Schwartz Peter, Adalsteinsson David, Colella Phillip, Arkin Adam Paul, Onsum Matthew
Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
Proc Natl Acad Sci U S A. 2005 Aug 9;102(32):11151-6. doi: 10.1073/pnas.0504953102. Epub 2005 Aug 2.
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.
我们提出了一种用于计算从图像数据导出的曲面上扩散输运的数值方法。我们的底层离散化方法使用笛卡尔网格嵌入边界方法来计算由距离曲面一小段距离的所有点组成的区域中的体积输运。我们通过基于水平集方法求解汉密尔顿-雅可比方程和程函方程的前沿传播计算，从图像数据中获得该区域的表示。我们证明该方法在空间和时间上具有二阶精度，并且能够在从细胞图像数据获得的复杂曲面几何形状上计算解。
