论文标题
在平均曲率的运动中值过滤器上
On Median Filters for Motion by Mean Curvature
论文作者
论文摘要
中值滤波器方案是通过平均曲率进行运动设定公式的优雅单调离散化。事实证明，它可以通过另一类称为阈值动力学的方法来发展初始条件的每个级别集。换句话说，中值过滤器是阈值动力学算法的自然级别设置版本。利用这种连接，我们根据阈值动力学方法的最新进展来重新访问中值过滤器。特别是，我们给出了中位过滤器的lyapunov函数的变异表述，从而产生了基于能量的无条件稳定性。该连接还可以在网络平均曲率流的多相设置中产生中值过滤器的类似物。这些新的多相设置方法不需要频繁的重新段落，并且可以适应各种表面紧张局势。
The median filter scheme is an elegant, monotone discretization of the level set formulation of motion by mean curvature. It turns out to evolve every level set of the initial condition precisely by another class of methods known as threshold dynamics. Median filters are, in other words, the natural level set versions of threshold dynamics algorithms. Exploiting this connection, we revisit median filters in light of recent progress on the threshold dynamics method. In particular, we give a variational formulation of, and exhibit a Lyapunov function for, median filters, resulting in energy based unconditional stability properties. The connection also yields analogues of median filters in the multiphase setting of mean curvature flow of networks. These new multiphase level set methods do not require frequent redistancing, and can accommodate a wide range of surface tensions.
