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基于调和分析方法的数字几何处理问题研究
其他题名Digital Geometry Processing Based on Harmonic Analysis Methods
高恩阳1,2
导师王天然 ; 刘伟军
分类号O177
关键词数字几何处理 离群点检测 网格曲面分割
索取号O177/G26/2013
页数119页
学位专业机械电子工程
学位名称博士
2013-02-01
学位授予单位中国科学院沈阳自动化研究所
学位授予地点沈阳
作者部门装备制造技术研究室
摘要数字几何是图形学中三维物体的主要表示方法之一,相应的数字几何处理理论和技术是计算机图形学研究的热点,在逆向工程,曲面造型、计算机辅助设计与制造等领域得到了广泛应用。近年来,数字几何处理取得了很大的发展,但是,目前针对数字几何的处理技术和能力非常有限,数字几何数据存在的一些固有性质,如拓扑、曲率及非均匀取样等等 使得多数传统工具难以适用该领域, 而现有的数字几何处理研究成果还无法为大多数几何处理应用提供一个统一的、理论上完备的框架。本文将主要围绕数字几何处理中的若干关键问题,包括点云数据去噪,网格曲面分割以及三维网格模型分类问题等展开论述,探索采用调和分析的方法对数字几何处理的若干关键问题开展研究。主要研究内容和贡献如下: 一、将调和场的定义推广到数字几何模型上。从场论和数理方程的角度研究了调和场的物理意义和数学意义,为了能够在数字几何处理领域使用调和分析方法,给出了曲面上的调和场定义方法,并将其定义推广到数字几何模型上,给出了离散调和场的定义。 二、对点云数据的离群点自动检测问题进行了研究,针对传统的离群点检测算法无法检出小聚类离群点的问题,提出了基于调和场的离群点检测方法,详细论述了从带有噪点的点云模型中剔除离群点的整个过程。 针对点云数据离群点检测问题,提出了“相邻的两个数据点,或者同时为离群点,或者同时为正常点”这样一个最简单的假设,通过这一假设,构造了离群点检测的调和场模型。该模型的建立,克服了传统方法无法检出小聚类离群点的问题。 提出了包含顶点能量和调和能量两部分的离群点检测能量模型,并且为了求解该模型,提出将这个能量模型最优化问题转化为整数规划问题;为了避免平凡解, 提出了将整数规划问题转化为加入约束条件的线性规划松弛问题。与已有的离群点检测方法相比,提出的基于调和场的方法具有更高的检测正确率。 三、研究了基于调和场的网格曲面分割问题。当网格曲面形状十分复杂时,传统的曲面分割方法分割效果将变得很差,针对这一问题,提出了“特征空间定距离,调和场上定标号”的解决方案,利用调和分析方法进行交互式分割。 提出采用isophotic距离度量方式描述两个相邻三角面片之间的差异,既考虑了两个三角面片空间上的距离,又考虑了两个面片法向上的差异,能够很好地作为网格曲面分割的依据。并且进一步地,提出将isophotic距离度量的三角面片映射到特征空间。
其他摘要The digital geometry graphics representation of three-dimensional objects, digital geometry processing theory and technology of computer graphics research has been widely applied in the field of reverse engineering, surface modeling, computer-aided design and manufacturing. In recent years, digital geometry processing achieved great development but with very limited capacity, some of the inherent nature of digital geometric data exist, such as topology, curvature, and non-uniform sampling, etc. Because the most of the traditional tools difficult to apply in the field, the existing digital geometry processing research can not provide a uniform tool for most geometry processing applications. This article focused on several key issues in digital geometry processing, including point cloud data denoising,mesh surface segmentation and 3D mesh model classification, to explore the use of harmonic analysis on digital geometry processing to carry out a number of key issues research. Research and contributions are as follows: Reconcile the definition of the field promotion to the digital geometry model. Reconcile field of physical meaning and mathematical significance to clarify the digital geometric model raised and the nature of the field from the point of view of the field theory and mathematical equations. In order to be able to use in digital geometry processing field, harmonic analysis method is given. The curved harmonic field and discrete harmonic field were defined. Secondly, the automatic detection of outliers of point cloud data was studied. Traditional outlier detection algorithms can not detect a small cluster of outliers. harmonic field-based outlier detection method was discussed. The whole process of eliminating outliers from the point cloud was described. For point cloud data outlier detection problem, "the two adjacent data points, or outliers, or at the same time normal points," was one of the most simple assumption by this hypothesis, then outlier point detection harmonic field model was constructed. The establishment of the model has avoid the problems that traditional methods can not detected a small cluster of outliers. The model contains two parts: the vertex energy and harmonic energy, and in order to solve the model proposed we transfer the energy optimization problem into an integer programming problem; In order to avoid the trivial solution, integer programming model was proposed. Compared with the existing outlier detection method , proposed harmonic field-based approach has higher detection accuracy rate. Thirdly, harmonic field-based mesh surface segmentation problem was studied. When the shape of the mesh surface is very complex, the segmentation effect of traditional curved surface segmentation method will become poor. To solve this problem, the distance was given in feature space, the label was given on harmonic fields, so the interactive segmentation was based on harmonic analysis methods. Differences of two adjacent triangular facets was described by adopt isophotic distance metrics , not only considering the distance in the space of the two triangular facets, but also consider the difference of the two faces tablet method upward, so mesh surface can be segmented well. And further, triangular facets isophotic distance metric is mapped into feature space $ F ^ 2 $, then the distance in the feature space was as the distance of the two triangular facets. This method can make a piece of mesh distinguish between different sub-region divided greater , so better segmentation result was achieved. Harmonic field of the tag data on the mesh surface was constructed. The mathematical model of this harmonic field laid a foundation for further mesh surface segmentation. In order to get better mesh surface segmentation result, interactive segmentation method was proposed. The partial mesh was specified by the user as a foreground and background, so you can make the split more flexible, more in line with the expectations of the users of the segmentation results. The paper handle interactive mesh surface segmentation process of the mesh surface segmentation into the restricted conditions optimization problems, and Lagrange multiplier method to solve the problem was proposed. Fourthly, Classification of 3D mesh model is proposed based on the classification of the harmonic analysis of three-dimensional mesh model. Traditional 3D mesh model classification method only concerned about the global shape characterized or only concerned with the local shape characteristics, ignoring the spatial relationship between the local feature, so the classification accuracy is not high in many cases. In order to avoid this defect, the harmonic analysis method for shape classification is proposed considering spatially adjacent relationship between the local and local features. In order to improve the correct rate of shape classification, heat kernel signature was proposed to describe local feature of mesh model. Because the heat kernel signature descriptors can describe the surface from multi-scale local shape characteristics, so a more accurate description of the mesh shape characteristics can achieved.
语种中文
产权排序1
文献类型学位论文
条目标识符http://ir.sia.cn/handle/173321/10778
专题装备制造技术研究室
作者单位1.中国科学院沈阳自动化研究所
2.中国科学院大学
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高恩阳. 基于调和分析方法的数字几何处理问题研究[D]. 沈阳. 中国科学院沈阳自动化研究所,2013.
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