基于采样点曲面重构的拓扑算法的研究

A Topological Approach Research on Surface Reconstruction from Sample Points

针对带噪声点的点云数据提出了一种曲面重构的新算法,称为TSR Topological Surface Reconstructor(拓扑曲面重构算法).这种算法避免了在很多重构算法中一般使用的如单元格标记以及距离函数近似的大量计算.定义在Delaunay四面体拓扑元素中的一个离散的Morse函数可以计算一个算法所使用的离散的梯度域,决定哪些面属于多面近似.离散Morse理论为该种方法提供了基础,它为算法提供了一个拓扑框架来导出一个曲面的分段线性近似.最后提供了一些重构的结果,并把TSR的性能与其它某些点集重构算法进行了比较.

We described the proposed approach and introduced the reconstruction algorithm from sample points, called TSR topological surface reconstruction. This algorithm may avoid considerable computation typically employed in many reconstruction algorithms. Discrete Morse theory offers the fundamentals for such an approach, providing a topological framework for an algorithm to derive a piecewise linear approximation of the surface. A discrete Morse function defined on the topological elements of the Delaanay tessellation allows computing a discrete gradient field used by the algorithm to decide which faces belong to the polyhedral approximation. This topological approach towards reconstruction results in a low - cost and robust algorithm capable of handling multiple components and cavities. At last some rec.onstruction results are presented and the performance of TSR is compared with that of other reconstruction approaches for some standard point sets.