FINITE-ELEMENT METHODS FOR ACTIVE CONTOUR MODELS AND BALLOONS FOR 2-DAND 3-D IMAGES

The use of energy-minimizing curves, known as ''snakes'' to extract fe atures of interest in images has been introduced by Kass, Witkin and T erzopoulos [23]. A balloon model was introduced in [12] as a way to ge neralize and solve some of the problems encountered with the original method. A 3-D generalization of the balloon model as a 3-D deformable surface, which evolves in 3-D images, is presented. It is deformed und er the action of internal and external forces attracting the surface t oward detected edgels by means of an attraction potential. We also sho w properties of energy-minimizing surfaces concerning their relationsh ip with 3-D edge points. To solve the minimization problem for a surfa ce, two simplified approaches are shown first, defining a 3-D surface as a series of 2-D planar curves. Then, after comparing finite-element method and finite-difference method in the 2-D problem, we solve the 3-D model using the finite-element method yielding greater stability a nd faster convergence. This model is applied for segmenting magnetic r esonance images.