基于流形学习的三维空间数据网格剖分方法

摘要

三维空间数据的三角网格剖分实质是寻找嵌入在三维空间中的二维流形,通过建立流形学习与网格剖分的本质联系,提出基于流形学习的空间数据网格剖分方法.依据流形学习的重构误差准则,实现三维空间数据的维数约简;对生成的二维数据按照Delaunay准则划分;将二维数据之间的拓扑关系映射到对应的三维数据点集.相对于其它数据降维方法,流形学习更能保持数据之间的本质联系,使重构的三角网格与物体表面拓扑差异性更小.实验表明,该方法对于非同胚于球物体的表面重建能够取得良好的效果.%The way of triangulating spatial points based on manifold study is advanced in this paper. According to the theory of manifold, spatial points is the measurement result of a certain 2D manifold in 3D space, so the process of triangulation is to search 2D manifold substantively. Therefore,the paper divides triangulating spatial points into three steps. The first step is to decrease the dimension of paints on basis of the correlative relation among points within a certain distance and the condition of minimizing the reconstruction error.The second step is to carry out Delaunay partition for points on plane. At last, the topology connection relation is mapped to 3D spatial points. The result is that the difference between the triangle net and object' s surface achieves minimum practicality.This way can be easily acknowledged, reduces complication and diminish the diversity in triangulation. Many experiments show the method provided in paper can achieve good result for objects which are not homeomorphism to sphere by choosing appropriate method of manifold study and neighborhoods.