样点邻域同构曲面约束的散乱点云曲率估计

梁增凯 1; 孙殿柱 1; 薄志成 1; 李延瑞 2; 林伟 1

doi:10.7652/xjtuxb201812008

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样点邻域同构曲面约束的散乱点云曲率估计

更新时间：2025-05-08

- 样点邻域同构曲面约束的散乱点云曲率估计
- An Estimation Method for Curvature of Unorganized Points Cloud Based on Local Isomorphic Surface
- 西安交通大学学报 2018年52卷第12期页码：50-56
- 作者机构：
  
  山东理工大学机械工程学院,山东,淄博,255049
- 作者简介：
- 基金信息：
  
  : 2018-06-26。作者简介: 梁增凯(1992-),男,硕士生;孙殿柱(通信作者),男,教授,博士生导师。基金项目: 国家自然科学基金资助项目(51575326);山东省自然科学基金资助项目(ZR2015EM031)
- DOI：10.7652/xjtuxb201812008
  中图分类号： TP391.72
- 网络首发：2018-12-10，
  
  纸质出版：2018
- 稿件说明：
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梁增凯 1, 孙殿柱 1, 薄志成 1, 等. 样点邻域同构曲面约束的散乱点云曲率估计[J]. 西安交通大学学报, 2018,52(12):50-56.

An Estimation Method for Curvature of Unorganized Points Cloud Based on Local Isomorphic Surface[J]. 2018, 52(12): 50-56.
梁增凯 1, 孙殿柱 1, 薄志成 1, 等. 样点邻域同构曲面约束的散乱点云曲率估计[J]. 西安交通大学学报, 2018,52(12):50-56. DOI： 10.7652/xjtuxb201812008.

An Estimation Method for Curvature of Unorganized Points Cloud Based on Local Isomorphic Surface[J]. 2018, 52(12): 50-56. DOI： 10.7652/xjtuxb201812008.

摘要

针对现有点云曲率估计算法难以兼顾估计结果的精度与稳健性问题

提出一种样点邻域同构曲面约束的散乱点云曲率估计算法。以目标样点的邻域点集作为局部样本

采用二维Delaunay网格剖分与三维Delaunay网格过滤相结合的策略对局部样本进行曲面重建

获得插值于采样点集并与原表面拓扑同构的局部网格曲面; 为稳健估计计算样点曲率所需的样点法向

通过局部网格曲面中顶点一阶邻域面的形状和尺寸确定邻域面法向的权重

以一阶邻域面法向的加权和作为法向估计结果; 基于网格曲面顶点一阶邻域面初步估计样点曲率

进而根据邻域样点与目标样点间测地距离对初步估计结果进行平滑修正获得最终曲率估计结果。实验结果表明

所提算法可有效反映曲面特征并兼顾样点曲率估计的精度和稳健性

实现样点曲率的平滑过渡; 相比于Meyer提出的Voronoi算法

所提算法对采样精度较高的点云数据可保证与其相当的计算精度

对存在噪声的点云数据计算精度和稳健性均可提高1～2倍。

Abstract

A precise curvature estimation algorithm based on local mesh reconstruction is presented to solve the problem that the existing curvature estimation algorithms for point clouds are difficult to achieve a trade-off between accuracy and robustness of estimation. A set of neighborhood points of the target sample is taken as the local sample. The strategy that combines the two-dimensional Delaunay mesh generation and the three-dimensional Delaunay mesh filtering is used to reconstruct a surface of the local sample and to obtain a local Delaunay mesh which interpolates on sampling points and is topologically equivalent to the original surface. In order to robustly estimate the normal direction of the sample points for calculating the curvature of the sample points

the weights of the normals of the first-order neighborhood patches of the vertex are determined by the shape and size of these patches in the local mesh surface

and the weighted summation of the normals of the first-order neighborhood patches is taken as the estimation result of the normal direction. A pre-estimation of curvature of sample points is obtained based on first-order neighborhood patches of sample points

and then the estimation results are modified according to the geodesic distance between neighborhood points and target point. Experimental results show that the proposed algorithm can effectively reflect the surface characteristics

take the accuracy and robustness of the sample curvature estimation into account

and realize the smooth transition of the sample curvature. Compared with the Voronoi algorithm proposed by Meyer

the proposed algorithm guarantees the calculation accuracy of point cloud with higher sampling accuracy

and improves the accuracy and robustness of point cloud with noise by 1-2 times.

关键词

Keywords

references

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