【作者】 胡国飞；

【导师】 彭群生；

【作者基本信息】 浙江大学 ， 计算机图形学， 2005， 博士

【摘要】 随着医学辅助诊断、航天模拟、工业设计、影视娱乐等等应用需求的推动,关于三维数据的获取和数字几何处理技术的研究越来越受到学者们的关注。实际上,近几年来三维模型获取的软硬件技术正不断深入,人们可以通过多种数据采样方法来获取现实物体的计算机表示,并对之进行预处理,加工,分析和应用。这种通过逆向工程来获取的三维数据主要包括CT数据(计算机断层成像)、MRI数据(核磁共振成像)以及三维非规则点模型和网格模型数据等。而本文主要研究对象是用三维扫描仪获取的三维点模型和网格模型数据,及其所涉及的数字几何处理技术包括三维扫描、参数化、去噪、重建等等。 在获取数据的过程中,因为人为的扰动或者扫描仪本身的缺陷使得生成三维数据往往带有噪声,从而使所获得的测量数据与实物存在一定的偏差。因此在对实测三维数据进行相关数字几何处理和应用之前必须对其进行去噪光顺。通常,光顺处理可以直接针对点数据,也可以针对经过网格化后的多边形数据。光顺的目标是在剔除噪声重建光滑表面的同时,保持采样表面原有的拓扑特征和几何特征不变,比如保证光顺过程中模型不收缩且无过光顺现象等。本文分别对点模型和三角网格模型的去噪光顺技术进行深入的研究,提出了一些创新的算法。主要内容包括: ·介绍了一些经典的三维离散数据模型的去噪光顺方法,着重分析了近年来提出的新方法,总结归纳了这些方法的基本原理以及它们的优缺点,结合作者在本领域的研究工作,对今后三维数据的去噪光顺的研究重点作一些分析。 ·针对具有单边界的三角网格或与球面同胚的零亏格封闭网格,提出了一种基于球面向量线性凸组合的三维网格球面参数化方法。然后基于这类凸组合参数化,对三维模型进行频谱分析以及滤波处理,特别地,设计了对模型光滑和增强等操作。 ·提出了一个基于三步顶点预测的特征保持的三角网格光顺算法。一方面利用了均值重心坐标来避免顶点预测时遇到的奇异情况,使算法更加鲁棒,另一方面,应用带均值重心坐标权的双边滤波器和准拉普拉斯光顺算子,通过三步预测顶点的坐标位置,更快速光顺模型,更有效地保持模型的几何特征。 ·提出了基于三维Meanshift过程的各向异性点模型去噪算法。主要考虑顶点法向和曲率作为特征空间分量,顶点坐标值作为空间分量,通过Meanshift过程更多还原

【Abstract】 For the demands from various application fields like Computer-aided medical diagnosis, aviation simulation, industrial design, entertainment and so on, studies on 3D data acquisition, processing and visualization are becoming more and more important and attractive among the computer graphics researchers. Actually, in the recent years, with rapid development and great improvement in the hardware and software for processing 3d data, people may obtain raw data representations of real objects with complex shape via a variety of ways, then analyze and process them. This kind method of acquiring and processing data is called reverse engineering, and the obtained data are mainly classified into CT data, MRI data, and irregular 3D point-based or mesh-based data. The work in this paper will process 3D point-based models and meshes, with operations like scanning, parameterization, denoising, surface reconstruction, etc.Due to a variety of physical factors of the acquisition procedure, the derived raw models always are prone to various kinds of undesirable noise and distortions. The purpose of 3D denoising is to remove the effects caused by isolated noises from the derived surface whilst preserving the appearance of geometrically sharp features and minimizing distortion locally or globally.In this paper, we focus on the research on denoising and smoothing of 3D geometry and propose a number of novel algorithms on smoothing/denoising for point-based models and triangular meshes, and main contributions include: A introduction to classical 3D smoothing algorithms as well as some new smoothing/-denoising methods in the recent years is presented. After analyzing and summarizing the fundamental theories, the disadvantages and advantages of different methods are induced. And brief comparisons between various algorithms on their theoretical basis, time and space complexity, applied environments and numerical implementations are presented. Based on a linear convex combination of spherical vectors, a spherical parameterization method for a genus-zero mesh or a mesh with single boundary are presented. The parameterization allows us to apply spectral analysis and filtering for 3D geometry, especially, the smoothing and enhancing of 3D models. A vertex-estimation-based, feature-preserving smoothing technique for meshes is pro-posed. One contribution is to introduce mean value coordinates, in essence barycentric coordinates on arbitrary irregular polygons, to make mesh smoothing robust. Another key insight is that we combine local predictions from the second order triangles with the mean value coordinates-weighted bilateral filter, in a three-pass way, to smooth meshes. The approach reduces shrinkage and preserves sharp features.? We extend image mean shift filtering to 3D surface smoothing by taking the vertex normal and curvature as range component and the vertex position as the spatial component. First use 3D mean shift procedure to cluster point-based surfaces and adaptively select neighbors of each vertex. Then apply a trilateral point filter which adjusts positions of sample points along their normal directions to reduce noise while preserving geometric features.? Extended functions for the hand-held scanner FastSCAN are presented and implemented. Especially practicable solutions to integration and denoising of multiple scans are discussed, and some other operations include automatic or interactive deletion, B-Spline surface based resampling, and feature restoration of point-based model. The stableness and reliability of FastSCAN system increase with our extended functions.? A digital geometry processing system of point-based models and triangular meshes is implemented and introduced. The system actually is a framework of 3D geometry acquisition, representation, processing and rendering. The main components of the system include various novel algorithms on representation, local geometry estimation, parameterization, smoothing, feature detection, boolean operation, deformation and morphing.更多还原