Area and Length Minimizing Flows for Shape Segmentation
A number of active contour models have been proposed which unify the curve
evolution framework with classical energy minimization techniques for
segmentation, such as 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. Recently the evolution equation
has been derived from first principles as the gradient flow that minimizes a
modified length functional, tailored to features such as edges. However,
because the flow may be slow to converge in practice, a constant (hyperbolic)
term is added to keep the curve/surface moving in the desired direction. In
this paper, we derive a modification of this term based on the gradient flow
derived from a weighted area functional, with image dependent weighting
factor. When combined with the earlier modified length gradient flow we
obtain a pde which offers a number of advantages, as illustrated by several
examples of shape segmentation on medical images. In many cases the weighted
area flow may be used on its own, with significant computational savings.