such equations, by deriving them as
gradient flows which minimize a particular length or area functional
(in 2D) or a surface area or volume functional (in 3D). The new flows
offer a number of theoretical and practical advantages over earlier
methods, as illustrated by segmentation results on CT and MRI medical
images.
[Joint work with Yves Berube Lauziere, Allen Tannenbaum and Steven W. Zucker]