点云的形状与曲线重建算法

Shapes of Point Clouds and Curves Reconstruction

针对平面无序带噪点云的曲线重建问题,给出了点云形状的定义并提出了构造点云形状的算法.该算法基于Delaunay三角剖分,在构造好点云的Delaunay三角剖分后对三角剖分进行细化,使得在点云中的点周围形成空间上的局部均匀采样;基于集合论中的基本概念定义点云中内点、外点和边界点,并且明确地定义了点云的形状,根据Delaunay三角剖分细化时,选择不同的参数得到不同层次的点云的形状;选择合适的参数得到相应形状后,通过薄化过程得到具有流形结构的曲线.实验结果表明,采用文中算法得到的重建曲线很好地反映了点云的形状,验证了该算法的有效性.

For the curve reconstruction from irregular and noisy planar data clouds, appropriate shape definition and a reconstruction algorithm are given. Delaunay triangulation of point clouds is constructed and then refined such that it is uniformly sampled in the neighborhood of points. Inner points, outer points and boundary points are defined from the basic concept of set theory, and different level shapes of point clouds are also well-defined depending on the choices of parameter. The final reconstructed curve is obtained by thinning the shape with the appropriate parameter setting . The experimental results demonstrate the efficiency of our proposed algorithm.