A direct method for solving an anisotropic mean curvature flow of plane curves with an external force
A direct method for solving an anisotropic mean curvature flow of plane curves with an external force
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DOI：
10.1002/mma.514
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发表时间：
2004-09
影响因子：
2.9
通讯作者：
K. Mikula;D. Ševčovič
中科院分区：
文献类型：
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作者：
K. Mikula;D. Ševčovič
提出了一种求解满足几何方程v=β（x，k，ν）的平面曲线演化的新方法，其中v是法向速度，k和ν是平面曲线在x∈Γ点处的曲率和切向角。我们推导出一个控制系统的偏微分方程的曲率，切角，当地的长度和位置向量的一个不断发展的家庭的平面曲线和证明当地的时间存在的经典解决方案。这些方程包括一个非平凡的切向速度泛函，控制网格点的均匀重新分布，从而防止数值计算的解形成各种不稳定性。我们离散的控制系统的方程，以找到一个数值解的二维各向异性界面运动和图像分割问题。版权所有© 2004年约翰威利父子有限公司。
A new method for solution of the evolution of plane curves satisfying the geometric equation v=β(x,k,ν), where v is the normal velocity, k and ν are the curvature and tangential angle of a plane curve Γ ⊂ ℝ2 at the point x∈Γ, is proposed. We derive a governing system of partial differential equations for the curvature, tangential angle, local length and position vector of an evolving family of plane curves and prove local in time existence of a classical solution. These equations include a non‐trivial tangential velocity functional governing a uniform redistribution of grid points and thus preventing numerically computed solutions from forming various instabilities. We discretize the governing system of equations in order to find a numerical solution for 2D anisotropic interface motions and image segmentation problems. Copyright © 2004 John Wiley & Sons, Ltd.