AREA AND LENGTH MINIMIZING FLOWS FOR SHAPE SEGMENTATION

A number of active contour models have been proposed that unify the cu rve evolution framework with classical energy minimization techniques for segmentation, such as snakes, The essential idea is to evolve a cu rve (in two dimensions) or a surface (in three dimensions) under const raints 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 dow that minimizes a modified le ngth functional, tailored to features such as edges, However, because the how may be slow to converge in practice, a constant (hyperbolic) t erm 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 gr adient how derived from a weighted area functional, with image depende nt weighting factor, When combined with the earlier modified Length gr adient dow, we obtain a partial differential equation (PDE) that offer s a number of advantages, as illustrated by several examples of shape segmentation on medical images. In many cases the weighted area how ma y be used on its own, with significant computational savings.