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中文摘要：
Level Set模型将运动界面表示为高维场函数的零等值面，自然而鲁棒地解决了界面演化中拓扑结构改变的问题，但计算效率不高．文中提出了基于窄带的自适应Level Set方法．自适应方法首先构建粗网格满足界面演化的整体需求，同时估算粗网格点的曲率值，使用快速扩散法聚类高曲率点，通过主元分析估算点集朝向，构建细网格捕捉演化中的细节区域．粗、细网格均为独茫的计算单元，定义为存储网格中的有向包围盒．这种数据结构可以有效避免频繁的坐标变换和插值操作，同时保证了数值解的精度．实验结果与误差分析表明，自适应方法能有效减少计算量，达到更好的界面跟踪效果．
英文摘要：
Level Set method traces interface evolution naturally by embedding it into a higher dimensional field function. However the computational cost is high in general. In this paper, an adaptive solution based on narrow band method is proposed to solve the Level Set equation effi ciently. A coarse resolution grid is built for the global evolution, meanwhile grid points with high curvature are detected and clustered using fast diffusion method. By evaluating the orientation of each cluster through PCA, a corresponding fine resolution grid is built for each cluster to capture details on the interface. Both coarse and fine grids are defined as the orientated bound boxes over a global grid and they are independent computing units. Numerical solutions of the Level Sel equation are conducted on them independently and the numerical results are merged at every time step. Thus, the Level Set evolution is performed on both coarse and fine resolution grids adaptively. A simple but efficient data structure is proposed to avoid frequent operations of coordinate transformations and data interpolations. Implementation results and error analysis show that the adaptive method has advantages on computational efficiency and accuracy.
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