基于三角网格的离散曲率计算方法研究

发布时间：2018-04-15 13:58

本文选题：点云 + 离散曲率　；参考：《扬州大学》2016年硕士论文

【摘要】：随着三维光学测量技术的快速发展,三维激光扫描仪在航空航天、汽车、家电、服装鞋帽、家具、玩具、医学修复、文物修复、考古、刑侦等领域得到了普及应用,大规模离散数据的处理越来越重要,其中基于点云离散曲率研究冗余数据精简、噪声去除成为近年来的热点。本文针对点云离散曲率计算方法存在精度不高、稳定性不好的问题,研究提高点云离散曲率计算精度和稳定性的方法,并将设计的点云离散曲率计算方法应用于实际扫描测量数据的光顺处理。论文以微分几何为理论基础,系统地研究了点云离散曲率的计算方法,通过球面、柱面、马鞍面不同间隔的采样数据,用曲面理论计算曲率与经典点云离散曲率计算方法的结果进行对比分析,发现目前应用于数据处理的主流离散曲率计算方法的计算结果差异较大、稳定性不好。论文基于离散点云生成的三角网格模型,首先定义三角形中最大角与最小角的余弦差作为三角形形状规整度的判定因子,采用球面为采样对象,通过Mayer算法计算三角面片不同规整程度下曲率的误差,来研究网格中三角面片的规整程度对曲率计算的影响,然后对马鞍面进行不同采样间隔的采样,通过离散曲率计算误差的对比,分析采样间隔对离散曲率计算的影响。论文通过引入三角面片的形状规整度,对Voronoi区域的面积计算进行了改进,设计并实现了Mayer改进算法,将该算法应用于球面、柱面、抛物面、马鞍面的曲率计算,实验结果表明该算法有效提高了点云离散曲率计算的精度和稳定性。论文将改进的算法应用于实际扫描测量数据的光顺处理,通过对离散点云数据局部形状特征的分析,设计了基于离散曲率的光顺去噪算法,利用平均曲率阈值提取曲率大的边缘特征点和噪声点,快速判别点云数据的特征点。实际处理结果表明改进后的算法不仅能够识别出测量物体的边缘轮廓而且也能较好地处理物体表面的细节特征,达到了在去除噪声、获取离散曲面更高阶光滑的同时,保持曲面固有几何特征的目的。论文的研究成果已与实验室自主开发的三维激光扫描测量软件集成,应用于实际扫描测量数据的处理,较好地解决了冗余数据精简和噪声去除的问题,得到了企业的认可,有利于激光扫描测量技术的推广普及。
[Abstract]:With the rapid development of 3D optical measurement technology, 3D laser scanner has been widely used in the fields of aerospace, automobile, household appliances, clothing, shoes and hats, furniture, toys, medical restoration, cultural relic restoration, archaeology, criminal investigation and so on.The processing of large-scale discrete data is becoming more and more important, among which the redundant data based on point cloud discrete curvature is simplified, and noise removal has become a hot topic in recent years.In this paper, the method to improve the accuracy and stability of point cloud discrete curvature calculation method is studied to solve the problem of low accuracy and poor stability.The point cloud discrete curvature calculation method is applied to the fairing of the actual scanning measurement data.Based on the theory of differential geometry, the method of calculating discrete curvature of point cloud is studied systematically in this paper. The sampling data of spherical surface, cylinder surface and saddle surface are sampled at different intervals.The results of surface theory and classical point cloud discrete curvature calculation are compared and analyzed. It is found that the results of the current mainstream discrete curvature calculation methods used in data processing are quite different and the stability is not good.In this paper, based on the triangular mesh model generated by discrete point cloud, the cosine difference between the maximum angle and the minimum angle in the triangle is defined as the judgement factor of the shape regularity of the triangle, and the spherical surface is used as the sampling object.Mayer algorithm is used to calculate the curvature error in different degree of triangulation, to study the effect of triangulation degree on curvature calculation, and then to sample saddle surface with different sampling intervals.By comparing the error of discrete curvature calculation, the influence of sampling interval on discrete curvature calculation is analyzed.In this paper, by introducing the shape regularity of triangular surface, the area calculation of Voronoi region is improved, and the improved Mayer algorithm is designed and implemented. The algorithm is applied to the curvature calculation of spherical, cylindrical, parabolic and saddle surfaces.Experimental results show that the algorithm improves the accuracy and stability of point cloud discrete curvature calculation.In this paper, the improved algorithm is applied to the fairing processing of the actual scanning measurement data. Based on the analysis of the local shape characteristics of the discrete point cloud data, a smoothing denoising algorithm based on discrete curvature is designed.The edge feature points and noise points with large curvature are extracted by the mean curvature threshold, and the feature points of point cloud data are quickly identified.The actual processing results show that the improved algorithm can not only recognize the edge contour of the measured object, but also deal with the detailed features of the surface of the object. It can remove the noise and obtain the higher order smooth surface of the discrete surface at the same time.The purpose of preserving the inherent geometric characteristics of a surface.The research results of this paper have been integrated with the 3D laser scanning measurement software developed by the laboratory, which has been applied to the processing of the actual scanning measurement data, which has solved the problems of redundant data reduction and noise removal, and has been recognized by the enterprise.It is beneficial to the popularization of laser scanning measurement technology.
【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O186.1

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