FINITE-ELEMENT METHODS FOR ACTIVE CONTOUR MODELS AND BALLOONS FOR 2-D AND 3-D IMAGES
FINITE-ELEMENT METHODS FOR ACTIVE CONTOUR MODELS AND BALLOONS FOR 2-D AND 3-D IMAGES
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DOI：
10.1109/34.244675
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发表时间：
1993-11-01
影响因子：
23.6
通讯作者：
COHEN, I
中科院分区：
文献类型：
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作者：
COHEN, LD;COHEN, I
Kass、Witkin和Terzopoulos [23]介绍了使用能量最小化曲线（称为“蛇"）来提取图像中感兴趣的特征。在[12]中引入了气球模型，作为推广和解决原始方法遇到的一些问题的方法。一个三维推广的气球模型作为一个3-D的可变形的表面，它在3-D图像的演变，提出。它在内部和外部力的作用下变形，通过吸引势将表面吸引向检测到的边缘凝胶。我们还展示了能量最小化曲面与3-D边缘点的关系。为了解决曲面的最小化问题，首先给出了两种简化的方法，将三维曲面定义为一系列二维平面曲线。然后，在比较了有限元法和有限差分法在二维问题中的应用后，我们采用有限元法求解三维模型，得到了更好的稳定性和更快的收敛速度。该模型适用于分割磁共振图像。
The use of energy-minimizing curves, known as ''snakes'' to extract features of interest in images has been introduced by Kass, Witkin and Terzopoulos [23]. A balloon model was introduced in [12] as a way to generalize 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 under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential. We also show properties of energy-minimizing surfaces concerning their relationship with 3-D edge points. To solve the minimization problem for a surface, 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 and faster convergence. This model is applied for segmenting magnetic resonance images.