两种简化标准Marching Cubes算法拓扑构形的方法

通过沿插值边移动等值点,提出了两种方法来简化标准MarchingCubes算法的拓扑构形。其一是将等值点移动到高于阈值的立方体顶点位置,其二是将等值点移动到低于阈值的立方体顶点位置。结果发现,这两种移动方式均可简化等值面的拓扑构形,明显减少重建三角片的数量,避免对等值点位置和法向量的插值计算,显著缩短重建时间。由于等值点的移动量不超过体素立方体的1个边长,这对于高分辨率图像数据集是可以忽略的。

Two Methods for Simplifying Topological Configurations of Standard Marching Cubes Algorithm

By changing the vertex positions of the extracted isosurfaces, two sets of patterns were proposed to simplify the standard Marching Cubes (MC) algorithm. The new patterns are constructed by moving the vertices on the isosurface along the cube edges from the interpolation points as in the MC method to either the corresponding cube vertices above the isovalue, or those below the isovalue. Topological analyses and reconstruction experiments show that such changes in vertex positions can simplify the triangulation patterns, considerably reduce the extracted triangles, omit the interpolation calculations for vertex positions and normal factors, and remarkably shorten the reconstruction time, in comparison with the standard MC approach. The position changes are within one pixel, and might be negligible for high-resolution datasets.