An Estimation Method for Curvature of Unorganized Points Cloud Based on Local Isomorphic Surface

doi:10.7652/xjtuxb201812008

您当前的位置：

首页 >

文章列表页 >

An Estimation Method for Curvature of Unorganized Points Cloud Based on Local Isomorphic Surface

更新时间：2025-05-08

- An Estimation Method for Curvature of Unorganized Points Cloud Based on Local Isomorphic Surface
- Vol. 52, Issue 12, Pages: 50-56(2018)
- 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：
- DOI：10.7652/xjtuxb201812008
  CLC： TP391.72
- Online First：10 December 2018，
  
  Published：2018
- 稿件说明：
移动端阅览
An Estimation Method for Curvature of Unorganized Points Cloud Based on Local Isomorphic Surface[J]. 2018, 52(12): 50-56.
DOI：

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

VÁA L, VAN CEK P, PRANTL M, et al. Mesh statistics for robust curvature estimation [J]. Computer Graphics Forum, 2016, 35(5): 271-280.

HOPPE H, DEROSE T, DUCHAMP T, et al. Surface reconstruction from unorganized points [J]. Computer Graphics, 1992, 26(2): 71-78.

QIU Yanjie, ZHOU Xionghui, YANG Pinghai, et al. Curvature estimation of point set data based on the moving-least square surface [J]. Journal of Shanghai Jiaotong University(Science), 2011, 16(4): 402-411.

王枭, 陈双敏, 陈叶芳, 等. 基于模板采样和MLS能函数的曲率计算 [J]. 计算机辅助设计与图形学学报, 2015(6): 1104-1109.

WANG Xiao, CHEN Shuangmin, et al. Computing curvature based on template sampling and MLS energy function [J]. Journal of Computer-Aided Design Computer Graphics, 2015(6): 1104-1109.

刘鹏鑫, 王扬, 刘璇. 反求工程中离散曲率估算方法 [J]. 吉林大学学报(工学版), 2011, 41(2): 479-483.

LIU Pengxin, WANG Yang, LIU Xuan. Discrete curvature estimation in reverse engineering [J]. Journal of Jilin(Engineering and Technology Edition), 2011, 41(2): 479-483.

NURUNNABI A, WEST G, BELTON D. Outlier detection and robust normal-curvature estimation in mobile laser scanning 3D point cloud data [J]. Pattern Recognition, 2015, 48(4): 1404-1419.

TAUBIN G. Estimating the tensor of curvature of a surface from a polyhedral approximation [C]∥IEEE International Conference on Computer Vision. Piscataway, NJ, USA: IEEE, 1995: 902-907.

MEYER M, DESBRUN M, SCHRODER P, et al. Discrete differential-geometry operators for triangulated 2-manifolds [J]. Visualization Mathematics, 2002, 3(8/9): 35-57.

YANG X, ZHENG J. Curvature tensor computation by piecewise surface interpolation [J]. Computer-Aided Design, 2013, 45(12): 1639-1650.

袁启明, 施侃乐, 雍俊海, 等. 曲面二阶几何连续性的混合曲率评价与可视化 [J]. 计算机辅助设计与图形学学报, 2011,(11): 1830-1837.

YUAN Qiming, SHI Kanle, YONG Junhai, et al. The mixed curvature and the G2 continuity visualization of surfaces [J]. Journal of Computer-Aided Design Computer Graphics, 2011(11): 1830-1837.

AMENTA N, CHOI S, DEY T K, et al. A simple algorithm for homeomorphic surface reconstruction [C]∥Proceedings of the sixteenth annual symposium on Computational Geometry. New York, USA: ACM, 2000: 213-222.

ZENG M, ZHAO F, ZHENG J, et al. Octree-based fusion for realtime 3D reconstruction [J]. Graphical Models, 2013, 75(3): 126-136.

MERRY B, GAIN J, MARAIS P. Accelerating kd-tree searches for all k-nearest neighbours [J]. Eurographics, 2013: 37-40.

孙殿柱, 王超, 刘华东, 等. 基于三角Bézier曲面平刀环切粗加工刀轨生成算法 [J]. 计算机集成制造系统, 2012, 10: 2191-2195.

SUN Dianzhu, WANG Chao, LIU Huadong, et al. Generating algorithm of contour-parallel rough tool-path for triangular Bezier surface [J]. Computer Integrated Manufacturing Systems, 2012, 18(10): 2191-2195.

孙殿柱, 康新才, 李延瑞, 等. 三角Bézier曲面粗加工刀轨生成算法 [J]. 西安交通大学学报, 2011, 45(3): 70-74.

SUN Dianzhu, KANG Xincai, LI Yanrui, et al. Algorithm for generating rough tool-path based on triangular Bézier surface [J]. Journal of Xian Jiaotong University, 2011, 45(3): 70-74.

BAUER R, DELLING D, SANDERS P, et al. Combining hierarchical and goal-directed speed-up techniques for Dijkstra's algorithm [J]. Journal of Experimental Algorithmics, 2010, 15(3): 1-31.

孙殿柱, 魏亮, 李延瑞, 等. 基于局部样本增益优化的α-shape曲面拓扑重建 [J]. 机械工程学报, 2016, 52(3): 136-142.

SUN Dianzhu, WEI Liang, LI Yanrui, et al. Surface reconstruction with α-shape曲面拓扑重建 [J]. 机械工程学报, 2016, 52(3): 136-142.

SUN Dianzhu, WEI Liang, LI Yanrui, et al. Surface reconstruction with ape based on optimization of surface local sample [J]. Journal of Mechanical Engineering, 2016, 52(3): 136-142.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Integrated and Joint Design Optimization of Centrifugal Compressor Impeller and Casing Treatment at Multiple Working Points

A Structure-Semantics-Residual Collaborative Image Compression Framework：Towards Privacy Protection and High-Fidelity Reconstruction

A Fast Calculation Method for Thermal Flow Fields in Transformer Windings Based on PI-DeepONet

Sensitivity Analysis of Foil Geometrical Parameters for the Third-Generation CO2 Gas Foil Bearings Based on Design of Experiments Method

Research on the Electrohydrodynamic Effects of Ionic Liquid-Modified Fuels

Related Author

No data

Related Institution

No data

⁰