网格划分在分子影像学中的应用

Mesh Generation on Optical Molecular Imaging

有限元是光学分子影像学分析的一个重要方法，网格划分是有限元方法的一个重要步骤，其中Delaunay划分是是众多网格划分方法中应用较为广泛的一种。本文主要介绍Delaunay、受限Delaunay网格划分特点以及逐点插入法和分治法两种划分算法。程序主要采用划分速度较快的分治法，并通过加入边界和改造不合格三角形来优化网格。

The finite element method is a popular method in optical molecular imaging. Mesh Generation is a process of splitting a physical domain into smaller sub-domains. And it is also an important procedure in finite element method. Delaunay triangulation is a characteristics method in variety of mesh triangulation methods. This paper introduces the characteristics of Delaunay and constructing Delaunay triangulations, and also mentions two constructing algorithms of incremental insertion algorithm and divide-and- conquer algorithm. The divide-and-conquer algorithm is used for constructing the mesh because of its fast speed. The methods of inserting boundaries and refining the mesh are also included for optimizing the meshes in this paper.