Deformable Models for 3D Medical Images using Finite Elements & Balloons∗

The use of energy-minimizing curves, known as “snakes” to extract features of interest in images has been introduced by Kass, Witkin and Terzopoulos [10]. A balloon model was introduced in [5] as a way to generalize and solve some of the problems encountered with the original method. We present a 3D generalization of the balloon model as a 3D deformable surface, which evolves in 3D images. It is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential. To solve the minimization problem for a surface, two simplified approaches are shown first, defining a 3D surface as a series of 2D planar curves. Then we solve the 3D model using the Finite Element Method yielding greater stability and faster convergence. We have applied this model for segmenting magnetic resonance images.