A binary level set model and some applications to Mumford-Shah image segmentation
A binary level set model and some applications to Mumford-Shah image segmentation
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DOI：
10.1109/tip.2005.863956
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发表时间：
2006-05-01
影响因子：
10.6
通讯作者：
Tai, XC
中科院分区：
文献类型：
--
作者：
Lie, J;Lysaker, M;Tai, XC
本文提出了一种基于pde的水平集方法。传统上，接口由连续水平集函数的零水平集表示。相反，我们让接口用分段常数水平集函数的不连续表示。每个水平集函数在收敛时只能取两个值，即只能取1或- 1；因此，我们的方法与相场方法有关。提出的方法保留了标准水平集方法的一些特性，而另一些则没有。用这种新方法求解界面问题，我们需要在二次约束下求光滑凸泛函的最小值。水平集函数在收敛处是不连续的，但最小化泛函是光滑的。我们展示了用该方法分割数字图像的数值结果。
In this paper, we propose a PDE-based level set method. Traditionally, interfaces are represented by the zero level set of continuous level set functions. Instead, we let the interfaces be represented by discontinuities of piecewise constant level set functions. Each level set function can at convergence only take two values, i.e., it can only be 1 or - 1; thus, our method is related to phase-field methods. Some of the properties of standard level set methods are preserved in the proposed method, while others are not. Using this new method for interface problems, we need to minimize a smooth convex functional under a quadratic constraint. The level set functions are discontinuous at convergence, but the minimization functional is smooth. We show numerical results using the method for segmentation of digital images.