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 under the action of internal and external forces attracting the surface toward detected edge elements by means of an attraction potential. To solve the minimization problem for a surface, two simplified approaches are shown, defining a 3-D surface as a series of 2-D planar curves. Then the 3-D model is solved using the finite-element method, yielding greater stability and faster convergence. This model has been used to segment magnetic resonance images.
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