Numerical computation of diffusion on a surface
Numerical computation of diffusion on a surface
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DOI：
10.1073/pnas.0504953102
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发表时间：
2005-08-09
影响因子：
11.1
通讯作者：
Onsum, M
中科院分区：
文献类型：
--
作者：
Schwartz, P;Adalsteinsson, D;Onsum, M
我们提出了一种数值方法来计算由图像数据得到的表面上的扩散输运。我们的基本离散化方法使用笛卡尔网格嵌入边界方法来计算由距离表面很小的所有点组成的区域内的体积输运。我们使用基于水平集方法的波前传播计算从图像数据中获得该区域的表示，用于求解哈密顿-雅可比方程和Eikonal方程。我们证明了该方法在空间和时间上是二阶精度的，并且能够计算从细胞图像数据获得的复杂曲面几何形状的解。
We present a numerical method for computing diffusive transport on a surface derived from image data. Our underlying discretization method uses a Cartesian grid embedded boundary method for computing the volume transport in a region consisting of all points a small distance from the surface. We obtain a representation of this region from image data by using a front propagation computation based on level set methods for solving the Hamilton-Jacobi and eikonal equations. We demonstrate that the method is second-order accurate in space and time and is capable of computing solutions on complex surface geometries obtained from image data of cells.